Word Problems with Fractions
Today we are going to look at some examples of word problems with fractions.
Although they may seem more difficult, in reality, word problems involving fractions are just as easy as those involving whole numbers. The only thing we have to do is:
- Read the problem carefully.
- Think about what it is asking us to do.
- Think about the information we need.
- Simplify, if necessary.
- Think about whether our solution makes sense (in order to check it).
As you can see, the only difference in fraction word problems is step 5 (simplify) .
There are some word problems which, depending on the information provided, we should express as a fraction. For example:
In my fruit basket, there are 13 pieces of fruit, 5 of which are apples.
How can we express the number of apples as a fraction?
5 – The number of apples (5) corresponds to the numerator (the number which expresses the number of parts that we wish to represent).
13 – The total number of fruits (13) corresponds to the denominator (the number which expresses the number of total possible parts).
The solution to this problem is an irreducible fraction (a fraction which cannot be simplified). Therefore, there is nothing left to do.
Word problems with fractions: involving two fractions
In these problems, we should remember how to carry out operations with fractions.
Carefully read the following problem and the steps we have taken to solve it:
What fraction of the payment has Maria spent?
We find the common denominator:
We calculate:
Word problems with fractions: involving a fraction and a whole number
Finally, we are going to look at an example of a word problem with a fraction and a whole number. Now we will have to convert all the information into a fraction with the same denominator (as we did in the example above) in order to calculate
We convert 1 into a fraction with the same denominator:
What do you think of this post? Do you see how easy it is to solve word problems with fractions?
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- Understand What a Fraction Is and When It Is Used
- Fraction Word Problems: Addition, Subtraction, and Mixed Numbers
- Learn and Practice How to Subtract or Add Fractions
- Learn How to Subtract Fractions
- Review and Practice the Two Methods of Dividing Fractions
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29 Comments
Thank you for such good explanations, it helped me a lot
It is really good it helped me improve my math a lot.
same it helps me in my math too
Wow, it really helps a lot
Good exercises
Interesting
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Hi can you not show the answer till the bottom of the page or your giving away the answer so if you solved number one problem the number one aware to the question will be there at the bottom of the page because it is way to easy if it is right there
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Roll two dices, the first dice is the numerator, the second is the denominator, this is the first fraction. Roll both dices again and repeat the process to generate the second fraction. Write a division story problem that incorporates these two fractions.
Seems easy of the examples but when I have fraction word promblems in front of me then its still hard for me to figure it out.The examples on this site still is helpful.I will use the site that you give on here to get further practice.Thank you for the examples on here
Interesting and very helpful. I’m going to continue using this site and tell others about it too.
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Hey I am in grade five and it is super helpful for my exams thanks and maybe if you could make more it would be appriciated thx 🙂
Good efforts
i kinda like it pls write some more problems
I think it was really good how you are helping fellow students! But I think you can improve if there were more problems for solving! Thanks
it is helpfull
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Fraction Word Problems: Examples
Lessons on solving fraction word problems using visual methods like bar models or tape diagrams.
Related Pages More Fraction Word Problems Harder Fraction Word Problems Singapore Math Lessons Fraction Problems Using Algebra
Here are some examples and solutions of fraction word problems. The first example is a one-step word problem. The second example shows how blocks can be used to help illustrate the problem. The third example is a two-step word problem.
More examples and solutions using the bar modeling method to solve fraction word problems are shown in the videos. The bar modeling method, also called tape diagrams, are used in Singapore Math and the Common Core.
3 units = 24 1 unit = 24 ÷ 3 = 8 5 units = 5 × 8 = 40
There were 40 children in the group.
He sold 80 teddy bears.
Step 2: Find how much money he received. 80 × 12 = 960
He received $960.
Bar Modeling With Fractions
- Grace thought that a plane journey would take 7/10 hr but the actual journey took 1/5 hr longer. How long did the actual journey take?
- Timothy took 2/3 hr to paint a portrait. This was 1/3 hr shorter than the time he took to paint scenery. How long did he take to paint scenery?
How To Solve Real World Problems Involving Multiplication Of Fractions By Using Visual Fraction Models Or Equations To Represent The Problem?
- At the animal shelter 4/6 of the animals are cats. Of the cats 1/2 are male. What fraction of the animals at the shelter are male cats?
- A taco recipe called for 2/3 cup of cheese per taco. If Andrew wanted to make 3 tacos, how much cheese would he need?
How To Solve Word Problems Using Tape Diagrams And Fraction-By-Fraction Multiplication?
- Ethan is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the remaining cupcakes. The rest will get vanilla frosting. How many cupcakes have vanilla frosting?
- Maddox puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back her sister. If she has $15 left, how much did she have at first?
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Solving word problems by adding and subtracting fractions and mixed numbers, learn how to solve fraction word problems with examples and interactive exercises.
Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
Analysis: To solve this problem, we will add two fractions with like denominators.
Answer: Rachel rode her bike for three-fifths of a mile altogether.
Analysis: To solve this problem, we will subtract two fractions with unlike denominators.
Answer: Stefanie swam one-third of a lap farther in the morning.
Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.
Answer: It took Nick three and one-fourth hours to complete his homework altogether.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.
Answer: Diego and his friends ate six pizzas in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.
Answer: The Cocozzelli family took one-half more days to drive home.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.
Answer: The warehouse has 21 and one-half meters of tape in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.
Answer: The electrician needs to cut 13 sixteenths cm of wire.
Analysis: To solve this problem, we will subtract a mixed number from a whole number.
Answer: The carpenter needs to cut four and seven-twelfths feet of wood.
Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems:
- Add fractions with like denominators.
- Subtract fractions with like denominators.
- Find the LCD.
- Add fractions with unlike denominators.
