Which fractions are equal to [tex] \frac{2}{3} [/tex]?

A. [tex] \frac{4}{6} [/tex]
B. [tex] \frac{3}{4} [/tex]
C. [tex] \frac{6}{9} [/tex]
D. [tex] \frac{8}{12} [/tex]

(Note: Ensure the correct options are provided if the list above is incomplete or inaccurate.)



Answer :

To determine which fractions are equivalent to [tex]\(\frac{2}{3}\)[/tex], we need to find fractions that have the same value when simplified. Fractions are equivalent if they represent the same portion of a whole. This can be achieved by multiplying the numerator and the denominator of the given fraction by the same number.

Here’s a step-by-step approach to find some fractions equivalent to [tex]\(\frac{2}{3}\)[/tex]:

1. Start with the given fraction:
[tex]\[ \frac{2}{3} \][/tex]

2. Multiply the numerator and the denominator by 2:
[tex]\[ 2 \times 2 = 4 \quad \text{and} \quad 3 \times 2 = 6 \][/tex]
So, the fraction becomes:
[tex]\[ \frac{4}{6} \][/tex]

3. Multiply the numerator and the denominator by 3:
[tex]\[ 2 \times 3 = 6 \quad \text{and} \quad 3 \times 3 = 9 \][/tex]
So, the fraction becomes:
[tex]\[ \frac{6}{9} \][/tex]

4. Multiply the numerator and the denominator by 4:
[tex]\[ 2 \times 4 = 8 \quad \text{and} \quad 3 \times 4 = 12 \][/tex]
So, the fraction becomes:
[tex]\[ \frac{8}{12} \][/tex]

Hence, the fractions that are equivalent to [tex]\(\frac{2}{3}\)[/tex] are:
[tex]\[ \frac{4}{6}, \frac{6}{9}, \text{ and } \frac{8}{12} \][/tex]