Question

Salim wants to create a table of ratios that are equivalent to 2/3 he includes the ratios 4/5 and 5/6 are these ratios equivalent to 2/3 explain your reasoning

Answer 1

We have to verify if 4/5 and 5/6 are eqauivalent to 2/3.

We can verify this dividing the numbers by 2/3, and if we get the value 1, then they are equivalent. If they are equivalent, then the fraction can be reduced up to 2/3, and this division will give us the value 1.

We start with 4/5:

$\frac{\frac{4}{5}}{\frac{2}{3}}=\frac{4}{5}\cdot\frac{3}{2}=\frac{12}{10}=\frac{6}{5}\neq1$

4/5 is not a 2/3 ratio.

We continue with 5/6:

$\frac{\frac{5}{6}}{\frac{2}{3}}=\frac{5}{6}\cdot\frac{3}{2}=\frac{15}{12}=\frac{5}{4}\neq1$

5/6 is not a 2/3 ratio.