how to solve two step multiplication problems

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Solving Two-Step Multiplication Word Problems

Two-step word problems can be difficult to solve as the student needs to work out what should be solved first and then determining and solving both steps. Most two-step word problems that involve multiplication have a multiplication step and an addition or subtraction step.

The easiest way to solve these problems is visually with bar charts to aid the student.

Let’s start with an example that involved a multiplication step and a subtraction step.

In this example, the multiplication step comes first and the subtraction step second.

A girl has 7 lollipops and she has 5 times as many candies. How many more candies than lollipops does she have?

You’ll have to start by working out how many candies she has. She has 5 x 7 as many candies. Here’s what that looks like in a bar diagram:

Now we can see how many more candies she has than lollipops. It’s this part:

She has 35 candies and 7 lollipops. So she has 35 – 7 = 28 more candies than lollipops.

Here’s an example of multiplication as a first step and addition as a second step.

There are 9 red apples. There are three times as many green apples. How many apples are there altogether?

So we know we have 9 red apples and that there are 3 times as many green apples. Here’s how that looks in a bar chart:

9 x 3 = 27, so there are 27 green apples. So in total we have 27 + 9 apples, which comes to 36 apples altogether.

If you are looking for some multiplication word problems you’ll find them in our free math worksheet center . Here are the multiplication word problem worksheets for grade 3 , grade 4 and grade 5 .

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$how to solve two step multiplication problems$

Home / United States / Math Classes / 4th Grade Math / Multi-step Multiplication of Two-digit Numbers

Multi-step Multiplication of Two-digit Numbers

Multiplication is one of the four basic operations in math. Multiplication simplifies problems that include repeated add ition, and it can be used to solve several maths problems. Some math problems cannot be solved in a single step. Learn how to solve multi-step math problems using multiplication. ...Read More Read Less

$how to solve two step multiplication problems$

What are Multi-step Problems?

Solving a multi-step multiplication problem, solved examples.

Frequently Asked Questions

Some math problems can be solved in a single step and these problems are usually direct and easy. There are also certain math problems that can only be solved in multiple steps. We need to apply a different strategy while dealing with such problems.

Here is an example of a single step multiplication problem:

There are 20 students in a classroom. Each student owns two pens. Find the total number of pens brought by the students to the classroom.

We can find the solution to this problem in a single multiplication step.

Here is an example of a multi-step multiplication problem:

There are 20 students in a classroom. Each student brings 3 notebooks to the classroom. If all notebooks have 200 pages and weigh 2 ounces, find the total weight of all the notebooks that the students bring to the classroom.

This math problem cannot be solved in a single step easily. We usually break down such problems into multiple steps.

We need to use special strategies while solving multi-step problems. In general, the steps involved in solving multi-step problems are as follows:

Step 1: Understand the problem.

The first thing to do is to read the problem thoroughly to analyze the little details. Here, we get to pick out the information provided to us and what we need to find with the provided information.

Step 2: Make a plan.

After having a clear idea about the information we have in hand and what we need to do with it, we need to decide how we are going to solve the problem. We take in the necessary information and discard the rest.

Step 3: Solve

The problem is solved in multiple steps.

Let’s solve the problem mentioned above using this strategy.

Question: There are 20 students in a classroom. Each student brings 3 notebooks to the classroom. If all notebooks have 200 pages and weigh 2 ounces, find the total weight of all the notebooks that the students bring to the classroom.

What do you need to find?

Weight of all the notebooks in the classroom

We always start by analyzing the information provided in the question. To solve such problems, we need to find the relationship between the known values and the unknown values and form an equation . The goal is always to find the unknown value in the equation with the help of the provided information.

Example 1: Which expression can be used to solve the following problem?

In a basketball match, all five players of Team A scored a 2-pointer. All five players of Team B scored a 3-pointer. Find the number of points scored in the basketball match.

We use the expression (5$\times$ 2) + (5$\times$ 3) to solve this math problem as this gives the right relationship between the values provided in the question. Since 5 players of Team A scored 2 pointers and the other 5 players of Team B scored 3 pointers, the total number of points scored is the sum of the points scored by each team.

