Question

3. Are these ratios equivalent? 35:28 and 10:8 *

Answer 1

Reduce each ratio to its minimum expression to find if they are equal.

35:28

`\begin{gathered} (35)/(28)=(7\cdot5)/(7\cdot4) \\ =(5)/(4) \end{gathered}`

10:8

`\begin{gathered} (10)/(8)=(2\cdot5)/(2\cdot4) \\ =(5)/(4) \end{gathered}`

Since both ratios reduce to 5:4, they are equivalent.

Another way to check a:b is equivalent to c:d, is that a*d = b*c

In this case, this will be true if 35 times 8 is equal to 10 times 28:

`\begin{gathered} 35\cdot8=280 \\ 10\cdot28=280 \end{gathered}`

Since both products are equal, then the ratios are equivalent.