Question

write three fractions equivalent to \\(\frac{2}{18}\\). 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 by scaling up, we multiply both the numerator and the denominator of $\frac{2}{18}$ by 2.
$2\times2 = 4$ and $18\times2 = 36$, so the equivalent fraction is $\frac{4}{36}$.

Step2: Scale up by 3

Multiply both the numerator and the denominator of $\frac{2}{18}$ by 3.
$2\times3 = 6$ and $18\times3 = 54$, so the equivalent fraction is $\frac{6}{54}$.

Step3: Scale down by 2

To scale down, we divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2 and 18 is 2. Divide both by 2: $2\div2 = 1$ and $18\div2 = 9$, so the equivalent fraction is $\frac{1}{9}$.

Answer:

Scale up by: 2 Equivalent fraction: $\frac{4}{36}$
Scale up by: 3 Equivalent fraction: $\frac{6}{54}$
Scale down by: 2 Equivalent fraction: $\frac{1}{9}$

(Note: The scale-up factors can vary, for example, using 4 for scale up would give $\frac{8}{72}$, and the scale-down factor is determined by the GCD, which is 2 here, but other valid scale factors can be used as long as the operation is correct.)