Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable
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Step-by-step solution for: Ratio Worksheets | Ratio Worksheets for Teachers
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Show Answer Key & Explanations
Step-by-step solution for: Ratio Worksheets | Ratio Worksheets for Teachers
To solve the problem of finding equivalent ratios, we need to use the concept of proportionality. Equivalent ratios are created by multiplying or dividing both terms of a ratio by the same non-zero number. Let's solve each part step by step.
1. \( 1 : 7 = \_\_ : 14 \)
To find the missing term, notice that \( 7 \times 2 = 14 \). Therefore, multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 7 = 2 : 14 \).
2. \( 1 : 7 = \_\_ : 21 \)
Here, \( 7 \times 3 = 21 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 7 = 3 : 21 \).
3. \( 1 : 7 = 4 : \_\_ \)
To find the missing term, notice that \( 1 \times 4 = 4 \). Therefore, multiply the second term by 4:
\( 7 \times 4 = 28 \).
So, \( 1 : 7 = 4 : 28 \).
4. \( 1 : 7 = 5 : \_\_ \)
Similarly, \( 1 \times 5 = 5 \). Multiply the second term by 5:
\( 7 \times 5 = 35 \).
So, \( 1 : 7 = 5 : 35 \).
5. \( 1 : 7 = \_\_ : 42 \)
Here, \( 7 \times 6 = 42 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 7 = 6 : 42 \).
\[ 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42 \]
---
1. \( 1 : 2 = \_\_ : 4 \)
Here, \( 2 \times 2 = 4 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = 3 : \_\_ \)
Here, \( 1 \times 3 = 3 \). Multiply the second term by 3:
\( 2 \times 3 = 6 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 2 \times 4 = 8 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = 5 : \_\_ \)
Here, \( 1 \times 5 = 5 \). Multiply the second term by 5:
\( 2 \times 5 = 10 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 2 \times 6 = 12 \).
So, \( 1 : 2 = 6 : 12 \).
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
1. \( 1 : 3 = \_\_ : 6 \)
Here, \( 3 \times 2 = 6 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 3 = 2 : 6 \).
2. \( 1 : 3 = 3 : \_\_ \)
Here, \( 1 \times 3 = 3 \). Multiply the second term by 3:
\( 3 \times 3 = 9 \).
So, \( 1 : 3 = 3 : 9 \).
3. \( 1 : 3 = \_\_ : 12 \)
Here, \( 3 \times 4 = 12 \). Multiply the first term by 4:
\( 1 \times 4 = 4 \).
So, \( 1 : 3 = 4 : 12 \).
4. \( 1 : 3 = 5 : \_\_ \)
Here, \( 1 \times 5 = 5 \). Multiply the second term by 5:
\( 3 \times 5 = 15 \).
So, \( 1 : 3 = 5 : 15 \).
5. \( 1 : 3 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 3 \times 6 = 18 \).
So, \( 1 : 3 = 6 : 18 \).
\[ 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \]
---
1. \( 1 : 2 = \_\_ : 4 \)
Here, \( 2 \times 2 = 4 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = \_\_ : 6 \)
Here, \( 2 \times 3 = 6 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = \_\_ : 8 \)
Here, \( 2 \times 4 = 8 \). Multiply the first term by 4:
\( 1 \times 4 = 4 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = \_\_ : 10 \)
Here, \( 2 \times 5 = 10 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 2 \times 6 = 12 \).
So, \( 1 : 2 = 6 : 12 \).
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
1. \( 1 : 8 = \_\_ : 16 \)
Here, \( 8 \times 2 = 16 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 8 = 2 : 16 \).
2. \( 1 : 8 = \_\_ : 24 \)
Here, \( 8 \times 3 = 24 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 8 = 3 : 24 \).
3. \( 1 : 8 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 8 \times 4 = 32 \).
So, \( 1 : 8 = 4 : 32 \).
4. \( 1 : 8 = \_\_ : 40 \)
Here, \( 8 \times 5 = 40 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 8 = 5 : 40 \).