Points scored by Team A = 5$\times$ 2

Points scored by Team B = 5$\times$ 3

So, the correct expression is (5$\times$ 2) + (5$\times$ 3)

Example 2: Jan drinks 2 cups of coffee every day. If a cup of coffee costs $5, how much money did she spend on coffee in April 2022?

Example 3: Ryan kept 5 full decks of playing cards on a table. Each deck has 52 cards. Two of these decks are kept face up, and the rest of the decks are kept face down. How many cards have their face down?

Example 4: A donut shop sells donuts in boxes of dozens and each donut costs $2. The shop serves 20 customers every day, and each customer buys two boxes of donuts. Find the total money earned by the shopkeeper on a Monday.

Step 2 : Make a plan.

What should be the approach to solve a multi-step word problem?

A multi-step word problem can be solved easily by analyzing the information provided in the question. We always use the useful information to form an equation to relate the known values with the unknown values. Then, we solve the equation to find the unknown value.

Why do we need to be more careful while solving multi-step problems?

Multi-step problems are often word problems. In some cases, we might be provided with information that is not relevant to the question. We need to filter out the irrelevant information and use only the relevant information to solve problems.

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Long Multiplication Calculator

Calculator Use

Multiplication of positive or negative whole numbers or decimal numbers as the multiplicand and multiplier to calculate the product using long multiplication. The solution shows the work for the Standard Algorithm.

How To Do Long Multiplication

Long multiplication means you're doing multiplication by hand. The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. These are the steps to do long multiplication by hand:

Long Multiplication with Decimals

Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow.

Example Long Multiplication with Decimals

Multiply 45.2 by 0.21

There's 3 total decimal places in both numbers.

Ignore the decimal places and complete the multiplication as if operating on two integers.

Rewrite the product with 3 total decimal places.

Answer = 9.492

Therefore: 45.2 × 0.21 = 9.492

Long Multiplication with Negative Numbers

When performing long multiplication you can ignore the signs until you have completed the standard algorithm for multiplication. Once you complete the multiplication follow these two rules:

Long Multiplication Example: Multiply 234 by 56

Long Multiplication Steps: Stack the numbers with the larger number on top. Align the numbers by place value columns.

Multiply the ones digit in the bottom number by each digit in the top number 6 × 4 = 24 Put the 4 in Ones place Carry the 2 to Tens place

6 × 3 = 18 Add the 2 that you carried = 20 Put the 0 in the Tens place Carry the 2 to the Hundreds place

6 × 2 = 12 Add the 2 that you carried = 14 This is the last number to multiply so write the whole number answer. No need to carry the 1.

Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number. 5 × 4 = 20 Add a row to your multiplication answer When you write your answer, shift one column to the left Put the 0 in Ones place Carry the 2 to Tens place

5 × 3 = 15 Add the 2 that you carried = 17 Put the 7 in the Tens place Carry the 1 to the Hundreds place

5 × 2 = 10 Add the 1 that you carried = 11 This is the last number to multiply so write the whole number answer. No need to carry the 1.

Add the numbers in the columns using long addition 4 + 0 = 4 0 + 0 = 0 4 + 7 = 11 write the 1 and carry 1 1 + 1 + 1 = 3

Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.

Related Calculators

If you need help with long addition see our Long Addition Calculator to add numbers by long addition and see the work.

For long division see the Long Division Calculator to divide numbers by using long division with remainders. This calculator also shows the work.

If you need to multiply fractions visit our Fractions Calculator . You can do fraction multiplication, addition, subtraction and division here.

Math is Fun shows examples of Long Multiplication in an animated video.

Long multiplication is an algorithm and you can find examples of multiplication algorithms at Wikipedia.

Goodman, Len . "Long Multiplication." From MathWorld --A Wolfram Web Resource, created by Eric W. Weisstein . Long Multiplication

Cite this content, page or calculator as:

Furey, Edward " Long Multiplication Calculator " at https://www.calculatorsoup.com/calculators/math/longmultiplication.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Solving Multi-Step Equations: Explanations, Review, and Examples

Whether you’re new to solving multi-step equations or simply studying before that big chapter test, Albert has you covered!

