Question

are these ratios equivalent?
2 old sweatshirts to 9 new sweatshirts
7 old sweatshirts to 20 new sweatshirts

yes no

Explanation:

Step1: Write the ratios as fractions

The first ratio is $\frac{2}{9}$ and the second is $\frac{7}{20}$.

Step2: Cross - multiply to check equivalence

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$, they are equivalent if $a\times d = b\times c$.
For $\frac{2}{9}$ and $\frac{7}{20}$, we calculate $2\times20 = 40$ and $9\times7=63$.
Since $40
eq63$, the two ratios are not equivalent.

Answer:

no