5. \( 1 : 8 = \_\_ : 48 \)
Here, \( 8 \times 6 = 48 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 8 = 6 : 48 \).
\[ 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48 \]
---
1. \( 2 : 5 = \_\_ : 10 \)
Here, \( 5 \times 2 = 10 \). Multiply the first term by 2:
\( 2 \times 2 = 4 \).
So, \( 2 : 5 = 4 : 10 \).
2. \( 2 : 5 = \_\_ : 15 \)
Here, \( 5 \times 3 = 15 \). Multiply the first term by 3:
\( 2 \times 3 = 6 \).
So, \( 2 : 5 = 6 : 15 \).
3. \( 2 : 5 = 8 : \_\_ \)
Here, \( 2 \times 4 = 8 \). Multiply the second term by 4:
\( 5 \times 4 = 20 \).
So, \( 2 : 5 = 8 : 20 \).
4. \( 2 : 5 = \_\_ : 25 \)
Here, \( 5 \times 5 = 25 \). Multiply the first term by 5:
\( 2 \times 5 = 10 \).
So, \( 2 : 5 = 10 : 25 \).
5. \( 2 : 5 = \_\_ : 30 \)
Here, \( 5 \times 6 = 30 \). Multiply the first term by 6:
\( 2 \times 6 = 12 \).
So, \( 2 : 5 = 12 : 30 \).
\[ 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30 \]
---
1. \( 5 : 9 = 10 : \_\_ \)
Here, \( 5 \times 2 = 10 \). Multiply the second term by 2:
\( 9 \times 2 = 18 \).
So, \( 5 : 9 = 10 : 18 \).
2. \( 5 : 9 = 15 : \_\_ \)
Here, \( 5 \times 3 = 15 \). Multiply the second term by 3:
\( 9 \times 3 = 27 \).
So, \( 5 : 9 = 15 : 27 \).
3. \( 5 : 9 = 20 : \_\_ \)
Here, \( 5 \times 4 = 20 \). Multiply the second term by 4:
\( 9 \times 4 = 36 \).
So, \( 5 : 9 = 20 : 36 \).
4. \( 5 : 9 = 25 : \_\_ \)
Here, \( 5 \times 5 = 25 \). Multiply the second term by 5:
\( 9 \times 5 = 45 \).
So, \( 5 : 9 = 25 : 45 \).
5. \( 5 : 9 = \_\_ : 54 \)
Here, \( 9 \times 6 = 54 \). Multiply the first term by 6:
\( 5 \times 6 = 30 \).
So, \( 5 : 9 = 30 : 54 \).
\[ 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54 \]
---
1. \( 1 : 2 = \_\_ : 4 \)
Here, \( 2 \times 2 = 4 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = \_\_ : 6 \)
Here, \( 2 \times 3 = 6 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 2 \times 4 = 8 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = \_\_ : 10 \)
Here, \( 2 \times 5 = 10 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 2 \times 6 = 12 \).
So, \( 1 : 2 = 6 : 12 \).
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
1. \( 1 : 2 = 2 : \_\_ \)
Here, \( 1 \times 2 = 2 \). Multiply the second term by 2:
\( 2 \times 2 = 4 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = \_\_ : 6 \)
Here, \( 2 \times 3 = 6 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 2 \times 4 = 8 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = \_\_ : 10 \)
Here, \( 2 \times 5 = 10 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = \_\_ : 12 \)
Here, \( 2 \times 6 = 12 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 2 = 6 : 12 \).
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
1. \( 1 : 3 = \_\_ : 6 \)
Here, \( 3 \times 2 = 6 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 3 = 2 : 6 \).
2. \( 1 : 3 = \_\_ : 9 \)
Here, \( 3 \times 3 = 9 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 3 = 3 : 9 \).
3. \( 1 : 3 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 3 \times 4 = 12 \).
So, \( 1 : 3 = 4 : 12 \).
