Question

write three fractions equivalent to \\(\frac{4}{10}\\). 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 $\frac{4}{10}$ by 2. So, $4\times2 = 8$ and $10\times2 = 20$. The equivalent fraction is $\frac{8}{20}$.

Step2: Scale up by 3

Multiply both the numerator and denominator of $\frac{4}{10}$ by 3. $4\times3 = 12$ and $10\times3 = 30$. The equivalent fraction is $\frac{12}{30}$.

Step3: Scale down by 2

To scale down, we divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 4 and 10 is 2. So, $4\div2 = 2$ and $10\div2 = 5$. The equivalent fraction is $\frac{2}{5}$.

Answer:

Scale up by: 2
Equivalent fraction: $\frac{8}{20}$

Scale up by: 3
Equivalent fraction: $\frac{12}{30}$

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

(Note: The scale - up factors can be other non - zero integers as well. For example, scaling up by 4 would give $\frac{16}{40}$, but the above are valid solutions.)