This blog post will guide you through defining multi-step equations, examples of multi-step equations, and how to solve multi-step equations (including problems with fractions and words). Let’s go!

Return to the Table of Contents

What We Review

What is a multi-step equation?

Remember, an equation is a mathematical sentence that uses an equal sign, = , to show that two expressions are equal.

We began our study of solving equations with one-step equations , then we moved on to two-step equations . (Check out those links if you need a quick refresher!)

Now we are moving to multi-step equations . A multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations.

So get your mathematical toolbox out! You never know what you might see in a multi-step equation!

how to solve two step multiplication problems

Examples of multi-step equations

Multi-step equations are a wide-ranging category of equations. Some can be very simple, while others become more complex. Never fear! We’re going to show you many examples of multi-step equations and how to solve these important aspects of Algebra 1.

Here are some examples of multi-step equations:

How to solve multi-step equations

Remember, an equation is solved when we have isolated the variable and found a value that makes the equation true. In order to solve equations, we use inverse operations to help us isolate the variable.

Order of Operations

Another mathematical concept that will help when solving multi-step equations is the Order of Operations . To use the order of operations, we must first do any operations inside grouping symbols (parentheses, brackets, etc), then exponents, then multiplication or division (whatever comes first, left to right), then finally addition or subtraction (whatever comes first, left to right). You can remember this by the acronym, PEMDAS .

Additionally, we may have to combine like terms on either side of the equation to help solve these equations. Eventually, you will create a one- or two-step equation that you will be able to solve similarly to previous problems!

Here is an example of a multi-step equation with variables on both sides:

Solve for x in the following equation:

Since there are variables on both sides, we must eliminate the variable from one side first. I suggest moving the 4x first, as to not create a negative.

Now we are back to a basic two-step equation.

To check you answer, you can simplify substitute 3 into the variable to see if the equation is true:

Thus, x = 3 is the correct solution.

Below is a short video from Mike DeVor showing more examples of solving multi-step equations:

Now that we have been introduced to Multi-Step Equations, let’s get those brain gears in motion and look at some more challenging examples!

Multi-step equations with fractions

When dealing with an equation with more than one fraction, the easiest way to solve the equation is by finding the Least Common Denominator . The least common denominator is the smallest number that can be a common denominator for a set of fractions.

Once we find the least common denominator, we will multiply each term by this value to eliminate the fraction. Here is an example of a multi-step equation with fractions:

Solve for y in the following equation:

The denominators above are 2, 4, 6 , therefore the least common denominator for these numbers is 12 . So we will multiply each term by 12 .

To check your answer, you can substitute 9 into the variable to see if the equation is true:

Therefore, y = 9 is the correct solution.

Multi-step equations with distributive property

Solve for z in the following equation:

To check you answer, you can substitute 3 into the variable to see if the equation is true:

Thus, z = 3 is the correct solution.

Solve for m in the following equation:

To check you answer, you can simplify substitute -9 into the variable to see if the equation is true:

Thus, m = -9 is the correct solution.

Multi-step equation word problems

First, let’s create an equation for the situation:

To check you answer, you can simplify substitute 15 into the variable to see if the equation is true:

Therefore, the breakeven point for Distributor A and Distributor B would be 15 pounds.

First, let’s set up an equation that models the situation:

Since each book costs the same amount, we denote this amount by the variable, c . Then we applied the \$5 coupon to each book, and finally, we will multiply the cost of each book after the coupon by 3 .

Now, simply solve for c like any other multi-step equation:

Therefore, each book cost \$20 before the coupon was applied.

Keys to Remember: Solving Multi-Step Equations

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Unit 8: Lesson 3

Setting up 2-step word problems

2-step word problem: truffles

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Video transcript

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Using multiplication, solving two-step equations.

Solve two-step equations using division

These two-step equations are solved by using addition and subtraction, then multiplication to eliminate a denominator. All problems resolve to integers. You can adjust the difficulty of the problems by increasing the values size, using negative coefficients and flipping the sides of the equations.