4. \( 1 : 3 = \_\_ : 15 \)
Here, \( 3 \times 5 = 15 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 3 = 5 : 15 \).
5. \( 1 : 3 = \_\_ : 18 \)
Here, \( 3 \times 6 = 18 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 3 = 6 : 18 \).
\[ 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \]
---
\[
\boxed{
\begin{aligned}
1. & \quad 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42 \\
2. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
3. & \quad 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \\
4. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
5. & \quad 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48 \\
6. & \quad 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30 \\
7. & \quad 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54 \\
8. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
9. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
10. & \quad 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \\
\end{aligned}
}
\]
Problem 1: \( 1 : 7 = \_\_ : 14 = \_\_ : 21 = 4 : \_\_ = 5 : \_\_ = \_\_ : 42 \)
1. \( 1 : 7 = \_\_ : 14 \)
To find the missing term, notice that \( 7 \times 2 = 14 \). Therefore, multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 7 = 2 : 14 \).
2. \( 1 : 7 = \_\_ : 21 \)
Here, \( 7 \times 3 = 21 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 7 = 3 : 21 \).
3. \( 1 : 7 = 4 : \_\_ \)
To find the missing term, notice that \( 1 \times 4 = 4 \). Therefore, multiply the second term by 4:
\( 7 \times 4 = 28 \).
So, \( 1 : 7 = 4 : 28 \).
4. \( 1 : 7 = 5 : \_\_ \)
Similarly, \( 1 \times 5 = 5 \). Multiply the second term by 5:
\( 7 \times 5 = 35 \).
So, \( 1 : 7 = 5 : 35 \).
5. \( 1 : 7 = \_\_ : 42 \)
Here, \( 7 \times 6 = 42 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 7 = 6 : 42 \).
Final Answer for Problem 1:
\[ 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42 \]
---
Problem 2: \( 1 : 2 = \_\_ : 4 = 3 : \_\_ = 4 : \_\_ = 5 : \_\_ = 6 : \_\_ \)
1. \( 1 : 2 = \_\_ : 4 \)
Here, \( 2 \times 2 = 4 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = 3 : \_\_ \)
Here, \( 1 \times 3 = 3 \). Multiply the second term by 3:
\( 2 \times 3 = 6 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 2 \times 4 = 8 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = 5 : \_\_ \)
Here, \( 1 \times 5 = 5 \). Multiply the second term by 5:
\( 2 \times 5 = 10 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 2 \times 6 = 12 \).
So, \( 1 : 2 = 6 : 12 \).
Final Answer for Problem 2:
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
Problem 3: \( 1 : 3 = \_\_ : 6 = 3 : \_\_ = \_\_ : 12 = 5 : \_\_ = 6 : \_\_ \)
1. \( 1 : 3 = \_\_ : 6 \)
Here, \( 3 \times 2 = 6 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 3 = 2 : 6 \).
2. \( 1 : 3 = 3 : \_\_ \)
Here, \( 1 \times 3 = 3 \). Multiply the second term by 3:
\( 3 \times 3 = 9 \).
So, \( 1 : 3 = 3 : 9 \).
3. \( 1 : 3 = \_\_ : 12 \)
Here, \( 3 \times 4 = 12 \). Multiply the first term by 4:
\( 1 \times 4 = 4 \).
So, \( 1 : 3 = 4 : 12 \).
4. \( 1 : 3 = 5 : \_\_ \)
Here, \( 1 \times 5 = 5 \). Multiply the second term by 5:
\( 3 \times 5 = 15 \).
So, \( 1 : 3 = 5 : 15 \).
5. \( 1 : 3 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 3 \times 6 = 18 \).
So, \( 1 : 3 = 6 : 18 \).
Final Answer for Problem 3:
\[ 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \]
---
Problem 4: \( 1 : 2 = \_\_ : 4 = \_\_ : 6 = \_\_ : 8 = \_\_ : 10 = 6 : \_\_ \)
1. \( 1 : 2 = \_\_ : 4 \)
Here, \( 2 \times 2 = 4 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = \_\_ : 6 \)
Here, \( 2 \times 3 = 6 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = \_\_ : 8 \)
Here, \( 2 \times 4 = 8 \). Multiply the first term by 4:
\( 1 \times 4 = 4 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = \_\_ : 10 \)
Here, \( 2 \times 5 = 10 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 2 \times 6 = 12 \).
