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Sagot :
To determine which pair of numbers contains like fractions, we need to simplify both fractions in each pair and see if they are equivalent. Let's go through each option step-by-step:
1. Pair A: [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]
- Simplify [tex]\(\frac{5}{4}\)[/tex]:
- [tex]\(\frac{5}{4}\)[/tex] is already in its simplest form.
- Simplify [tex]\(\frac{4}{5}\)[/tex]:
- [tex]\(\frac{4}{5}\)[/tex] is already in its simplest form.
- Compare [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]:
- They are not equal.
2. Pair B: [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex]
- Simplify [tex]\(\frac{1}{2}\)[/tex]:
- [tex]\(\frac{1}{2}\)[/tex] is already in its simplest form.
- Simplify [tex]\(\frac{3}{2}\)[/tex]:
- [tex]\(\frac{3}{2}\)[/tex] is already in its simplest form.
- Compare [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex]:
- They are not equal.
3. Pair C: [tex]\(\frac{4}{8}\)[/tex] and [tex]\(\frac{12}{16}\)[/tex]
- Simplify [tex]\(\frac{4}{8}\)[/tex]:
- [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]
- Simplify [tex]\(\frac{12}{16}\)[/tex]:
- [tex]\(\frac{12}{16} = \frac{3}{4}\)[/tex]
- Compare [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]:
- They are not equal.
4. Pair D: [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{60}{70}\)[/tex]
- Simplify [tex]\(\frac{6}{7}\)[/tex]:
- [tex]\(\frac{6}{7}\)[/tex] is already in its simplest form.
- Simplify [tex]\(\frac{60}{70}\)[/tex]:
- [tex]\(\frac{60}{70} = \frac{6}{7}\)[/tex]
- Compare [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex]:
- They are equal, but we need to compare the fractions in Pair C instead.
We have determined that the following pairs contain like fractions:
3. Pair C: [tex]\(\frac{4}{8}\)[/tex] and [tex]\(\frac{12}{16}\)[/tex]
- After simplification:
- [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]
- [tex]\(\frac{12}{16} = \frac{3}{4}\)[/tex]
- Since [tex]\(\frac{1}{2}\)[/tex] is not equal to [tex]\(\frac{3}{4}\)[/tex], but the result confirms this comparison.
Thus, the best answer for the pair of numbers that contains like fractions is:
- The answer is None.
1. Pair A: [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]
- Simplify [tex]\(\frac{5}{4}\)[/tex]:
- [tex]\(\frac{5}{4}\)[/tex] is already in its simplest form.
- Simplify [tex]\(\frac{4}{5}\)[/tex]:
- [tex]\(\frac{4}{5}\)[/tex] is already in its simplest form.
- Compare [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]:
- They are not equal.
2. Pair B: [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex]
- Simplify [tex]\(\frac{1}{2}\)[/tex]:
- [tex]\(\frac{1}{2}\)[/tex] is already in its simplest form.
- Simplify [tex]\(\frac{3}{2}\)[/tex]:
- [tex]\(\frac{3}{2}\)[/tex] is already in its simplest form.
- Compare [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex]:
- They are not equal.
3. Pair C: [tex]\(\frac{4}{8}\)[/tex] and [tex]\(\frac{12}{16}\)[/tex]
- Simplify [tex]\(\frac{4}{8}\)[/tex]:
- [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]
- Simplify [tex]\(\frac{12}{16}\)[/tex]:
- [tex]\(\frac{12}{16} = \frac{3}{4}\)[/tex]
- Compare [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]:
- They are not equal.
4. Pair D: [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{60}{70}\)[/tex]
- Simplify [tex]\(\frac{6}{7}\)[/tex]:
- [tex]\(\frac{6}{7}\)[/tex] is already in its simplest form.
- Simplify [tex]\(\frac{60}{70}\)[/tex]:
- [tex]\(\frac{60}{70} = \frac{6}{7}\)[/tex]
- Compare [tex]\(\frac{6}{7}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex]:
- They are equal, but we need to compare the fractions in Pair C instead.
We have determined that the following pairs contain like fractions:
3. Pair C: [tex]\(\frac{4}{8}\)[/tex] and [tex]\(\frac{12}{16}\)[/tex]
- After simplification:
- [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]
- [tex]\(\frac{12}{16} = \frac{3}{4}\)[/tex]
- Since [tex]\(\frac{1}{2}\)[/tex] is not equal to [tex]\(\frac{3}{4}\)[/tex], but the result confirms this comparison.
Thus, the best answer for the pair of numbers that contains like fractions is:
- The answer is None.
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