Solving one step equations answers

With math, there are always multiple solutions - so why not explore all the possibilities? From addition to subtraction and beyond, discover different ways of Solving one step equations answers!

Solving One

To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. The inverse operations are: Addition and subtraction. Multiplication and division.

Solving word questions

Word questions can be tricky, but there are some helpful tips you can follow to solve them.

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How to divide decimal division

Divide decimals by multiplying both numbers by a factor of 10 so the divisor no longer has a decimal value. Then, use long division to divide as normal. Place

How to Divide a Decimal by a Decimal

Dividing Decimals

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Division Word Problems (2-step word problems)

Here are some examples of division word problems that can be solved in two steps. We will illustrate how block diagrams or tape diagrams can be used to help you to visualize the division word problems in terms of the information given and the data that needs to be found. We also learn how to solve multiplication and division word problems by identifying key terms.

Block diagrams are used in Singapore Math and tape diagrams are used in the Common Core Math.

We use division or multiplication when the problem involves equal parts of a whole. Sometimes, the problem involves comparison and it becomes a 2-step problem. The following diagram shows how to use equal parts of a whole and comparison. Scroll down the page for examples and solutions.

Example: Marcus had 700 marbles. He gave away 175 marbles and put the remaining marbles equally into 5 bags. How many marbles were there in each bag?

Solution: Step 1: Find how many marbles he had left.

700 – 175 = 525 He had 525 marbles left.

Step 2: Find the number of marbles in each box.

525 ÷ 5 = 105 There were 105 marbles in each box.

Example: Rosalind made 364 donuts. She put 8 donuts into each box. a) How many boxes of donuts were there? How many donuts were left over? b) If she sold each box for $3, how much money would she receive?

Solution: Step 1: Find the number of boxes of donuts.

364 ÷ 8 = 45 remainder 4 There were 45 boxes of donuts. 4 donuts were left over.

Step 2: Find how much money she would receive.

45 × 3 = 135 She would receive $135.

How to solve a 2-step division word problem using multiple tape diagrams?

Example: Ben is making math manipulatives to sell. He needs to make at least $450. Each manipulative costs $18 to make. He is selling them for $30 each. What is the minimum number he can sell to reach his goal?

How to use tape diagrams to solve fractional division problems? Basic algorithms and checks are also demonstrated.

Example: When someone donated 14 gallons of paint to Rosendale Elementary School, the fifth grade decided to use it to paint murals. They split the gallons equally among the four classes. a) How much paint did each class have to paint their mural? b) How much pain will three classes use? Show your thinking using words, numbers, or pictures. c) If 4 students share a 30 square foot wall equally, how many square feet of the wall will be painted by each student?

How to solve division word problems using the Algebra method and the Singapore Math method?

Example: Jeremy bought 8 identical pens and 5 identical notebooks. The cost of 8 pens is the same as the cost of 5 notebooks. Each notebook costs 30 cents more than each pen. How much did Jeremy spend altogether?

How to solve a multiplication and division 2-step problem? Using the comparison model, this video teaches how to approach a given 2-step problem on multiplication and division, and shows the detailed steps of how to solve it.

Example: Billy bought 5 bags of balls. Each bag contained 40 balls. He packed the balls into packets of 8 balls each. How many packets did he get?

How to solve a subtraction and division 2-step problem? Using the comparison model, this video teaches how to approach a given 2-step problem on subtraction and division, and shows the detailed steps of how to solve it.

Example: A boy collects a total of 316 stamps, stickers and coins. He collects 4 times as many stamps as stickers. There are 46 coins. How many stickers are there?

How to solve a division and fraction word problem visually?

Example: Mimi’s market sold 24 heads of lettuce one morning. That afternoon 2/7 of the remaining heads of lettuce were sold. The number of heads left was now 1/2 of the number the market had at the beginning of the day. How many heads of lettuce were there at the beginning of the day?

