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Equations with Multiplication and Division

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Basics on the topic Equations with Multiplication and Division

Solving Equations Using Multiplication and Division

An equation is where we represent a question using mathematical figures, sometimes we can use multiplication to solve the problem and sometimes we need to use division.

Equations with Multiplication and Division from Word Problems

How do you solve multiplication equations? Solving equations with multiplication and division is simple because it follows the basic rules of multiplication and division. However, before we can solve, we need to determine the equation based on the information from the word problem. The next section shows an example of solving one step equations with multiplication and division that come from a word problem.

Solving Equations with Multiplication and Division – Example

The first step is to read the word problem. As you read, think; 'what do I need to find?', and highlight the question you need to solve!

25279_SEO_line16-01.svg Next, highlight all the other important information.

25279_SEO_line22-01.svg Now we need to identify the operation. The keywords in each means to divide in this problem because the sandwiches are being shared equally.

25279_SEO_line24-01.svg Then, write the equation using a variable to represent the unknown value. A variable is a letter that we use to represent an unknown value. Our equation is: twenty-two sandwiches divided by two bags equals S because we are dividing the number of sandwiches they have into two bags. We use the letter S as the variable to represent the number of sandwiches.

25279_SEO_line29-01.svg The last step is to solve the equation. We can draw pictures to help us solve, so here you see twenty-two sandwiches and two bags.

25279_SEO_line34-01.svg What is twenty-two divided by two? Eleven, so they have eleven sandwiches in each bag. Write the answer using our variable: S equals eleven.

25279_SEO_line37-01.svg

Solving Equations with Multiplication and Division – Summary

How do you solve equations by multiplication and division? Solving equations with multiplication and division is simple because it follows the basic rules of multiplication and division. However, before we can solve, we need to determine the equation based on the information from the word problem. In order to determine the equation, we follow the steps for solving a word problem:

Step # What to do
1 Read the word problem. As you read, think;
'what do I need to find?',
and highlight the question you need to solve.
2 Highlight all the other important information.
3 Identify the operation.
4 Write the equation using a variable
to represent the unknown value.
5 Solve the equation. We can also draw
pictures to help us solve.

Want some more solving equations using multiplication and division practice? After watching the video, you can find interactive exercises for solving equations using multiplication and division as well as worksheets and further activities.

Transcript Equations with Multiplication and Division

Ahh, another sunny day on the open sea. "Look out!" "We're stuck!" "Don't worry, I think we have enough food here to last us until we get some help." Let's see how much food Mr. Squeaks and Imani have, by solving equations with multiplication and division. An equation tells us that the expression on either side of the equals sign is equal to the other. We can use equations to help solve word problems. First, read the word problem. As you read, ask yourself; what do I need to find, and highlight the question you need to solve! For example, Mr. Squeaks and Imani have two bags equally full of sandwiches. They have twenty-two in total. How many sandwiches are in each bag? Here we should highlight, ‘how many sandwiches are in each bag?’ because that's what we need to solve! Now, re-read and think, what is the important information? While re-reading, highlight keywords, numbers, or units of measurement, that will help answer the question. In, ‘Mr. Squeaks and Imani have two bags equally full of sandwiches’ highlight 'two bags equally full', because this tells us how many bags they have with the same amount in each. In the next sentence, highlight 'twenty-two in total' because it tells us how many sandwiches they have altogether. Next, identify the operation. The keywords 'in each’ mean to divide in this problem because the sandwiches are being shared equally. Then, write the equation using a variable to represent the unknown value. A variable is a letter that we use to represent an unknown value. Our equation is: twenty-two sandwiches divided by two bags equals because the sandwiches have been divided between two bags. We use the letter as the variable to represent the number of sandwiches. The last step is to solve the equation. Let's draw pictures to help us solve. Draw twenty-two sandwiches and two bags. What is twenty-two divided by two? Eleven, so they have eleven sandwiches in each bag. Write the answer using our variable: equals eleven. Oh! It looks like they found a few more bags, let's look at another problem! First, read the word problem and ask yourself, what do I need to find out, and highlight the key question you need to solve! Mr. Squeaks and Imani have four bags with eleven sandwiches in each. How many sandwiches do they have in total? Highlight ‘How many sandwiches do they have in total?’ because this tells us what we need to solve. Now, re-read and think, what is the important information? First, highlight ‘four bags’ because this tells us how many they have. Highlight ‘eleven sandwiches in each’ because this tells us how many are in each bag. Next, identify the operation. The keyword ‘total’ means to add or multiply because the number of sandwiches is getting larger. We could use repeated addition or multiplication but we will multiply because it's more efficient. Next, write the equation using a variable to represent the unknown value. Our equation is: eleven times four equals . The variable represents the number of sandwiches they have. The last step is to solve the equation. We can draw pictures to help us solve the problem. Draw four bags and label each bag to represent the number of sandwiches. What is eleven times four? Forty-four, so Mr. Squeaks and Imani have forty-four sandwiches in total. Remember, an equation tells us that the expression on either side of the equals sign is equal to the other. Equations can be used to solve word problems, and we can use drawings to help us solve them. When writing the equation we use a variable to represent the unknown value. Always include the variable in your answer using an equals sign. "Alright Imani, we have enough sandwiches to last us, whoa!" "I guess this means we've been rescued!" "I mean, I still plan on eating all the sandwiches."

