Practice finding missing values in ratio pairs and converting them into fractions with this engaging math worksheet.

Problem Explanation:

The task involves finding equivalent ratios for given ratios and expressing them as fractions. Equivalent ratios are ratios that represent the same relationship between two quantities, even though the numbers may be different. To solve this, we need to scale the given ratios up or down by multiplying or dividing both terms of the ratio by the same number.

Solution:

#### Step 1: Understand the structure
Each row has a given ratio (e.g., \(1 : 2\)), and we need to find two equivalent ratios:
1. One where the second term is a specific number (e.g., \(10\)).
2. Another where the first term is a specific number (e.g., \(9\)).

Additionally, we need to express each ratio as a fraction.

#### Step 2: Solve each row

##### Row 1: \(1 : 2\)
- Equivalent ratio with second term as 10:
- The original ratio is \(1 : 2\). To make the second term 10, multiply both terms by 5.
- \(1 \times 5 : 2 \times 5 = 5 : 10\).
- Equivalent ratio with first term as 9:
- The original ratio is \(1 : 2\). To make the first term 9, multiply both terms by 9.
- \(1 \times 9 : 2 \times 9 = 9 : 18\).
- Fraction:
- The ratio \(1 : 2\) can be written as the fraction \(\frac{1}{2}\).

##### Row 2: \(1 : 3\)
- Equivalent ratio with second term as 15:
- Multiply both terms by 5.
- \(1 \times 5 : 3 \times 5 = 5 : 15\).
- Equivalent ratio with first term as 2:
- Multiply both terms by 2.
- \(1 \times 2 : 3 \times 2 = 2 : 6\).
- Fraction:
- The ratio \(1 : 3\) can be written as the fraction \(\frac{1}{3}\).

##### Row 3: \(1 : 4\)
- Equivalent ratio with second term as 24:
- Multiply both terms by 6.
- \(1 \times 6 : 4 \times 6 = 6 : 24\).
- Equivalent ratio with first term as 5:
- Multiply both terms by 5.
- \(1 \times 5 : 4 \times 5 = 5 : 20\).
- Fraction:
- The ratio \(1 : 4\) can be written as the fraction \(\frac{1}{4}\).

##### Row 4: \(1 : 5\)
- Equivalent ratio with second term as 35:
- Multiply both terms by 7.
- \(1 \times 7 : 5 \times 7 = 7 : 35\).
- Equivalent ratio with first term as 3:
- Multiply both terms by 3.
- \(1 \times 3 : 5 \times 3 = 3 : 15\).
- Fraction:
- The ratio \(1 : 5\) can be written as the fraction \(\frac{1}{5}\).

##### Row 5: \(1 : 6\)
- Equivalent ratio with second term as 12:
- Multiply both terms by 2.
- \(1 \times 2 : 6 \times 2 = 2 : 12\).
- Equivalent ratio with first term as 4:
- Multiply both terms by 4.
- \(1 \times 4 : 6 \times 4 = 4 : 24\).
- Fraction:
- The ratio \(1 : 6\) can be written as the fraction \(\frac{1}{6}\).

##### Row 6: \(1 : 7\)
- Equivalent ratio with second term as 21:
- Multiply both terms by 3.
- \(1 \times 3 : 7 \times 3 = 3 : 21\).
- Equivalent ratio with first term as 6:
- Multiply both terms by 6.
- \(1 \times 6 : 7 \times 6 = 6 : 42\).
- Fraction:
- The ratio \(1 : 7\) can be written as the fraction \(\frac{1}{7}\).

##### Row 7: \(1 : 8\)
- Equivalent ratio with second term as 16:
- Multiply both terms by 2.
- \(1 \times 2 : 8 \times 2 = 2 : 16\).
- Equivalent ratio with first term as 7:
- Multiply both terms by 7.
- \(1 \times 7 : 8 \times 7 = 7 : 56\).
- Fraction:
- The ratio \(1 : 8\) can be written as the fraction \(\frac{1}{8}\).

##### Row 8: \(1 : 9\)
- Equivalent ratio with second term as 72:
- Multiply both terms by 8.
- \(1 \times 8 : 9 \times 8 = 8 : 72\).
- Equivalent ratio with first term as 6:
- Multiply both terms by 6.
- \(1 \times 6 : 9 \times 6 = 6 : 54\).
- Fraction:
- The ratio \(1 : 9\) can be written as the fraction \(\frac{1}{9}\).

Final Answer:

\[
\begin{array}{l}
1. \ 1 : 2 = 5 : 10 = 9 : 18 \quad \text{(Fraction: } \frac{1}{2} \text{)} \\
2. \ 1 : 3 = 5 : 15 = 2 : 6 \quad \text{(Fraction: } \frac{1}{3} \text{)} \\
3. \ 1 : 4 = 6 : 24 = 5 : 20 \quad \text{(Fraction: } \frac{1}{4} \text{)} \\
4. \ 1 : 5 = 7 : 35 = 3 : 15 \quad \text{(Fraction: } \frac{1}{5} \text{)} \\
5. \ 1 : 6 = 2 : 12 = 4 : 24 \quad \text{(Fraction: } \frac{1}{6} \text{)} \\
6. \ 1 : 7 = 3 : 21 = 6 : 42 \quad \text{(Fraction: } \frac{1}{7} \text{)} \\
7. \ 1 : 8 = 2 : 16 = 7 : 56 \quad \text{(Fraction: } \frac{1}{8} \text{)} \\
8. \ 1 : 9 = 8 : 72 = 6 : 54 \quad \text{(Fraction: } \frac{1}{9} \text{)} \\
\end{array}
\]

\boxed{
\begin{array}{l}
1. \ 1 : 2 = 5 : 10 = 9 : 18 \quad \text{(Fraction: } \frac{1}{2} \text{)} \\
2. \ 1 : 3 = 5 : 15 = 2 : 6 \quad \text{(Fraction: } \frac{1}{3} \text{)} \\
3. \ 1 : 4 = 6 : 24 = 5 : 20 \quad \text{(Fraction: } \frac{1}{4} \text{)} \\
4. \ 1 : 5 = 7 : 35 = 3 : 15 \quad \text{(Fraction: } \frac{1}{5} \text{)} \\
5. \ 1 : 6 = 2 : 12 = 4 : 24 \quad \text{(Fraction: } \frac{1}{6} \text{)} \\
6. \ 1 : 7 = 3 : 21 = 6 : 42 \quad \text{(Fraction: } \frac{1}{7} \text{)} \\
7. \ 1 : 8 = 2 : 16 = 7 : 56 \quad \text{(Fraction: } \frac{1}{8} \text{)} \\
8. \ 1 : 9 = 8 : 72 = 6 : 54 \quad \text{(Fraction: } \frac{1}{9} \text{)} \\
\end{array}
}