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..."