Test Prep Math Practice Worksheets Grade 6 - Free Printable

Let’s solve each problem on the worksheet step by step.

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Problem 1:
> There are 15 girls and 10 boys running a race in gym class. What is the ratio of girls to boys?

Step-by-step:
- Ratio means comparing two numbers using “to” or a colon (:).
- Girls : Boys = 15 : 10
- We can simplify this ratio by dividing both numbers by their greatest common factor, which is 5.
- 15 ÷ 5 = 3
- 10 ÷ 5 = 2
→ So, simplified ratio is 3:2

✔ Final Answer for Problem 1: 3:2

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Problem 2:
> At a warehouse, the employees can unload 24 trucks in 4 hours. What is the unit rate for unloading trucks?

Step-by-step:
- Unit rate means “per one hour”.
- Divide total trucks by total hours: 24 ÷ 4 = 6
→ So, they unload 6 trucks per hour

✔ Final Answer for Problem 2: 6 trucks per hour

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Problem 3:
> What is the ratio of gray triangles to total triangles?
Triangles shown: ▲ △ ▲ ▲ △ ▲ △ → That’s 7 triangles total. Gray ones: positions 1, 3, 4, 6 → that’s 4 gray triangles.

Wait — let me count again from the image description (since we’re not describing the image, but based on standard interpretation):

The sequence given in text:
▲ △ ▲ ▲ △ ▲ △
That’s 7 triangles.

Gray (▲): 1st, 3rd, 4th, 6th → 4 gray
White (△): 2nd, 5th, 7th → 3 white
Total = 7

Ratio of gray to total = 4 : 7

This cannot be simplified further.

✔ Final Answer for Problem 3: 4:7

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Problem 4:
> James had 27 hits at 60 times at bat last season. Write a ratio to compare the number of hits to the number of times at bat.

Step-by-step:
- Hits : At-bats = 27 : 60
- Simplify by dividing both by 3:
- 27 ÷ 3 = 9
- 60 ÷ 3 = 20
→ Simplified ratio: 9:20

✔ Final Answer for Problem 4: 9:20

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Problem 5:
> Sarah wants to buy cereal that comes in large and small boxes. The 32-ounce box costs $4.89, and the 12-ounce box costs $2.79. Which box is less expensive per ounce? Explain.

Step-by-step:
We need to find cost per ounce for each.

Large box:
$4.89 ÷ 32 ounces = ?

Calculate:
4.89 ÷ 32 = 0.1528125 → about $0.153 per ounce

Small box:
$2.79 ÷ 12 ounces = ?

2.79 ÷ 12 = 0.2325 → about $0.233 per ounce

Compare:
$0.153 < $0.233 → Large box is cheaper per ounce.

✔ Final Answer for Problem 5: The 32-ounce box is less expensive per ounce.

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Problem 6:
> Complete the ratio table.

Given:

| | |
|---|---|
| 45 | 21 |
| | 42 |
| 135| |
| 180| 84 |

We need to find missing values.

First, check the relationship between first row: 45 and 21.

Find the ratio: 45 : 21 → divide both by 3 → 15 : 7

So, the pattern is multiply by 15/7? Or better: think of it as scaling.

Check if 21 × 2 = 42 → then 45 × 2 = 90 → so second row should be 90 and 42.

Check third row: 135 ÷ 45 = 3 → so 21 × 3 = 63 → so third row: 135 and 63

Fourth row: 180 ÷ 45 = 4 → 21 × 4 = 84 → matches!

So completed table:

| 45 | 21 |
|-----|-----|
| 90 | 42 |
| 135 | 63 |
| 180 | 84 |

✔ Final Answer for Problem 6:
Missing values are:
Second row left: 90
Third row right: 63

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Now, compiling all final answers clearly:

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Final Answer:
1. 3:2
2. 6 trucks per hour
3. 4:7
4. 9:20
5. The 32-ounce box is less expensive per ounce.
6. Missing values: 90 and 63