- Subtract fractions with unlike denominators.
- Add mixed numbers with like denominators.
- Subtract mixed numbers with like denominators.
- Add mixed numbers with unlike denominators.
- Subtract mixed numbers with unlike denominators.
Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.
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Word Problems on Fraction
In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.
1. 4/7 of a number is 84. Find the number. Solution: According to the problem, 4/7 of a number = 84 Number = 84 × 7/4 [Here we need to multiply 84 by the reciprocal of 4/7]
= 21 × 7 = 147 Therefore, the number is 147.
2. Rachel took \(\frac{1}{2}\) hour to paint a table and \(\frac{1}{3}\) hour to paint a chair. How much time did she take in all?
3. If 3\(\frac{1}{2}\) m of wire is cut from a piece of 10 m long wire, how much of wire is left?
Total length of the wire = 10 m
Fraction of the wire cut out = 3\(\frac{1}{2}\) m = \(\frac{7}{2}\) m
Length of the wire left = 10 m – 3\(\frac{1}{2}\) m
= [\(\frac{10}{1}\) - \(\frac{7}{2}\)] m, [L.C.M. of 1, 2 is 2]
= [\(\frac{20}{2}\) - \(\frac{7}{2}\)] m, [\(\frac{10}{1}\) × \(\frac{2}{2}\)]
= [\(\frac{20 - 7}{2}\)] m
= \(\frac{13}{2}\) m
= 6\(\frac{1}{2}\) m
4. One half of the students in a school are girls, 3/5 of these girls are studying in lower classes. What fraction of girls are studying in lower classes?
Fraction of girls studying in school = 1/2
Fraction of girls studying in lower classes = 3/5 of 1/2
= 3/5 × 1/2
= (3 × 1)/(5 × 2)
= 3/10
Therefore, 3/10 of girls studying in lower classes.
5. Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson? Solution: Maddy reads = 3/5 of 75 = 3/5 × 75
= 45 pages. Maddy has to read = 75 – 45. = 30 pages. Therefore, Maddy has to read 30 more pages. 6. A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd? Solution: A herd of cows gives 4 litres of milk each day. Each cow gives one-third of total milk each day = 1/3 of 4 Therefore, each cow gives 4/3 of milk each day. Total no. of cows = 4 ÷ 4/3 = 4 × ¾ = 3 Therefore there are 3 cows in the herd.
Questions and Answers on Word problems on Fractions:
1. Shelly walked \(\frac{1}{3}\) km. Kelly walked \(\frac{4}{15}\) km. Who walked farther? How much farther did one walk than the other?
2. A frog took three jumps. The first jump was \(\frac{2}{3}\) m long, the second was \(\frac{5}{6}\) m long and the third was \(\frac{1}{3}\) m long. How far did the frog jump in all?
3. A vessel contains 1\(\frac{1}{2}\) l of milk. John drinks \(\frac{1}{4}\) l of milk; Joe drinks \(\frac{1}{2}\) l of milk. How much of milk is left in the vessel?
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Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction
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Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples
The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with respect to the whole shape in the figures from (i) to (viii) In; (i) Shaded
Subtraction of Fractions having the Same Denominator | Like Fractions
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Comparison of Like Fractions | Comparing Fractions | Like Fractions
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Worksheet on Equivalent Fractions | Questions on Equivalent Fractions
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● Multiplication is Repeated Addition.
● Multiplication of Fractional Number by a Whole Number.
● Multiplication of a Fraction by Fraction.
● Properties of Multiplication of Fractional Numbers.
● Multiplicative Inverse.
● Worksheet on Multiplication on Fraction.
● Division of a Fraction by a Whole Number.
● Division of a Fractional Number.
● Division of a Whole Number by a Fraction.
● Properties of Fractional Division.
● Worksheet on Division of Fractions.
● Simplification of Fractions.
● Worksheet on Simplification of Fractions.
● Word Problems on Fraction.
● Worksheet on Word Problems on Fractions.
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5th Grade Math Problems
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Unit 6: Lesson 6
Multiplying fractions word problem: muffins.
- Multiplying fractions word problem: laundry
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- Multiply fractions: FAQ
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Video transcript
Solving Word Problems By Multiplying Fractions
This video shows how to solve two word problems involving fraction multiplication. This video demonstrates how the word "of" signifies that multiplication should be used.
Related Articles
Dividing a whole number by a fraction, reducing fractions to simplest form, compare and order fractions.
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IMAGES
VIDEO
COMMENTS
Word Problems with Fractions · Read the problem carefully. · Think about what it is asking us to do. · Think about the information we need. · Solve
Use this as a lesson with Edpuzzle at https://edpuzzle.com/media/5fa58725d7840f40bf7f722f.
Check out this original InstructaBeats lesson on how to solve fraction multiplication word problems using a tape diagram#Instructabeats
Solve fraction word problems: using key words and picturesIn this lesson you will learn how to solve fraction word problems by using key
How To Solve Word Problems Using Tape Diagrams And Fraction-By-Fraction Multiplication? · Ethan is icing 30 cupcakes. He spreads mint icing on 1/5 of the
Learn How to Solve Fraction Word Problems with Examples and Interactive Exercises Girl Bike · Add fractions with like denominators. · Subtract fractions with like
Word Problems on Fraction · 1. 4/7 of a number is 84. · 2. Rachel took 12 hour to paint a table and 13 hour to paint a chair. · 3. If 312 m of wire is cut from a
To solve, can't you also do 3/4 divided by 2? 3/4*1/2=3/8, right? Answer
This video shows how to solve two word problems involving fraction multiplication. This video demonstrates how the word of signifies that multiplication
Step 1: Read through the given word problem. If we are trying to find a fraction of a whole number we need to multiply the fraction and the whole number. Start