To determine which pair of numbers contains like fractions, we need to check if the two fractions in each pair simplify to the same value. Here are the steps to find the pair that contains like fractions:
### Pair A: [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{2} \)[/tex]
1. Simplify [tex]\( \frac{1}{2} \)[/tex]:
- The fraction [tex]\( \frac{1}{2} \)[/tex] is already in its simplest form.
2. Simplify [tex]\( \frac{3}{2} \)[/tex]:
- The fraction [tex]\( \frac{3}{2} \)[/tex] is already in its simplest form.
3. Compare [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{2} \)[/tex]:
- These fractions are not the same.
### Pair B: [tex]\( \frac{6}{7} \)[/tex] and [tex]\( \frac{60}{70} \)[/tex]
1. Simplify [tex]\( \frac{6}{7} \)[/tex]:
- The fraction [tex]\( \frac{6}{7} \)[/tex] is already in its simplest form.
2. Simplify [tex]\( \frac{60}{70} \)[/tex]:
- Divide both the numerator and the denominator by the greatest common divisor (GCD) of 60 and 70, which is 10.
- [tex]\( \frac{60 \div 10}{70 \div 10} = \frac{6}{7} \)[/tex].
3. Compare [tex]\( \frac{6}{7} \)[/tex] and [tex]\( \frac{6}{7} \)[/tex]:
- These fractions are the same.
### Pair C: [tex]\( \frac{5}{4} \)[/tex] and [tex]\( \frac{4}{5} \)[/tex]
1. Simplify [tex]\( \frac{5}{4} \)[/tex]:
- The fraction [tex]\( \frac{5}{4} \)[/tex] is already in its simplest form.
2. Simplify [tex]\( \frac{4}{5} \)[/tex]:
- The fraction [tex]\( \frac{4}{5} \)[/tex] is already in its simplest form.
3. Compare [tex]\( \frac{5}{4} \)[/tex] and [tex]\( \frac{4}{5} \)[/tex]:
- These fractions are not the same.
### Pair D: [tex]\( \frac{4}{8} \)[/tex] and [tex]\( \frac{12}{16} \)[/tex]
1. Simplify [tex]\( \frac{4}{8} \)[/tex]:
- Divide both the numerator and the denominator by the GCD of 4 and 8, which is 4.
- [tex]\( \frac{4 \div 4}{8 \div 4} = \frac{1}{2} \)[/tex].
2. Simplify [tex]\( \frac{12}{16} \)[/tex]:
- Divide both the numerator and the denominator by the GCD of 12 and 16, which is 4.
- [tex]\( \frac{12 \div 4}{16 \div 4} = \frac{3}{4} \)[/tex].
3. Compare [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex]:
- These fractions are not the same.
Based on these comparisons, the pair of numbers that contains like fractions is:
B. [tex]\( \frac{6}{7} \)[/tex] and [tex]\( \frac{60}{70} \)[/tex].