How to solve a part whole division word problems using bar models? Tips for Bar Modeling Division Problems

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How to Do Long Multiplication

Last Updated: February 17, 2023 References

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 128 people, some anonymous, worked to edit and improve it over time. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 2,136,388 times. Learn more...

Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large. If you take it step by step, though, you'll be able to do long multiplication in no time. Get ready to ace those math quizzes by going to Step 1 below to get started.

Doing Standard Long Multiplication

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Taking a Shortcut

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About This Article

To do long multiplication quickly, start by splitting up the tens and ones place in the smaller number. For example, if the number was 12, you would end up with 10 and 2. Next, multiply the bigger number by both the tens number and the ones number. Finally, add the 2 products together to get your final answer. To learn how to write out a long multiplication problem by hand, keep reading! Did this summary help you? Yes No

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COMMENTS

Solving Two-Step Multiplication Word Problems
Most two-step word problems that involve multiplication have a multiplication step and an addition or subtraction step. The easiest way to solve these problems is visually with bar charts to aid the student. Let's start with an example that involved a multiplication step and a subtraction step.
Problem Solving With Multistep Multiplication
This lesson uses multisteps (more than one step) to solve multiplication problems, using the "Draw a Diagram" strategy.
3 Ways to Solve Two Step Algebraic Equations
You can solve a two step equation while keeping the variable on the right side. As long as you isolate it, you'll still get the same answer. Let's take the problem, 11 = 3 - 7x. To solve it, your first step will be to combine the constants by subtracting 3 from both sides of the equation.
2-step word problems (practice)
2-step word problems CCSS.Math: 3.OA.D.8 Google Classroom The cash register at the ice cream store started the day with \$120 $120. During the day, the store earned \$56 $56 selling ice cream. The manager also paid for a delivery out of the cash register. At the end of the day, the cash register had \$141 $141. How much did the delivery cost? \$ $
Solving Multi-step Problems Involving Multiplication and ...
Solving Multi-step Problems Involving Multiplication and Addition or Subtraction Cherry's Classroom 1.71K subscribers Subscribe 2.1K views 1 year ago Learn how to Solve Multi-step...
PDF Two-Step Problems Using the Four Operations
across grades as it builds on problem solving with addition and subtraction (2.OA.A.1) and prepares students for multi-step problem solving (4.OA.A.3). Standard 3.OA.D.8 and this miniassessment target - application, one of the three elements of rigor, through word problems. A CLOSER LOOK . Standard 3.OA.D.8 encompasses a significant amount of
Multi-step Multiplication of Two-digit Numbers
In general, the steps involved in solving multi-step problems are as follows: Step 1: Understand the problem. The first thing to do is to read the problem thoroughly to analyze the little details. Here, we get to pick out the information provided to us and what we need to find with the provided information. Step 2: Make a plan.
Two Step Word Problems
Two Step Word Problems - Multiplication for 3rd Grade | Kids Academy Kids Academy 579K subscribers Dislike Share 32,435 views Jan 10, 2018 Thousands of parents and educators are turning to the...
Long Multiplication Calculator
Multiply the numbers using long multiplication. Insert a decimal point in the product so it has the same number of decimal places equal to the total from step 1. Example Long Multiplication with Decimals Multiply 45.2 by 0.21 There's 3 total decimal places in both numbers.
Two-Step Word Problems Addition, then Multiplication
Addition, then Multiplication. Solve word problems that require an extra step to solve. Two-step word problems have three numbers which must be operated on separately, and in the right order. They take much more understanding of the problem than simple word problems because they provide the information in a less structured form.
Multiplication Word Problems (2-step word problems)
Step 1: Find the number of sheets of paper that she gave out. 62 × 5 = 310 She gave out 310 sheets of paper. Step 2: Find the number of sheets of paper she has left. 400 - 310 = 90 She has 90 sheets of paper left. How to identify the operations in two step word problems by using problem solving steps and a model?
Two-Step Word Problems Multiplication, then Division
Solve word problems that require two separate operations. Two-step word problems have three numbers which must be operated on separately, and in the right order. They take much more understanding of the problem than simple word problems because they provide the information in a less structured form. For these problems, finding the answer ...
