Question

write three fractions equivalent to \\(\frac{12}{16}\\). scale the numerator and denominator up for the first two and down for the third.

scale up by: \\(\square\\) equivalent fraction: \\(\frac{\square}{\square}\\)

scale up by: \\(\square\\) equivalent fraction: \\(\frac{\square}{\square}\\)

scale down by: \\(\square\\) equivalent fraction: \\(\frac{\square}{\square}\\)

Explanation:

Step1: Scale up by 2

To find an equivalent fraction, we multiply both the numerator and denominator of $\frac{12}{16}$ by 2.
$\frac{12\times2}{16\times2}=\frac{24}{32}$

Step2: Scale up by 3

Multiply both the numerator and denominator of $\frac{12}{16}$ by 3.
$\frac{12\times3}{16\times3}=\frac{36}{48}$

Step3: Scale down by 4

First, find the greatest common divisor (GCD) of 12 and 16, which is 4. Then divide both the numerator and denominator by 4.
$\frac{12\div4}{16\div4}=\frac{3}{4}$

Answer:

Scale up by: 2, Equivalent fraction: $\frac{24}{32}$
Scale up by: 3, Equivalent fraction: $\frac{36}{48}$
Scale down by: 4, Equivalent fraction: $\frac{3}{4}$

(Note: The scale - up and scale - down factors can have other valid values as well. For example, scale - up by 5 would give $\frac{60}{80}$, and scale - down by 2 would give $\frac{6}{8}$)