Question

Are the fractions equivalent? If so, what number were both the numerator and denominator multiplied by to arrive at the equivalent fraction?
1/3 = 5/12
2/5 = 4/10
5/12 = 15/36
2/11 = 8/44

Answer 1

To determine if the fractions are equivalent, we can cross-multiply or analyze them directly.

1. **1/3 = 5/12**:
- Cross-multiplying gives us \(1 \cdot 12 = 12\) and \(3 \cdot 5 = 15\). Since \(12 \neq 15\), these fractions are **not equivalent**.

2. **2/5 = 4/10**:
- Cross-multiplying gives us \(2 \cdot 10 = 20\) and \(5 \cdot 4 = 20\). Since both products are equal, these fractions are **equivalent**.
- To find the number both the numerator and denominator were multiplied by, we can see that \(2 \cdot 2 = 4\) (numerator), and \(5 \cdot 2 = 10\) (denominator), so they were both multiplied by **2**.

3. **5/12 = 15/36**:
- Cross-multiplying gives us \(5 \cdot 36 = 180\) and \(12 \cdot 15 = 180\). Since both products are equal, these fractions are **equivalent**.
- The first fraction multiplied by \(3\) gives the second fraction: \(5 \cdot 3 = 15\) (numerator) and \(12 \cdot 3 = 36\) (denominator), so they were both multiplied by **3**.

4. **2/11 = 8/44**:
- Cross-multiplying gives us \(2 \cdot 44 = 88\) and \(11 \cdot 8 = 88\). Since both products are equal, these fractions are **equivalent**.
- The first fraction multiplied by \(4\) gives the second fraction: \(2 \cdot 4 = 8\) (numerator) and \(11 \cdot 4 = 44\) (denominator), so they were both multiplied by **4**.

In summary:
- **1/3** and **5/12**: Not equivalent
- **2/5** and **4/10**: Equivalent (multiplied by 2)
- **5/12** and **15/36**: Equivalent (multiplied by 3)
- **2/11** and **8/44**: Equivalent (multiplied by 4)