Which of the following pairs of fractions are not equivalent?

Options

A. `12/14,60/70`
B. `36/81,72/162`
C. `21/20,63/60`
D. `8/13,72/78`

Answer

To determine which pairs of fractions are not equivalent, we will simplify each pair of fractions step by step.

### Step 1: Analyze the first pair of fractions: \( \frac{12}{14} \) and \( \frac{60}{70} \)

1. Simplify \( \frac{12}{14} \):
- The greatest common divisor (GCD) of 12 and 14 is 2.
- Divide both the numerator and the denominator by 2:
\[ \frac{12 \div 2}{14 \div 2} = \frac{6}{7} \]

2. Simplify \( \frac{60}{70} \):
- The GCD of 60 and 70 is also 10.
- Divide both the numerator and the denominator by 10:
\[ \frac{60 \div 10}{70 \div 10} = \frac{6}{7} \]

**Conclusion for the first pair:** Both fractions simplify to \( \frac{6}{7} \), so they are equivalent.

### Step 2: Analyze the second pair of fractions: \( \frac{36}{81} \) and \( \frac{72}{162} \)

1. Simplify \( \frac{36}{81} \):
- The GCD of 36 and 81 is 9.
- Divide both the numerator and the denominator by 9:
\[ \frac{36 \div 9}{81 \div 9} = \frac{4}{9} \]

2. Simplify \( \frac{72}{162} \):
- The GCD of 72 and 162 is 18.
- Divide both the numerator and the denominator by 18:
\[ \frac{72 \div 18}{162 \div 18} = \frac{4}{9} \]

**Conclusion for the second pair:** Both fractions simplify to \( \frac{4}{9} \), so they are equivalent.

### Step 3: Analyze the third pair of fractions: \( \frac{21}{20} \) and \( \frac{63}{60} \)

1. Simplify \( \frac{21}{20} \):
- The GCD of 21 and 20 is 1 (they have no common factors).
- Therefore, \( \frac{21}{20} \) remains \( \frac{21}{20} \).

2. Simplify \( \frac{63}{60} \):
- The GCD of 63 and 60 is 3.
- Divide both the numerator and the denominator by 3:
\[ \frac{63 \div 3}{60 \div 3} = \frac{21}{20} \]

**Conclusion for the third pair:** Both fractions simplify to \( \frac{21}{20} \), so they are equivalent.

### Step 4: Analyze the fourth pair of fractions: \( \frac{8}{13} \) and \( \frac{72}{78} \)

1. Simplify \( \frac{8}{13} \):
- The GCD of 8 and 13 is 1 (they have no common factors).
- Therefore, \( \frac{8}{13} \) remains \( \frac{8}{13} \).

2. Simplify \( \frac{72}{78} \):
- The GCD of 72 and 78 is 6.
- Divide both the numerator and the denominator by 6:
\[ \frac{72 \div 6}{78 \div 6} = \frac{12}{13} \]

**Conclusion for the fourth pair:** The fractions simplify to \( \frac{8}{13} \) and \( \frac{12}{13} \), so they are not equivalent.

### Final Answer:
The pair of fractions that are not equivalent is \( \frac{8}{13} \) and \( \frac{72}{78} \).

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