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Solving Equations with Multiplication and Division

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Solving Equations with Multiplication and Division
CCSS.MATH.CONTENT.4.OA.A.2

Basics on the topic Solving Equations with Multiplication and Division

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Mr. Squeaks and Imani are sailing on the open sea when all of a sudden, their boat takes a wrong turn and gets stuck on a deserted island! They don’t know how long they will be stuck so they want to make sure they have enough food. Let’s help them calculate the amount of food they have by solving equations using multiplication and division.

One-step Multiplication & Division Equations from Word Problems

How do you solve one step equations with multiplication and division? 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 one step equations with multiplication and division that come from a word problem.

Solving Equations Using Multiplication and Division from a Word Problem 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!

Mr-Squeaks-and-Imani-have-two-bags-full-of-sandwiches-they-have-twenty-two-sandwiches-in-all-how-many-sandwiches-are-in-each-bag-highlighted-solving-equations-using-multiplication-and-division.svg

Next, highlight all the other important information.

Mr-Squeaks-and-Imani-have-two-bags-highlighted-full-of-sandwiches-they-have-twenty-two-sandwiches-in-all-highlighted-how-many-sandwiches-are-in-each-bag-highlighted-solving-equations-using-multiplication-and-division.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.

Mr-Squeaks-and-Imani-have-two-bags-highlighted-full-of-sandwiches-they-have-twenty-two-sandwiches-in-all-highlighted-how-many-sandwiches-are-in-each-highlighted-bag-highlighted-solving-equations-using-multiplication-and-division.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.

twenty-two-divided-by-two-equals-s-solving-equations-using-multiplication-and-division.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.

twenty-two-divided-by-two-equals-s-twenty-two-sandwiches-two-bags-solving-equations-using-multiplication-and-division.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.

twenty-two-divided-by-two-equals-eleven-two-bags-solving-equations-using-multiplication-and-division.svg

Solving Equations Using 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 1: Read the word problem. As you read, think; 'what do I need to find?', and highlight the question you need to solve

  • Step 2: Highlight all the other important information

  • Step 3: Identify the operation

  • Step 4: Write the equation using a variable to represent the unknown value

  • Step 5: Solve the equation. We can also draw pictures to help us solve

Want some more solving equations using multiplication and division practice? On this website you can find solving equations using multiplication and division worksheets and a solving equations using multiplication and division worksheet along with activities and exercises.

Transcript Solving 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 equal sign (...) is EQUAL to the other. We can use equations to help solve word problems. First, “Read the word problem”. As you read, think; '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 all. How many sandwiches are in each bag? Here we highlight, “How many sandwiches are in each bag?”... because that's what we need to solve! Now, reread and think; 'What is the important information?' While rereading, 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 all'... because it tells us how many sandwiches they have. 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 we are dividing the number of sandwiches they have into 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 solve! First, read the word problem and ask yourself: 'what do I need to find?'... and highlight the 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, reread and think; “What is the important information?” First, highlight "four bags" (...) because this tells 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. Let's draw pictures to help us solve (...) 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 equal sign (...) is EQUAL to the other. Equations can be used to solve word problems, and we can use drawings to help us solve. When writing the equation we use a variable to represent the unknown value. Always include the variable in your answer using an equal 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..."

Solving Equations with Multiplication and Division exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Solving 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 ÷ 2, 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 want to 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.

  • Identify the math terms and how they help us solve word problem.

    Hints

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

    What operation matches the action word?

    What do we create to help solve a word problem?

    Solution

    The correct pairs are:

    • Multiplication and product of multiple items
    • Division and share equally
    • Equation and used to help solve word problems
    • Solution and 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.

  • Solve the word problem

    Hints

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

    Think about multiple items

    Draw a picture to help identify the equation.

    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 in all and each bag.

    Draw a picture to represent the equation. For example, 6 x 7. I would draw six circles and put seven dots in each circle. I 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 each 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 4 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 in all? 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 in all. How many sandwiches are in each bag? Solution 40 ÷ 5 = 8

  • Identify the digit that completes each equation.

    Hints

    Draw pictures to help you visualize the problem.

    Let's look at 21 ÷ 7= ?

    I would draw 7 circles to represent my groups and then I would break up 21 equally among the 7 groups. I can represent those with dots. You will see that each group gets 3 dots, so 21 ÷ 7 = 3.

    Division means sharing equally and multiplication means how many are there in total.

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

    Solution

    The solutions are:

    24 ÷ 3 = 8

    2 x 11 = 22

    6 x 9 = 54

    10 ÷ 5 = 2

  • Given the equation 12 x 3, select the word problems that relate.

    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 fruit baskets. John delivered 12 baskets with 3 apples in them, so this is showing us 12 x 3.

    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.
    • Mom bought 3 dozen boxes of donuts. A dozen means twelve. So this also is showing 12 x 3.
    • At the grocery store, cans of lemonade are sold in packs of 12. Ashley bought 3. The equation would again be 12 x 3.
    You should not have selected the following answers because they do not relate to multiplication which is what we are looking for since the equation is 12 x 3:

    • I have 12 sticks of gum that I want to share with my friends equally. I am hanging out with 3 friends. For this problem you would need to use division because you are share equally among friends.
    • My sister picked 12 flowers from our garden. She gave me 3 flowers. For this problems you would need to use subtraction because you are taking the flowers away and trying to figure out how many are left.
    • Tim and Kyle are playing with race cars. How many more yellow race cars are there than blue race cars? Again, you would need to use subtraction because you want to know how many more yellow cars there are compared to blue cars.