Printable ratio and Proportion worksheets for grade 5 and 6 math - Free Printable

Problem Explanation:

The task involves finding equivalent ratios for given ratios. Equivalent ratios are ratios that represent the same relationship between two quantities but are expressed with different numbers. To find equivalent ratios, you can multiply or divide both terms of the ratio by the same non-zero number.

Solution:

#### 1) \( 1 : 7 = \_\_:14 = \_\_:21 = 4:\_\_ = 5:\_\_ = \_\_:42 \)

- \( 1 : 7 = \_\_:14 \): Multiply both terms by 2.
\[
1 \times 2 : 7 \times 2 = 2 : 14
\]
- \( 1 : 7 = \_\_:21 \): Multiply both terms by 3.
\[
1 \times 3 : 7 \times 3 = 3 : 21
\]
- \( 1 : 7 = 4:\_\_ \): Multiply both terms by 4.
\[
1 \times 4 : 7 \times 4 = 4 : 28
\]
- \( 1 : 7 = 5:\_\_ \): Multiply both terms by 5.
\[
1 \times 5 : 7 \times 5 = 5 : 35
\]
- \( 1 : 7 = \_\_:42 \): Multiply both terms by 6.
\[
1 \times 6 : 7 \times 6 = 6 : 42
\]

Answer: \( 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42 \)

---

#### 2) \( 1 : 2 = \_\_:4 = 3:\_\_ = 4:\_\_ = 5:\_\_ = 6:\_\_ \)

- \( 1 : 2 = \_\_:4 \): Multiply both terms by 2.
\[
1 \times 2 : 2 \times 2 = 2 : 4
\]
- \( 1 : 2 = 3:\_\_ \): Multiply both terms by 3.
\[
1 \times 3 : 2 \times 3 = 3 : 6
\]
- \( 1 : 2 = 4:\_\_ \): Multiply both terms by 4.
\[
1 \times 4 : 2 \times 4 = 4 : 8
\]
- \( 1 : 2 = 5:\_\_ \): Multiply both terms by 5.
\[
1 \times 5 : 2 \times 5 = 5 : 10
\]
- \( 1 : 2 = 6:\_\_ \): Multiply both terms by 6.
\[
1 \times 6 : 2 \times 6 = 6 : 12
\]

Answer: \( 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \)

---

#### 3) \( 1 : 3 = \_\_:6 = 3:\_\_ = \_\_:12 = 5:\_\_ = 6:\_\_ \)

- \( 1 : 3 = \_\_:6 \): Multiply both terms by 2.
\[
1 \times 2 : 3 \times 2 = 2 : 6
\]
- \( 1 : 3 = 3:\_\_ \): Multiply both terms by 3.
\[
1 \times 3 : 3 \times 3 = 3 : 9
\]
- \( 1 : 3 = \_\_:12 \): Multiply both terms by 4.
\[
1 \times 4 : 3 \times 4 = 4 : 12
\]
- \( 1 : 3 = 5:\_\_ \): Multiply both terms by 5.
\[
1 \times 5 : 3 \times 5 = 5 : 15
\]
- \( 1 : 3 = 6:\_\_ \): Multiply both terms by 6.
\[
1 \times 6 : 3 \times 6 = 6 : 18
\]

Answer: \( 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \)

---

#### 4) \( 1 : 2 = \_\_:4 = \_\_:6 = \_\_:8 = \_\_:10 = 6:\_\_ \)

- \( 1 : 2 = \_\_:4 \): Multiply both terms by 2.
\[
1 \times 2 : 2 \times 2 = 2 : 4
\]
- \( 1 : 2 = \_\_:6 \): Multiply both terms by 3.
\[
1 \times 3 : 2 \times 3 = 3 : 6
\]
- \( 1 : 2 = \_\_:8 \): Multiply both terms by 4.
\[
1 \times 4 : 2 \times 4 = 4 : 8
\]
- \( 1 : 2 = \_\_:10 \): Multiply both terms by 5.
\[
1 \times 5 : 2 \times 5 = 5 : 10
\]
- \( 1 : 2 = 6:\_\_ \): Multiply both terms by 6.
\[
1 \times 6 : 2 \times 6 = 6 : 12
\]

Answer: \( 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \)

---

#### 5) \( 1 : 8 = \_\_:16 = \_\_:24 = 4:\_\_ = \_\_:40 = \_\_:48 \)

- \( 1 : 8 = \_\_:16 \): Multiply both terms by 2.
\[
1 \times 2 : 8 \times 2 = 2 : 16
\]
- \( 1 : 8 = \_\_:24 \): Multiply both terms by 3.
\[
1 \times 3 : 8 \times 3 = 3 : 24
\]
- \( 1 : 8 = 4:\_\_ \): Multiply both terms by 4.
\[
1 \times 4 : 8 \times 4 = 4 : 32
\]
- \( 1 : 8 = \_\_:40 \): Multiply both terms by 5.
\[
1 \times 5 : 8 \times 5 = 5 : 40
\]
- \( 1 : 8 = \_\_:48 \): Multiply both terms by 6.
\[
1 \times 6 : 8 \times 6 = 6 : 48
\]

Answer: \( 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48 \)

