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Mixture problems with solutions.
Mixture problems and their solutions are presented along with their solutions. Percentages are also used to solve these types of problems.
Problem 1: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
Problem 2: John wants to make a 100 ml of 5% alcohol solution mixing a quantity of a 2% alcohol solution with a 7% alcohol solution. What are the quantities of each of the two solutions (2% and 7%) he has to use?
Problem 3: Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy?
Problem 4: How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution.
Problem 5: A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?
Solution to Problem 5: The amount of the final mixture is given by 50 ml + 30 ml = 80 ml The amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence 0 + 30% 50 ml = x (80) Solve for x x = 0.1817 = 18.75%
Problem 6: You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.
Solution to Problem 6: Let us first find the amount of alcohol in the 10% solution of 200 ml. 200 * 10% = 20 ml The amount of alcohol in the x ml of 25% solution is given by 25% x = 0.25 x The total amount of alcohol in the final solution is given by 20 + 0.25 x The ratio of alcohol in the final solution to the total amount of the solution is given by [ ( 20 + 0.25 x ) / (x + 200)] If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution. To have a percentage of 15%, we need to have [ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15 Solve the above equation for x 20 + 0.25 x = 0.15 * (x + 200) x = 100 ml
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Algebra Problems
Algebra problems are not only based on algebraic expressions but also on various types of equations in Maths where a quantity or variable is unknown to us. Many of us are familiar with the word problem, but are we aware of the fact and problems related to variables and constants? When we say 5 it means a number but what if we say x=5 or 5y or something like that?
This is where algebra came into existence algebra is that branch of mathematics which not only deals with numbers but also variable and alphabets. The versatility of Algebra is very deep and very conceptual, all the non-numeric character represents variable and numeric as constants. Let us solve some problems based algebra with solutions which will cover the syllabus for class 6, 7, 8. Below are some of the examples of algebraic expressions .
For example.
Algebra Word Problems deal with real-time situations and solutions which can be solved using algebra.
Basic Algebra Identities
- (a + b) 2 = a 2 + b 2 + 2ab
- (a – b) 2 = a 2 + b 2 – 2ab
- a 2 – b 2 = (a + b)(a – b)
- a 2 + b 2 = (a + b) 2 – 2ab = (a – b) 2 + 2ab
- a 3 + b 3 = (a + b)(a 2 – ab + b 2 )
- a 3 – b 3 = (a – b)(a 2 + ab + b 2 )
- (a + b) 3 = a 3 + 3ab(a + b) + b 3
- (a – b) 3 = a 3 – 3ab(a – b) – b 3
Algebra problems With Solutions
Example 1: Solve, (x-1) 2 = [4√(x-4)] 2 Solution: x 2 -2x+1 = 16(x-4)
x 2 -2x+1 = 16x-64
x 2 -18x+65 = 0
(x-13) (x-5) = 0
Hence, x = 13 and x = 5.
Algebra Problems for Class 6
In class 6, students will be introduced with an algebra concept. Here, you will learn how the unknown values are represented in terms of variables. The given expression can be solved only if we know the value of unknown variable. Let us see some examples.
Example: Solve, 4x + 5 when, x = 3.
Solution: Given, 4x + 5
Now putting the value of x=3, we get;
4 (3) + 5 = 12 + 5 = 17.
Example: Give expressions for the following cases:
(i) 12 added to 2x
(ii) 6 multiplied by y
(iii) 25 subtracted from z
(iv) 17 times of m
(i) 12 + 2x
Algebra Problems for Class 7
In class 7, students will deal with algebraic expressions like x+y, xy, 32x 2 -12y 2 , etc. There are different kinds of the terminology used in case algebraic equations such as;
- Coefficient
Let us understand these terms with an example. Suppose 4x + 5y is an algebraic expression, then 4x and 5y are the terms. Since here the variables used are x and y, therefore, x and y are the factors of 4x + 5y. And the numerical factor attached to the variables are the coefficient such as 4 and 5 are the coefficient of x and y in the given expression.
Any expression with one or more terms is called a polynomial. Specifically, a one-term expression is called a monomial; a two-term expression is called a binomial, and a three-term expression is called a trinomial.
Terms which have the same algebraic factors are like terms . Terms which have different algebraic factors are unlike terms . Thus, terms 4xy and – 3xy are like terms; but terms 4xy and – 3x are not like terms.