Equations with Multiplication and Division exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Equations with Multiplication and Division.
  • Identify equations.

    Hints

    For division we use the symbol ÷.

    Remember, multiplication means "times" and the symbol x is used.

    Solution

    The division equations are:

    • 22 ÷ 11
    • 99 ÷ 9
    • 25 ÷ 5
    They all show division because they are showing a larger number being split amongst a smaller number. The division symbol ÷ is also used in each of these equations.

    The multiplication equations are:

    • 12 x 7
    • 11 x 4
    • 2 x 6
    We know to multiply because the "x" represents times. When multiplying you get a larger number.

    9 + 10 is an addition problem and 30 - 17 is a subtraction problem, so we do not want to highlight those.

  • What do these terms mean?

    Hints

    Which operation matches the action word?

    If something is being shared equally, which operation might that be?

    What do we create to help solve a word problem?

    Solution

    The correct pairs are:

    • Multiplication: product of multiple items
    • Division: share equally
    • Equation: used to help solve word problems
    • Solution: answer to an equation
    All of these are key words to know when solving a word problem. Make sure to look for and highlight them when reading word problems.

  • How many sandwiches do Mr. Squeaks and Imani have?

    Hints

    Identify keywords that help you determine whether you should multiply or divide.

    Could you draw a picture to help you find the answer?

    We are being asked to find how many sandwiches they have altogether which means we need to multiply.

    Solution

    Mr. Squeaks and Imani have 24 sandwiches.

    They have 3 bags with 8 sandwiches in each. We are asked to find the total number of sandwiches, so we multiply 3 x 8 to get 24.

  • Match the word problem to the equation.

    Hints

    Look for keywords such as altogether and each bag to help you decide whether it is a multiplication or division problem.

    Draw a picture to represent the equation. For example, if you were solving 6 x 7, you could draw six circles and put seven dots in each circle. You can count the dots to get the total which is 42.

    Solution

    The first word problem is displayed in the image above. The image shows 36 sandwiches in four rows. If you count the number of sandwiches in a row, you will see that there are nine sandwiches in each row which is the answer to the equation.

    Imani has 36 sandwiches. They want to share the sandwiches equally with their 3 friends. How many sandwiches does each friend get? Solution: 36 ÷ 4 = 9

    The remaining matches are:

    • Mr. Squeaks has 3 bags. In each bag there are 10 sandwiches. How many sandwiches does Mr. Squeaks have altogether? Solution: 3 x 10 = 30
    • Mr. Squeaks and Imani have 11 sandwiches each. How many sandwiches do they have in total? Solution: 11 x 2 = 22
    • Mr. Squeaks and Imani have 5 bags equally full of sandwiches. They have 40 sandwiches altogether. How many sandwiches are in each bag? Solution: 40 ÷ 5 = 8
  • Identify the number that completes each equation.

    Hints

    Use the numbers in the problem to create a fact family to help you solve the missing variable.

    Draw pictures to help you visualise the problem.

    Let's look at 21 ÷ 7= ?

    You could draw 7 circles to represent the groups and then break up 21 equally among the 7 groups. You will see that each group has 3 dots, so 21 ÷ 7 = 3.

    When multiplying, you can also use drawings to help you. For example, when solving 6 x 9, you could draw 6 groups of 9 objects. How many do you have altogether?

    Solution

    The solutions are:

    24 ÷ 3 = 8

    2 x 11 = 22

    6 x 9 = 54

    10 ÷ 5 = 2

  • Which problems match the equation?

    Hints

    Look for key words such as in total and each.

    Draw pictures to represent the equation and see how it relates to the problems.

    A dozen means twelve.

    Solution

    The image above shows the solution to the first word problem about John and his baskets of fruit. John delivered 12 baskets with 3 apples in them so to find the total number of apples we need to solve 12 x 3. Therefore, this is a correct answer.

    Other word problems that show 12 x 3 are:

    • At the library there are 12 stacks each with 3 books, so again, it is showing us 12 x 3.
    • Mum bought 3 dozen boxes of doughnuts. A dozen means twelve. So this is also showing 12 x 3.
    • At the supermarket, cans of lemonade are sold in packs of 12. Ashley bought 3. The equation would again be 12 x 3.
    To solve these word problems we would not multiply 12 x 3 so these are incorrect in this question.
    • I have 12 sweets that I want to share with my friends equally. I am with 3 friends. For this problem you would need to use division because you share equally among friends. We would also divide by 4 as there are 4 people altogether. We would solve 12 ÷ 4.
    • My sister picked 12 flowers from our garden. She gave me 3 flowers. For this problem you would need to use subtraction because you are subtracting the flowers she gave away: 12 - 3.
    • Tim and Kyle are playing with toy cars. How many more yellow cars are there than blue cars? Again, you would need to use subtraction because you want to know how many more yellow cars there are compared to blue cars: 12 - 3.