Question
Are the pairs of fractions equivalent?
1/2 = 4/8
2/3 = 6/9
6/10 = 3/5
2/3 = 5/6
1/2 = 4/8
2/3 = 6/9
6/10 = 3/5
2/3 = 5/6
Answers
GPT-4o mini
To determine if the pairs of fractions are equivalent, we can simplify each pair and see if they are equal.
1. **1/2 and 4/8**:
\[
\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
These fractions are equivalent.
2. **2/3 and 6/9**:
\[
\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\]
These fractions are equivalent.
3. **6/10 and 3/5**:
\[
\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]
These fractions are equivalent.
4. **2/3 and 5/6**:
\[
\text{To compare these fractions, we can cross-multiply: } 2 \times 6 \text{ and } 3 \times 5:
\]
\[
2 \times 6 = 12 \quad \text{and} \quad 3 \times 5 = 15
\]
Since 12 is not equal to 15, these fractions are not equivalent.
In summary:
- **1/2 = 4/8** (Equivalent)
- **2/3 = 6/9** (Equivalent)
- **6/10 = 3/5** (Equivalent)
- **2/3 = 5/6** (Not Equivalent)
1. **1/2 and 4/8**:
\[
\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
These fractions are equivalent.
2. **2/3 and 6/9**:
\[
\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\]
These fractions are equivalent.
3. **6/10 and 3/5**:
\[
\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]
These fractions are equivalent.
4. **2/3 and 5/6**:
\[
\text{To compare these fractions, we can cross-multiply: } 2 \times 6 \text{ and } 3 \times 5:
\]
\[
2 \times 6 = 12 \quad \text{and} \quad 3 \times 5 = 15
\]
Since 12 is not equal to 15, these fractions are not equivalent.
In summary:
- **1/2 = 4/8** (Equivalent)
- **2/3 = 6/9** (Equivalent)
- **6/10 = 3/5** (Equivalent)
- **2/3 = 5/6** (Not Equivalent)