Test Prep Math Practice Worksheets Grade 6 - Free Printable

The image shows a promotional graphic for 6th Grade Math Test Prep Practice Worksheets. The worksheet includes various math problems related to ratios, proportions, and other mathematical concepts. Below, I will solve the problems visible in the worksheet:

---

Worksheet Problems and Solutions

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

Solution:
1. Identify the number of girls and boys:
- Girls = 15
- Boys = 10

2. Write the ratio of girls to boys:
\[
\text{Ratio} = \frac{\text{Girls}}{\text{Boys}} = \frac{15}{10}
\]

3. Simplify the ratio by dividing both numbers by their greatest common divisor (GCD), which is 5:
\[
\frac{15 \div 5}{10 \div 5} = \frac{3}{2}
\]

4. Express the ratio in simplest form:
\[
\text{Ratio of girls to boys} = 3:2
\]

Answer: \( \boxed{3:2} \)

---

#### Problem 2: Unit Rate for Unloading Trucks
Question: At a warehouse, the employees can unload 24 trucks in 4 hours. What is the unit rate for unloading trucks?

Solution:
1. Identify the total number of trucks unloaded and the total time taken:
- Trucks unloaded = 24
- Time taken = 4 hours

2. Calculate the unit rate (trucks per hour) by dividing the total number of trucks by the total time:
\[
\text{Unit rate} = \frac{\text{Trucks unloaded}}{\text{Time taken}} = \frac{24}{4}
\]

3. Perform the division:
\[
\frac{24}{4} = 6
\]

4. Express the unit rate:
\[
\text{Unit rate} = 6 \text{ trucks per hour}
\]

Answer: \( \boxed{6 \text{ trucks per hour}} \)

---

#### Problem 3: Ratio of Gray Triangles to Total Triangles
Question: What is the ratio of gray triangles to total triangles?

Visual Representation:
- Total triangles: 7
- Gray triangles: 4

Solution:
1. Count the total number of triangles:
- Total triangles = 7

2. Count the number of gray triangles:
- Gray triangles = 4

3. Write the ratio of gray triangles to total triangles:
\[
\text{Ratio} = \frac{\text{Gray triangles}}{\text{Total triangles}} = \frac{4}{7}
\]

4. The ratio is already in simplest form:
\[
\text{Ratio of gray triangles to total triangles} = 4:7
\]

Answer: \( \boxed{4:7} \)

---

#### Problem 4: Ratio of Hits to Times at Bat
Question: 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.

Solution:
1. Identify the number of hits and the number of times at bat:
- Hits = 27
- Times at bat = 60

2. Write the ratio of hits to times at bat:
\[
\text{Ratio} = \frac{\text{Hits}}{\text{Times at bat}} = \frac{27}{60}
\]

3. Simplify the ratio by finding the greatest common divisor (GCD) of 27 and 60, which is 3:
\[
\frac{27 \div 3}{60 \div 3} = \frac{9}{20}
\]

4. Express the ratio in simplest form:
\[
\text{Ratio of hits to times at bat} = 9:20
\]

Answer: \( \boxed{9:20} \)

---

#### Problem 5: Cost per Ounce of Cereal
Question: 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.

Solution:
1. Calculate the cost per ounce for the 32-ounce box:
\[
\text{Cost per ounce (32-ounce box)} = \frac{\text{Total cost}}{\text{Total ounces}} = \frac{4.89}{32}
\]
Perform the division:
\[
\frac{4.89}{32} \approx 0.1528 \text{ dollars per ounce}
\]

2. Calculate the cost per ounce for the 12-ounce box:
\[
\text{Cost per ounce (12-ounce box)} = \frac{\text{Total cost}}{\text{Total ounces}} = \frac{2.79}{12}
\]
Perform the division:
\[
\frac{2.79}{12} \approx 0.2325 \text{ dollars per ounce}
\]

3. Compare the two costs per ounce:
- 32-ounce box: $0.1528 per ounce
- 12-ounce box: $0.2325 per ounce

4. The 32-ounce box is less expensive per ounce.

Answer: \( \boxed{\text{32-ounce box}} \)

---

#### Problem 6: Complete the Ratio Table
Question: Complete the ratio table.

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

Solution:
1. Identify the given ratio:
\[
\frac{45}{21}
\]

2. Simplify the ratio:
\[
\frac{45}{21} = \frac{45 \div 3}{21 \div 3} = \frac{15}{7}
\]

3. Use the simplified ratio \( \frac{15}{7} \) to fill in the missing values.

- For the second row (where the second column is 42):
\[
\frac{x}{42} = \frac{15}{7}
\]
Cross-multiply:
\[
x \cdot 7 = 15 \cdot 42
\]
\[
x = \frac{15 \cdot 42}{7} = \frac{630}{7} = 90
\]

- For the third row (where the first column is 135):
\[
\frac{135}{y} = \frac{15}{7}
\]
Cross-multiply:
\[
135 \cdot 7 = 15 \cdot y
\]
\[
y = \frac{135 \cdot 7}{15} = \frac{945}{15} = 63
\]

- For the fourth row (where the second column is 84):
\[
\frac{z}{84} = \frac{15}{7}
\]
Cross-multiply:
\[
z \cdot 7 = 15 \cdot 84
\]
\[
z = \frac{15 \cdot 84}{7} = \frac{1260}{7} = 180
\]

4. Fill in the completed table:
\[
\begin{array}{c|c}
45 & 21 \\
\hline
90 & 42 \\
\hline
135 & 63 \\
\hline
180 & 84 \\
\end{array}
\]

Answer: \( \boxed{90, 63, 180} \)

---

Final Answers:

1. \( \boxed{3:2} \)
2. \( \boxed{6 \text{ trucks per hour}} \)
3. \( \boxed{4:7} \)
4. \( \boxed{9:20} \)
5. \( \boxed{\text{32-ounce box}} \)
6. \( \boxed{90, 63, 180} \)