Example: Add 3x + 5x
Solution: Since 3x and 5x have the same algebraic factors, hence, they are like terms and can be added by their coefficient.
3x + 5x = 8x
Example: Collect like terms and simplify the expression: 12x 2 – 9x + 5x – 4x 2 – 7x + 10.
Solution: 12x 2 – 9x + 5x – 4x 2 – 7x + 10
= (12 – 4)x 2 – 9x + 5x – 7x + 10
= 8x 2 – 11x + 10
Algebra Problems for Class 8
Here, students will deal with algebraic identities. See the examples.
Example: Solve (2x+y) 2
Solution: Using the identity: (a+b) 2 = a 2 + b 2 + 2 ab, we get;
(2x+y) = (2x) 2 + y 2 + 2.2x.y = 4x 2 + y 2 + 4xy
Example: Solve (99) 2 using algebraic identity.
Solution: We can write, 99 = 100 -1
Therefore, (100 – 1 ) 2
= 100 2 + 1 2 – 2 x 100 x 1 [By identity: (a -b) 2 = a 2 + b 2 – 2ab
= 10000 + 1 – 200
Algebra Word Problems
Question 1: There are 47 boys in the class. This is three more than four times the number of girls. How many girls are there in the class?
Solution: Let the number of girls be x
As per the given statement,
4 x + 3 = 47
4x = 47 – 3
Question 2: The sum of two consecutive numbers is 41. What are the numbers?
Solution: Let one of the numbers be x.
Then the other number will x+1
Now, as per the given questions,
x + x + 1 = 41
2x + 1 = 41
So, the first number is 20 and second number is 20+1 = 21
Linear Algebra Problems
There are various methods For Solving the Linear Equations
- Cross multiplication method
- Replacement method or Substitution method
- Hit and trial method
There are Variety of different Algebra problem present and are solved depending upon their functionality and state. For example, a linear equation problem can’t be solved using a quadratic equation formula and vice verse for, e.g., x+x/2=7 then solve for x is an equation in one variable for x which can be satisfied by only one value of x. Whereas x 2 +5x+6 is a quadratic equation which is satisfied for two values of x the domain of algebra is huge and vast so for more information. Visit BYJU’S. where different techniques are explained different algebra problem.
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120 Math Word Problems To Challenge Students Grades 1 to 8
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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.
A jolt of creativity would help. But it doesn’t come.
Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.
This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.
There are 120 examples in total.
The list of examples is supplemented by tips to create engaging and challenging math word problems.
120 Math word problems, categorized by skill
Addition word problems.
Best for: 1st grade, 2nd grade
1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?
2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?
3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?
5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?
6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?
7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?
8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?
Subtraction word problems
Best for: 1st grade, second grade
9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?
10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?
11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
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12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?
13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?
14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?
15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?
16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?
Multiplication word problems
Best for: 2nd grade, 3rd grade
17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?
18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?
19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?
20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?
21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?
Division word problems
Best for: 3rd grade, 4th grade, 5th grade
22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?
23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?
24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?
25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?
26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?
Mixed operations word problems
27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?
28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?
29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?
30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?
Ordering and number sense word problems
31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?
32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?
33. Composing Numbers: What number is 6 tens and 10 ones?
34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?
35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?
Fractions word problems
Best for: 3rd grade, 4th grade, 5th grade, 6th grade
36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?
37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?
38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?
39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?
40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?
41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?
42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?
43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?
44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.
45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?
46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.
Decimals word problems
Best for: 4th grade, 5th grade
47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?
48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?
49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?
50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?
51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?
52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?
Comparing and sequencing word problems
Best for: Kindergarten, 1st grade, 2nd grade
53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?
54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?
55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?
56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?
57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?
58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?
59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?
Time word problems
66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?
69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?
70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?
71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?
Money word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade
60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?
61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?
62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?
63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?
64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?
65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?
67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.
68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?
Physical measurement word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade
72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?
73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?
74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?
75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?
76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?
77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?
78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?
79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?
80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?
81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?
Ratios and percentages word problems
Best for: 4th grade, 5th grade, 6th grade
82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?
83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?
84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?
85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?
86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?
87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?
88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?
Probability and data relationships word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade
89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?
90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?
91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.
92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?
93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?
