Question

compare \\(\frac{1}{2}\\) and \\(\frac{1}{6}\\). first, think about \\(\frac{1}{2}\\). show how you can use multiplication to find an equivalent fraction. \\(\frac{1\times\square}{2\times?}=\frac{3}{6}\\)

Explanation:

Step1: Recall equivalent fractions rule

To find an equivalent fraction, we multiply the numerator and denominator by the same non - zero number. The formula for equivalent fractions is $\frac{a}{b}=\frac{a\times k}{b\times k}$ where $k
eq0$.

Step2: Analyze the numerator

We know that the original numerator is 1 and the new numerator is 3. So we need to find $k$ such that $1\times k = 3$. Solving for $k$, we get $k = 3$.

Step3: Apply to the denominator

Since we multiply the numerator by 3, we must also multiply the denominator by 3. The original denominator is 2, so $2\times3=6$, which matches the denominator of the equivalent fraction $\frac{3}{6}$. So both the boxes should be filled with 3.

Answer:

The number to fill in both boxes is 3. So the completed equation is $\frac{1\times\boldsymbol{3}}{2\times\boldsymbol{3}}=\frac{3}{6}$