Question

write three fractions equivalent to \\(\frac{10}{12}\\). 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 $\frac{10}{12}$ by 2.
$10\times2 = 20$, $12\times2 = 24$, so the equivalent fraction is $\frac{20}{24}$.

Step2: Scale up by 3

Multiply both the numerator and the denominator of $\frac{10}{12}$ by 3.
$10\times3 = 30$, $12\times3 = 36$, so the equivalent fraction is $\frac{30}{36}$.

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 10 and 12 is 2.
Divide 10 by 2: $10\div2 = 5$, divide 12 by 2: $12\div2 = 6$, so the equivalent fraction is $\frac{5}{6}$.

Answer:

Scale up by: 2
Equivalent fraction: $\frac{20}{24}$

Scale up by: 3
Equivalent fraction: $\frac{30}{36}$

Scale down by: 2
Equivalent fraction: $\frac{5}{6}$

(Note: The first "Scale up by" in the original problem had a pre-filled "1", but scaling by 1 gives the same fraction, so we can choose other integers like 2, 3 for scaling up. The scaling down uses the GCD 2 to simplify the fraction.)