So, \( 1 : 2 = 6 : 12 \).
Final Answer for Problem 4:
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
Problem 5: \( 1 : 8 = \_\_ : 16 = \_\_ : 24 = 4 : \_\_ = \_\_ : 40 = \_\_ : 48 \)
1. \( 1 : 8 = \_\_ : 16 \)
Here, \( 8 \times 2 = 16 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 8 = 2 : 16 \).
2. \( 1 : 8 = \_\_ : 24 \)
Here, \( 8 \times 3 = 24 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 8 = 3 : 24 \).
3. \( 1 : 8 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 8 \times 4 = 32 \).
So, \( 1 : 8 = 4 : 32 \).
4. \( 1 : 8 = \_\_ : 40 \)
Here, \( 8 \times 5 = 40 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 8 = 5 : 40 \).
5. \( 1 : 8 = \_\_ : 48 \)
Here, \( 8 \times 6 = 48 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 8 = 6 : 48 \).
Final Answer for Problem 5:
\[ 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48 \]
---
Problem 6: \( 2 : 5 = \_\_ : 10 = \_\_ : 15 = 8 : \_\_ = \_\_ : 25 = \_\_ : 30 \)
1. \( 2 : 5 = \_\_ : 10 \)
Here, \( 5 \times 2 = 10 \). Multiply the first term by 2:
\( 2 \times 2 = 4 \).
So, \( 2 : 5 = 4 : 10 \).
2. \( 2 : 5 = \_\_ : 15 \)
Here, \( 5 \times 3 = 15 \). Multiply the first term by 3:
\( 2 \times 3 = 6 \).
So, \( 2 : 5 = 6 : 15 \).
3. \( 2 : 5 = 8 : \_\_ \)
Here, \( 2 \times 4 = 8 \). Multiply the second term by 4:
\( 5 \times 4 = 20 \).
So, \( 2 : 5 = 8 : 20 \).
4. \( 2 : 5 = \_\_ : 25 \)
Here, \( 5 \times 5 = 25 \). Multiply the first term by 5:
\( 2 \times 5 = 10 \).
So, \( 2 : 5 = 10 : 25 \).
5. \( 2 : 5 = \_\_ : 30 \)
Here, \( 5 \times 6 = 30 \). Multiply the first term by 6:
\( 2 \times 6 = 12 \).
So, \( 2 : 5 = 12 : 30 \).
Final Answer for Problem 6:
\[ 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30 \]
---
Problem 7: \( 5 : 9 = 10 : \_\_ = 15 : \_\_ = 20 : \_\_ = 25 : \_\_ = \_\_ : 54 \)
1. \( 5 : 9 = 10 : \_\_ \)
Here, \( 5 \times 2 = 10 \). Multiply the second term by 2:
\( 9 \times 2 = 18 \).
So, \( 5 : 9 = 10 : 18 \).
2. \( 5 : 9 = 15 : \_\_ \)
Here, \( 5 \times 3 = 15 \). Multiply the second term by 3:
\( 9 \times 3 = 27 \).
So, \( 5 : 9 = 15 : 27 \).
3. \( 5 : 9 = 20 : \_\_ \)
Here, \( 5 \times 4 = 20 \). Multiply the second term by 4:
\( 9 \times 4 = 36 \).
So, \( 5 : 9 = 20 : 36 \).
4. \( 5 : 9 = 25 : \_\_ \)
Here, \( 5 \times 5 = 25 \). Multiply the second term by 5:
\( 9 \times 5 = 45 \).
So, \( 5 : 9 = 25 : 45 \).
5. \( 5 : 9 = \_\_ : 54 \)
Here, \( 9 \times 6 = 54 \). Multiply the first term by 6:
\( 5 \times 6 = 30 \).