94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?
95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .
Geometry word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade
96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?
97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?
98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?
99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?
100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?
101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?
102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?
103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?
104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?
105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?
106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?
107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?
108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?
109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?
110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?
111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?
112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?
113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?
114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?
Variables word problems
Best for: 6th grade, 7th grade, 8th grade
115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?
116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.
117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.
118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.
119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.
120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?
How to easily make your own math word problems & word problems worksheets
Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:
- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.
A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.
Final thoughts about math word problems
You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.
Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.
The result?
A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.
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Although the method which one is going to use when solving a math problem depends on the exact issue in question, there are general steps and guidelines one can follow. This is the reason why so many students are looking for a math problem solver. Having it on hand will definitely speed up the whole process. Here are the strategies that might come in handy. Having familiarized yourself with these tips, you won’t even have to search for a free math problem solver.
The first step you need to take is to understand the problem. Begin with identifying the type of the problem and determine whether it is a fraction, a quadratic equation or a word problem. This is one of the most significant aspects even if you are searching for a math problem solver with steps as it helps you figure out what you are supposed to do. The next step is to read the problem carefully and don’t attempt to solve it right away. If you realize that it’s too complex, find an online math problem solver to get qualified assistance with your assignment. What is vital to mention is that sometimes it takes time to figure out how to best approach the task at hand. Then, try to create a visual representation of the problem to better understand how to deal with it. Drawing a problem is a smarter choice than looking for a free math problem solver as you acquire new skills as well as complete your assignment on your own. Another great tip is to look for patterns when you are reviewing your problem and the available information. The reason why these patterns are important is because finding them will lead to the needed math problem solver you’ve been looking for all this time.
Having gathered all the information you need, it’s time to get down to developing a plan on how you are going to deal with your issue without using a free math problem solver. If you are in need of a math problem solver with steps, what you need to do next is figure out the formulas you’re going to use to complete your math assignment. Then, write down a step-by-step guide on all the things you are supposed to do to solve your problem and start working on it to get the correct answer. This process may be time-consuming as you need to double-check that the method you have chosen is the right one. While you are solving the problem, try to look for alternatives in order to check all the possible variants. Ask for help from an online math problem solver if necessary. Compare the answers you got to your estimates. When you are done, allocate some time to reflect on the problem, as well as make sure you have chosen the correct solution. Solving a math problem sometimes takes more time and effort. Yet, you’ll be really pleased when you manage to complete such an assignment on your own.
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Short Answer
In problems \(15\) and \(16\) interpret each statement as a differential equation. on the graph of \(y = \phi (x)\) the rate at which the slope changes with respect to x at a point \(p(x,y)\) is the negative of the slope of the tangent line at \(p(x,y)\)..
The differential equation is \(\frac{{dy}}{{dx}} = {x^2} + {y^2}\).
Step by Step Solution
Step 1: define a derivative of the function..
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value (output value) to changes in its argument (input value).
Calculus uses derivatives as a fundamental tool. When a derivative of a single-variable function exists at a given input value, it is the slope of the tangent line to the function's graph at that point.
Step 2: Determine the differential equation for the height.
Let the slope of the tangent line of the graph of \(y = \phi (x)\) at the point \(P(x,y)\) be \(y'\).
And let the rate at which the slope changes be \(y''\).
Hence, the statement describes the differential equation,
\(y'' = - y'\)
\(y'' + y' = 0\).
Most popular questions for Math Textbooks
In Problems \(31 - 34\) find values of m so that the function \(y = m{e^{mx}}\) is a solution of the given differential equation.
\(y' + 2y = 0\)
In Problems \(1 - 8\( state the order of the given ordinary differential equation. Determine whether the equation is linear or nonlinear by matching it with \((6)\(.
\({\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^2} = \sqrt {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \(
In Problems 27–30 use (12) of Section 1.1 to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of each solution.
\(\frac{{dy}}{{dx}} - 2xy = {e^{{x_z}}}; y = {e^{{x^2}}}\int_0^x {{e^{t - {t^2}}}} dt\)
Raindrops Keep Falling In meteorology the term virga refers to falling raindrops or ice particles that evaporate before they reach the ground. Assume that a typical raindrop is spherical. Starting at some time, which we can designate as t = 0, the raindrop of radius r0 falls from rest from a cloud and begins to evaporate.