---

#### 6) \( 2 : 5 = \_\_:10 = \_\_:15 = 8:\_\_ = \_\_:25 = \_\_:30 \)

- \( 2 : 5 = \_\_:10 \): Multiply both terms by 2.
\[
2 \times 2 : 5 \times 2 = 4 : 10
\]
- \( 2 : 5 = \_\_:15 \): Multiply both terms by 3.
\[
2 \times 3 : 5 \times 3 = 6 : 15
\]
- \( 2 : 5 = 8:\_\_ \): Multiply both terms by 4.
\[
2 \times 4 : 5 \times 4 = 8 : 20
\]
- \( 2 : 5 = \_\_:25 \): Multiply both terms by 5.
\[
2 \times 5 : 5 \times 5 = 10 : 25
\]
- \( 2 : 5 = \_\_:30 \): Multiply both terms by 6.
\[
2 \times 6 : 5 \times 6 = 12 : 30
\]

Answer: \( 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30 \)

---

#### 7) \( 5 : 9 = 10:\_\_ = 15:\_\_ = 20:\_\_ = 25:\_\_ = \_\_:54 \)

- \( 5 : 9 = 10:\_\_ \): Multiply both terms by 2.
\[
5 \times 2 : 9 \times 2 = 10 : 18
\]
- \( 5 : 9 = 15:\_\_ \): Multiply both terms by 3.
\[
5 \times 3 : 9 \times 3 = 15 : 27
\]
- \( 5 : 9 = 20:\_\_ \): Multiply both terms by 4.
\[
5 \times 4 : 9 \times 4 = 20 : 36
\]
- \( 5 : 9 = 25:\_\_ \): Multiply both terms by 5.
\[
5 \times 5 : 9 \times 5 = 25 : 45
\]
- \( 5 : 9 = \_\_:54 \): Multiply both terms by 6.
\[
5 \times 6 : 9 \times 6 = 30 : 54
\]

Answer: \( 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54 \)

---

#### 8) \( 1 : 2 = \_\_:4 = \_\_:6 = 4:\_\_ = \_\_:10 = 6:\_\_ \)

- \( 1 : 2 = \_\_:4 \): Multiply both terms by 2.
\[
1 \times 2 : 2 \times 2 = 2 : 4
\]
- \( 1 : 2 = \_\_:6 \): Multiply both terms by 3.
\[
1 \times 3 : 2 \times 3 = 3 : 6
\]
- \( 1 : 2 = 4:\_\_ \): Multiply both terms by 4.
\[
1 \times 4 : 2 \times 4 = 4 : 8
\]
- \( 1 : 2 = \_\_:10 \): Multiply both terms by 5.
\[
1 \times 5 : 2 \times 5 = 5 : 10
\]
- \( 1 : 2 = 6:\_\_ \): Multiply both terms by 6.
\[
1 \times 6 : 2 \times 6 = 6 : 12
\]

Answer: \( 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \)

---

#### 9) \( 1 : 2 = 2:\_\_ = \_\_:6 = 4:\_\_ = \_\_:10 = \_\_:12 \)

- \( 1 : 2 = 2:\_\_ \): Multiply both terms by 2.
\[
1 \times 2 : 2 \times 2 = 2 : 4
\]
- \( 1 : 2 = \_\_:6 \): Multiply both terms by 3.
\[
1 \times 3 : 2 \times 3 = 3 : 6
\]
- \( 1 : 2 = 4:\_\_ \): Multiply both terms by 4.
\[
1 \times 4 : 2 \times 4 = 4 : 8
\]
- \( 1 : 2 = \_\_:10 \): Multiply both terms by 5.
\[
1 \times 5 : 2 \times 5 = 5 : 10
\]
- \( 1 : 2 = \_\_:12 \): Multiply both terms by 6.
\[
1 \times 6 : 2 \times 6 = 6 : 12
\]

Answer: \( 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \)

---

#### 10) \( 1 : 3 = \_\_:6 = \_\_:9 = 4:\_\_ = \_\_:15 = \_\_:18 \)

- \( 1 : 3 = \_\_:6 \): Multiply both terms by 2.
\[
1 \times 2 : 3 \times 2 = 2 : 6
\]
- \( 1 : 3 = \_\_:9 \): Multiply both terms by 3.
\[
1 \times 3 : 3 \times 3 = 3 : 9
\]
- \( 1 : 3 = 4:\_\_ \): Multiply both terms by 4.
\[
1 \times 4 : 3 \times 4 = 4 : 12
\]
- \( 1 : 3 = \_\_:15 \): Multiply both terms by 5.
\[
1 \times 5 : 3 \times 5 = 5 : 15
\]
- \( 1 : 3 = \_\_:18 \): Multiply both terms by 6.
\[
1 \times 6 : 3 \times 6 = 6 : 18
\]

Answer: \( 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \)

---

Final Answer:

\[
\boxed{
\begin{array}{l}
1) \ 2 : 14 = 3 : 21 = 4 : 28 = 5 : 35 = 6 : 42 \\
2) \ 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
3) \ 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \\
4) \ 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
5) \ 2 : 16 = 3 : 24 = 4 : 32 = 5 : 40 = 6 : 48 \\
6) \ 4 : 10 = 6 : 15 = 8 : 20 = 10 : 25 = 12 : 30 \\
7) \ 10 : 18 = 15 : 27 = 20 : 36 = 25 : 45 = 30 : 54 \\
8) \ 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
9) \ 2 : 4 = 3 : 6 = 4 : 8 = 5 : 10 = 6 : 12 \\
10) \ 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 \\
\end{array}
}
\]