Question

show how you can use division to find an equivalent fraction. complete the equation. \\(\frac{8 \div \boxed{?}}{12 \div \boxed{?}} = \frac{2}{3}\\)

Explanation:

Step1: Recall fraction equivalence rule

To find equivalent fractions, we divide numerator and denominator by the same non - zero number. Let the number we divide by be \(x\). So we have the equations \(8\div x = 2\) and \(12\div x=3\).

Step2: Solve for \(x\) from numerator

From \(8\div x = 2\), we can rewrite it as \(\frac{8}{x}=2\). Multiplying both sides by \(x\) gives \(8 = 2x\), and then dividing both sides by 2, we get \(x = 4\).

Step3: Verify with denominator

Check with the denominator: \(12\div4 = 3\), which matches the denominator of the equivalent fraction \(\frac{2}{3}\). So we divide both the numerator and the denominator by 4.

Answer:

The number to divide by is 4 for both. So \(\frac{8\div\boldsymbol{4}}{12\div\boldsymbol{4}}=\frac{2}{3}\)