(a) If it is assumed that a raindrop evaporates in such a manner that its shape remains spherical, then it also makes sense to assume that the rate at which the raindrop evaporates—that is, the rate at which it loses mass—is proportional to its surface area. Show that this latter assumption implies that the rate at which the radius r of the raindrop decreases is a constant. Find r(t). (Hint: See Problem 55 in Exercises 1.1.)
(b) If the positive direction is downward, construct a mathematical model for the velocity v of the falling raindrop at time t > 0. Ignore air resistance. (Hint: Use the form of Newton’s second law of motion given in (17).)
In Problems \(1\) and \(2\) Fill in the blank and then write this result as a linear first-order differential equation that is free of the symbol \({c_1}\) and has the form \(dy/dx = f(x,y)\). The symbol \({c_1}\) represents a constant.
\(\frac{d}{{dx}}{c_1}{e^{10x}} = \_\_\_\_\_\)
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Studies have shown that students who practice math problems frequently have better math grades. Too often, parents and teachers think students do not have an aptitude for math when the problem actually lies in the lack of math practice .
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Luckily for parents and teachers, there are plenty of websites that provide math problems for extra math practice. These problems are usually classified based on the age group they’re meant for, or the problem type. For example, for primary and middle school students there are 1st grade math problems, 2nd grade math problems, 3rd grade math problems, 4th grade math problems, 5th grade math problems, 6th grade math problems and 7th grade math problems . There are also math problems classified as addition problems , subtraction problems , multiplication problems and division problems .
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Children will benefit greatly from using math problems to practice their math skills . Improved math skills will in turn boost the child’s confidence and make them feel good about mathematics. Developing a positive attitude towards math will help them learn new skills and concepts and further contribute to the child’s improvement in the subject. This is why many parents like to give their children additional math practice at home with freely available math problems from the internet.
Math Word Problems
Math word problems require greater skill than simple math problems. This is because math word problems require reading and comprehension skills in addition to basic math skills. Further, in order to solve math word problems, children must be able to understand the relationship between math equations and simple everyday situations. Therefore, math word problems are a good way to highlight the importance of math in everyday life. Practicing math word problems helps kids master the skills they need to answer such questions.
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Get step-by-step solutions to your math problems Try Math Solver Type a math problem Solve Quadratic equation x2 − 4x − 5 = 0 Trigonometry 4sinθ cosθ = 2sinθ Linear equation y = 3x + 4 Arithmetic 699 ∗533 Matrix [ 2 5 3 4][ 2 −1 0 1 3 5] Simultaneous equation { 8x + 2y = 46 7x + 3y = 47 Differentiation dxd (x −5)(3x2 −2) Integration ∫ 01 xe−x2dx
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Problem 6 sent by Κυριάκος There is a two-digit number whose digits are the same, and has got the following property: When squared, it produces a four-digit number, whose first two digits are the same and equal to the original's minus one, and whose last two digits are the same and equal to the half of the original's.
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120 Math word problems, categorized by skill Addition word problems Best for: 1st grade, 2nd grade 1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total? 2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends.
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Free Math Problem Solver - MathSolve.pro Free solve math problems Although the method which one is going to use when solving a math problem depends on the exact issue in question, there are general steps and guidelines one can follow. Choose discipline Disciplines Basic Math Solve Pre-Algebra Solve Algebra Solve Trigonometry Solve Precalculus Solve
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In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation ...
In Problems 15 and 16 interpret each statement as a differential equation. On the graph of y = ϕ ( x) the rate at which the slope changes with respect to x at a point P ( x, y) is the negative of the slope of the tangent line at P ( x, y). The differential equation is d y d x = x 2 + y 2. See the step by step solution.
Even simple math problems become easier to solve when broken down into steps. From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them.
Geography and Math Made Easy. $5.00. Zip. Note this is a PowerPoint Presentation & Activity, all in one.Double Bubble Car Wash: Intro. to Problem Solving through Depth and ComplexityThe beginning of the year problem-solving activity is designed to engage your students with mathematical reasoning and critical thinking.
Math Problems. Studies have shown that students who practice math problems frequently have better math grades. Too often, parents and teachers think students do not have an aptitude for math when the problem actually lies in the lack of math practice.. Use our fun worksheets and resources to engage kids and help them get better at solving math problems: