# Equations with Addition and Subtraction

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Equations with Addition and Subtraction
CCSS.MATH.CONTENT.4.OA.A.3

## Solving Equations by Adding or Subtracting

What is an Equation? An equation tells us that the expression on either side of the equal sign is equal to the other. Sometimes, when writing an equation, you may have an unknown value that you need to solve for. A variable is a letter used to represent the value that we're solving for.

Equations can be used to solve word problems by following these steps:

Step # What to do
1 Read the word problem
2 Highlight the important information
3 Identify the operation
4 Write the equation using a variable
to represent the unknown value
5 Solve the equation

## Solving Equations by Adding or Subtracting – Example

How do you solve addition and subtraction equations? Let’s take a look at the example from the video:

In order to reverse the experiment, Imani needs seventy-eight ingredients altogether. The directions say they need twenty-four jars of mist and fourteen rose petals. The rest of the ingredients they need are crystals. How many crystals does Imani need?

Our equation is: twenty-four jars of mist plus fourteen rose petals plus c equals seventy-eight because if we add all the ingredients together, the total number they need is seventy-eight.

## How to Solve an Equation by Adding or Subtracting

First, we add twenty four jars of mist and fourteen rose petals to get thirty-eight, but we still don't know how many crystals we need!

This is an addition equation, but since we do not know the value of c, we need to practice solving an addition equation using inverse operations.

The inverse operation of addition is subtraction, so we subtract thirty-eight from the number of ingredients in total, which is seventy-eight. Seventy-eight minus thirty-eight is forty, and we write the answer using the variable c equals forty.

## Solving Equations by Adding or Subtracting – Summary

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. When writing the equation we use a variable to represent the unknown value. Sometimes when solving equations with addition and subtraction you may have to use the inverse operation to find the answer. Always include the variable in your answer using an equal sign.

Want some more solving equations with addition and subtraction practice? On this website there are many interactive exercises for solving equations with addition and subtraction along with worksheets and other activities waiting to be completed.

## Equations with Addition and Subtraction exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Equations with Addition and Subtraction.
• ### Complete the sentences.

Hints

Here's an example of an equation.

The 'c' in this equation is a variable.

Solution

Equations tell us that the expression on either side of the equal sign is equal to the other.

Equations can be used to solve word problems.

We use variables to represent the unknown values ​​in equations.

• ### Solve the story problem.

Hints

Reread the problem and think: what is the important information?

Write the equation using a variable to represent the unknown value. Here we could use 'r' to represent the rose petals.

Add any numbers together first.

To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5 - 4 to solve for b.

Solution

After highlighting the important information shown, then this is the equation with the variable solved.
64 = 31 + 12 + r
31 + 12 = 43
64 = 43 + r
64 - 43 = r
21 = r
So, 21 rose petals are needed.

• ### Solve for each variable.

Hints

Remember, you are solving for the variable, or the letter. In all of these equations it is x.

Add any numbers together first.

To solve for the variable, do the opposite operation to the answer.

For example in 4 + x = 5, you would subtract 5 - 4 to solve for x.

Another strategy to check your answer is to plug in the number for x to see if it's correct.

Solution

x + 10 = 25
x = 25 - 10
x = 15

37 = 26 + x
37 - 26 = x
x = 11

13 + 22 + x = 42
13 + 22 = 35
35 + x = 42
x = 42 - 35
x = 7

57 = 32 + 12 + x
32 + 12 = 44
57 = 44 + x
57 - 44 = x
x = 13

• ### Solve each story problem.

Hints

Reread the problem and think: what is the important information?

Write the equation using a variable to represent the unknown value.

Add any numbers together first.

To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5 - 4 to solve for b.

Solution

For the first problem:
27 + 36 + x = 72
27 + 36 = 63
63 + x = 72
x = 72 - 63
x = 9, so 9 jars of mist.
For the second problem:
65 = 22 + 32 + x
22 + 32 = 54
65 = 54 + x
65 - 54 = x
11 = x, so 11 leaves .

• ### Solve for the variable.

Hints

Remember, you are solving for the variable, or the letter.

Add any numbers together first.

To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5 - 4 to solve for b.

Solution

13 + 25 + b = 50
13 + 25 = 38
38 + b = 50
b = 50 - 38
b = 12

• ### Solve each story problem.

Hints

Reread the problem and think: what is the important information?

Write the equation using a variable to represent the unknown value.

Add any numbers together first.

To solve for the variable, do the opposite operation to the answer. For example in 4 + b = 5, you would subtract 5 - 4 to solve for b.

Solution

For the first smoothie:
17 + 44 + b = 75
17 + 44 = 61
61 + b = 75
b = 75 - 61
b = 14, so that answer was correct.
For the second smoothie:
64 = 32 + 18 + r
32 + 18 = 50
64 = 50 + r
64 - 50 = r
14 = r, so that answer was incorrect.
For the last smoothie:
52 = 19 + 27 + i
19 + 27 = 46
52 = 46 + i
52 - 46 = i
6 = i, so that answer was incorrect.