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Which fractions are equivalent to [tex]\frac{1}{2}[/tex]?

Choose ALL the correct answers.

A. [tex]\frac{3}{6}[/tex]
B. [tex]\frac{4}{5}[/tex]
C. [tex]\frac{6}{12}[/tex]
D. [tex]\frac{6}{7}[/tex]
E. [tex]\frac{5}{10}[/tex]
F. [tex]\frac{7}{8}[/tex]

Sagot :

GinnyAnsweridn
To determine which of the given fractions are equivalent to [tex]\(\frac{1}{2}\)[/tex], we need to simplify each fraction and see if it simplifies to [tex]\(\frac{1}{2}\)[/tex].

Let's go through each fraction one by one:

1. [tex]\(\frac{3}{6}\)[/tex]:
- To simplify [tex]\(\frac{3}{6}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
- [tex]\(\frac{3 ÷ 3}{6 ÷ 3} = \frac{1}{2}\)[/tex]
- Therefore, [tex]\(\frac{3}{6}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].

2. [tex]\(\frac{4}{5}\)[/tex]:
- This fraction is already in its simplest form. The numerator (4) and the denominator (5) have no common divisors other than 1.
- [tex]\(\frac{4}{5}\)[/tex] cannot be simplified to [tex]\(\frac{1}{2}\)[/tex].
- Therefore, [tex]\(\frac{4}{5}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].

3. [tex]\(\frac{6}{12}\)[/tex]:
- To simplify [tex]\(\frac{6}{12}\)[/tex], we divide both the numerator and the denominator by their GCD, which is 6.
- [tex]\(\frac{6 ÷ 6}{12 ÷ 6} = \frac{1}{2}\)[/tex]
- Therefore, [tex]\(\frac{6}{12}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].

4. [tex]\(\frac{6}{7}\)[/tex]:
- This fraction is already in its simplest form. The numerator (6) and the denominator (7) have no common divisors other than 1.
- [tex]\(\frac{6}{7}\)[/tex] cannot be simplified to [tex]\(\frac{1}{2}\)[/tex].
- Therefore, [tex]\(\frac{6}{7}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].

5. [tex]\(\frac{5}{10}\)[/tex]:
- To simplify [tex]\(\frac{5}{10}\)[/tex], we divide both the numerator and the denominator by their GCD, which is 5.
- [tex]\(\frac{5 ÷ 5}{10 ÷ 5} = \frac{1}{2}\)[/tex]
- Therefore, [tex]\(\frac{5}{10}\)[/tex] is equivalent to [tex]\(\frac{1}{2}\)[/tex].

6. [tex]\(\frac{7}{8}\)[/tex]:
- This fraction is already in its simplest form. The numerator (7) and the denominator (8) have no common divisors other than 1.
- [tex]\(\frac{7}{8}\)[/tex] cannot be simplified to [tex]\(\frac{1}{2}\)[/tex].
- Therefore, [tex]\(\frac{7}{8}\)[/tex] is not equivalent to [tex]\(\frac{1}{2}\)[/tex].

Based on the analysis above, the fractions equivalent to [tex]\(\frac{1}{2}\)[/tex] are:

[tex]\[ \frac{3}{6}, \frac{6}{12}, \frac{5}{10} \][/tex]
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