4th Grade Common Core Math Worksheets - Free Printable

Let's solve each problem step by step and provide clear explanations.

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1. Write an equation for each statement below using a variable. What does the variable represent?

#### a. Sophie has eight pairs of slippers. One pair is green. Three pairs are red. The rest are pink.

Step-by-step:
- Total pairs = 8
- Green = 1
- Red = 3
- Let p = number of pink pairs

So:
$$
\text{Green} + \text{Red} + \text{Pink} = \text{Total}
$$
$$
1 + 3 + p = 8
$$
$$
4 + p = 8
$$

✔ Equation: $ p = 8 - 4 $ → $ p = 4 $

➡️ Variable p represents the number of pink pairs of slippers.

#### b. James caught seven chickens on their trip to the chicken farm. He gave away some to the soup kitchen on his way home. He brought four chickens back to his home.

Let c = number of chickens given away

He started with 7, gave away c, and had 4 left:

$$
7 - c = 4
$$

✔ Equation: $ 7 - c = 4 $

➡️ Variable c represents the number of chickens James gave away.

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2. Solve the equation.

#### a. $ x + 11 = 17 $
Subtract 11 from both sides:
$$
x = 17 - 11 = 6
$$
✔ x = 6

#### b. $ m - 4 = 6 $
Add 4 to both sides:
$$
m = 6 + 4 = 10
$$
✔ m = 10

#### c. $ 8 - r = 2 $
Subtract 8 from both sides:
$$
-r = 2 - 8 = -6
$$
Multiply both sides by -1:
$$
r = 6
$$
✔ r = 6

#### d. $ q + 7 = 13 $
Subtract 7:
$$
q = 13 - 7 = 6
$$
✔ q = 6

#### e. $ 6 + (13 - w) = 12 $
Simplify inside parentheses:
$$
6 + 13 - w = 12
$$
$$
19 - w = 12
$$
Subtract 19:
$$
-w = 12 - 19 = -7
$$
$$
w = 7
$$
✔ w = 7

#### f. $ p - 8 = 0 $
Add 8:
$$
p = 8
$$
✔ p = 8

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3. Write an equation to find out the missing score to reach student total. Solve the equation.

We are given:

| Student's Name | Science Score | Math Score | Total Score |
|----------------|---------------|------------|-------------|
| M. Sam | 92 | ? | 178 |
| L. Ken | ? | 95 | 188 |
| W. Mary | 84 | ? | 175 |

Let’s find missing scores.

#### a. M. Sam:
Science = 92, Total = 178
Let m = Math score

$$
92 + m = 178
$$
$$
m = 178 - 92 = 86
$$
✔ Math score = 86

#### b. L. Ken:
Math = 95, Total = 188
Let s = Science score

$$
s + 95 = 188
$$
$$
s = 188 - 95 = 93
$$
✔ Science score = 93

#### c. W. Mary:
Science = 84, Total = 175
Let m = Math score

$$
84 + m = 175
$$
$$
m = 175 - 84 = 91
$$
✔ Math score = 91

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4. Write a word problem for each of the equations below.

#### a. $ k - 5 = 4 $

Word Problem:
Kaitlyn had some candies. She ate 5 of them and now has 4 left. How many candies did she start with?

✔ Answer: $ k = 9 $

#### b. $ g + 16 = 108 $

Word Problem:
A book has 108 pages. George read 16 pages today. How many pages did he read before today?

OR:
George has read 16 pages so far and needs to read more to complete the 108-page book. How many pages remain?

But better:
"George has read some pages of a 108-page book. After reading 16 more pages, he will have read 108 pages in total. How many pages had he read before?"

✔ Answer: $ g = 92 $

#### c. $ 36 - w = 25 $

Word Problem:
There were 36 apples in a basket. Some were taken out. Now there are 25 left. How many apples were taken out?

✔ Answer: $ w = 11 $

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5. If $ x - 4 = 6 $ and $ 3x + y = 38 $, find x and y. Explain your method.

#### Step 1: Solve for x
Given:
$ x - 4 = 6 $
Add 4 to both sides:
$$
x = 6 + 4 = 10
$$

✔ So, x = 10

#### Step 2: Plug x into second equation
Given:
$ 3x + y = 38 $

Substitute $ x = 10 $:
$$
3(10) + y = 38
$$
$$
30 + y = 38
$$
$$
y = 38 - 30 = 8
$$

✔ So, y = 8

#### ✔ Final Answer:
- $ x = 10 $
- $ y = 8 $

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Final Answers Summary:

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1. Equations with Variables

a. $ 1 + 3 + p = 8 $ → $ p = 4 $
→ p = number of pink slipper pairs

b. $ 7 - c = 4 $ → $ c = 3 $
→ c = number of chickens given away

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2. Solve Equations

a. $ x = 6 $
b. $ m = 10 $
c. $ r = 6 $
d. $ q = 6 $
e. $ w = 7 $
f. $ p = 8 $

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3. Missing Scores

- M. Sam: Math = 86
- L. Ken: Science = 93
- W. Mary: Math = 91

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4. Word Problems

a. $ k - 5 = 4 $: Kaitlyn had k candies, ate 5, 4 left → $ k = 9 $

b. $ g + 16 = 108 $: George read g pages, then 16 more, total 108 → $ g = 92 $

c. $ 36 - w = 25 $: 36 apples, w removed, 25 left → $ w = 11 $

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5. System of Equations

From $ x - 4 = 6 $ → $ x = 10 $
Then $ 3(10) + y = 38 $ → $ 30 + y = 38 $ → $ y = 8 $

✔ x = 10, y = 8

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