Solving Multi-Step Equations: Review and Examples
A multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations. So get your mathematical toolbox out!
2-step word problem: truffles (video)
So g times 3 is also going to be the number of truffles at the party-- number of truffles total. So these two things need to be equal to each other. So we could figure out what 4 times 6 is. And then we say, well, 4 times 6 is going to be some number. And g times 3 has to equal that same number.
Two Step Multiplication Problems Teaching Resources
In this game, students practice solving 2-step word problems involving multiplication, including multiplying by multiples of 10, and division. There are also 2 no prep printable pages (10 total problems) to use for extra practice, homework, or assessment. This set is part of a 2-step problem solving bundle.
Two-Step Math Word Problems
Two-step math word problems require you to solve two equations (or number sentences) before you come to an answer. The problem might have two different operations (like...
Using Multiplication Solving Two-Step Equations
Solving Two-Step Equations. Solve two-step equations using division. These two-step equations are solved by using addition and subtraction, then multiplication to eliminate a denominator. All problems resolve to integers. You can adjust the difficulty of the problems by increasing the values size, using negative coefficients and flipping the ...
Year 5 word problems multiplication
Two step, Multiplication word problems. ... This PowerPoint will help your Year 5 class to master higher-level problem solving using multiplication and division. Decide mathematic. Mathematics is the study of numbers, shapes, and patterns. It is used to solve problems in a variety of fields, from engineering to economics.
Two-Step Multiplication Word Problems Challenge Cards
Print and distribute the two-step multiplication challenge cards and ask students to answer the questions in pairs. You could even give children a time limit to complete the questions and ask them to pass on their challenge cards to the next pair until all pairs have completed each problem.
Word math problems for 5th grade
These multi-step word problems incorporate addition, subtraction, multiplication, and division as well as time, money, place value, and. Better than just an application ... Students will add, subtract, multiply, and divide fractions to solve two-step word problems. 5th grade. Math.
Division Word Problems (2-step word problems)
Using the comparison model, this video teaches how to approach a given 2-step problem on multiplication and division, and shows the detailed steps of how to solve it. Example: Billy bought 5 bags of balls. Each bag contained 40 balls. He packed the balls into packets of 8 balls each.
3 Ways to Do Long Multiplication
8. Multiply the number in the tens place of the bottom number by the number in hundreds place of the top number. Multiply 3 times 7 to equal 21. Add the 1 you carried to equal 22. You don't need to carry the 2 in 22, as there are no more numbers to multiply on this line, so you can just write it down next to the 6. 9.
How to Write & Solve a 2-Step Equation for a Word Problem
Step 4: Solve the 2-step equation from step 3 using two mathematical operations. We can go ahead and perform the multiplication and addition steps to solve for s. {eq}2 * 30 = \frac {s-5}{30} * 30 ...
2 Step Multiplication Problems 3rd Grade Teaching Resources
Topics: Solve Multiplication and Division 2 Steps Word Problems for Whole Numbers using Bar Models/Tape Diagrams. (For Distance Learning)The word problems in this worksheets pack are based on multiplication and division situations of :- Equal groups- Comparison with Difference- Comparison with SumPrior Skill Required:Students need to have prior knowledge or skill in solving one step ...
How to do division equations
Solving Algebra Equations with Multiplication and Division. Demonstrates, step-by-step and with illustrations, how to solve one-step linear equations using multiplication and division. 1. Determine mathematic problem. ... Figure out mathematic problems. Mathematics is the study of numbers, shapes and patterns. ...
Problem solving two step problems
2. Begin your two-step word problem like you would any other word problem by reading it carefully to decide what you need to do, including which. You can always count on our 24/7 customer support to be there for you when you need it. Math can be difficult to understand, but with a little clarification it can be easy!
Results for solve multi-step problems using order of operations
PDF. Easel Activity. These Two Step Word Problem task cards give students practice using keywords in multi-step word problems to solve 40 multiple step word problems tasks. These two-step addition, subtraction, multiplication, and division word problems require students to use multiple order of operations to add, subtract, multiply, and divide.