Simplify [tex]\frac{4}{16}[/tex] to lowest terms and find an equivalent fraction that has a denominator of 32.

A. [tex]\frac{1}{4}, \frac{4}{32}[/tex]
B. [tex]\frac{1}{4}, \frac{8}{32}[/tex]
C. [tex]\frac{2}{8}, \frac{4}{32}[/tex]
D. [tex]\frac{2}{8}, \frac{8}{32}[/tex]



Answer :

Let's solve the problem step-by-step.

1. Simplify [tex]\(\frac{4}{16}\)[/tex] to its lowest terms:

To simplify a fraction, we need to divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).

Here, the numerator is 4 and the denominator is 16. The GCD of 4 and 16 is 4.

[tex]\[ \frac{4 \div 4}{16 \div 4} = \frac{1}{4} \][/tex]

Therefore, [tex]\(\frac{4}{16}\)[/tex] simplified to its lowest terms is [tex]\(\frac{1}{4}\)[/tex].

2. Find an equivalent fraction that has a denominator of 32:

To find an equivalent fraction with a specific denominator, you can set up the following proportion:

[tex]\[ \frac{1}{4} = \frac{x}{32} \][/tex]

To find [tex]\(x\)[/tex], we solve the proportion by cross-multiplying:

[tex]\[ 1 \cdot 32 = 4 \cdot x \][/tex]

[tex]\[ x = \frac{32}{4} = 8 \][/tex]

So, an equivalent fraction for [tex]\(\frac{1}{4}\)[/tex] with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].

Therefore, the solution is:

- The simplified form of [tex]\(\frac{4}{16}\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
- An equivalent fraction with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].

Thus, the correct choice is:
[tex]\[ \boxed{\frac{1}{4}, \frac{8}{32}} \][/tex]