So, \( 5 : 9 = 30 : 54 \).
Final Answer for Problem 7:
\[ 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54 \]
---
Problem 8: \( 1 : 2 = \_\_ : 4 = \_\_ : 6 = 4 : \_\_ = \_\_ : 10 = 6 : \_\_ \)
1. \( 1 : 2 = \_\_ : 4 \)
Here, \( 2 \times 2 = 4 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = \_\_ : 6 \)
Here, \( 2 \times 3 = 6 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 2 \times 4 = 8 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = \_\_ : 10 \)
Here, \( 2 \times 5 = 10 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = 6 : \_\_ \)
Here, \( 1 \times 6 = 6 \). Multiply the second term by 6:
\( 2 \times 6 = 12 \).
So, \( 1 : 2 = 6 : 12 \).
Final Answer for Problem 8:
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
Problem 9: \( 1 : 2 = 2 : \_\_ = \_\_ : 6 = 4 : \_\_ = \_\_ : 10 = \_\_ : 12 \)
1. \( 1 : 2 = 2 : \_\_ \)
Here, \( 1 \times 2 = 2 \). Multiply the second term by 2:
\( 2 \times 2 = 4 \).
So, \( 1 : 2 = 2 : 4 \).
2. \( 1 : 2 = \_\_ : 6 \)
Here, \( 2 \times 3 = 6 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 2 = 3 : 6 \).
3. \( 1 : 2 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 2 \times 4 = 8 \).
So, \( 1 : 2 = 4 : 8 \).
4. \( 1 : 2 = \_\_ : 10 \)
Here, \( 2 \times 5 = 10 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 2 = 5 : 10 \).
5. \( 1 : 2 = \_\_ : 12 \)
Here, \( 2 \times 6 = 12 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 2 = 6 : 12 \).
Final Answer for Problem 9:
\[ 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \]
---
Problem 10: \( 1 : 3 = \_\_ : 6 = \_\_ : 9 = 4 : \_\_ = \_\_ : 15 = \_\_ : 18 \)
1. \( 1 : 3 = \_\_ : 6 \)
Here, \( 3 \times 2 = 6 \). Multiply the first term by 2:
\( 1 \times 2 = 2 \).
So, \( 1 : 3 = 2 : 6 \).
2. \( 1 : 3 = \_\_ : 9 \)
Here, \( 3 \times 3 = 9 \). Multiply the first term by 3:
\( 1 \times 3 = 3 \).
So, \( 1 : 3 = 3 : 9 \).
3. \( 1 : 3 = 4 : \_\_ \)
Here, \( 1 \times 4 = 4 \). Multiply the second term by 4:
\( 3 \times 4 = 12 \).
So, \( 1 : 3 = 4 : 12 \).
4. \( 1 : 3 = \_\_ : 15 \)
Here, \( 3 \times 5 = 15 \). Multiply the first term by 5:
\( 1 \times 5 = 5 \).
So, \( 1 : 3 = 5 : 15 \).
5. \( 1 : 3 = \_\_ : 18 \)
Here, \( 3 \times 6 = 18 \). Multiply the first term by 6:
\( 1 \times 6 = 6 \).
So, \( 1 : 3 = 6 : 18 \).
Final Answer for Problem 10:
\[ 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \]
---
Final Answers for All Problems:
\[
\boxed{
\begin{aligned}
1. & \quad 1 : 7 = 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42 \\
2. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
3. & \quad 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \\
4. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
5. & \quad 1 : 8 = 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48 \\
6. & \quad 2 : 5 = 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30 \\
7. & \quad 5 : 9 = 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54 \\
8. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
9. & \quad 1 : 2 = 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
10. & \quad 1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \\
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of ratios worksheet grade 6.
![Writing Ratios Worksheets [PDF] (6.RP.A.3): 6th Grade Math](/images2/ratios-worksheet-grade-6/ratios-worksheet-grade-6-33.png)
