A ratio compares quantities in a stated order. For like quantities, convert to the same units first. Multiply or divide every part by the same nonzero number to obtain an equivalent ratio. For fractional parts, clear denominators before simplifying. Example 34: 56=9:10, multiplying both parts by 12. Also 1.2 m:45 cm=120:45=8:3. To divide $660 in the ratio 8:3, there are 11 equal parts. One part is 66011=$60; the shares are $480 and $180. In A:B=8:3, A is 811 of the total, not 83 of the total.

A ratio compares quantities in a stated order. For like quantities, convert to the same units first. Multiply or divide every part by the same nonzero number to obtain an equivalent ratio. For fractional parts, clear denominators before simplifying.

$\dfrac34:\dfrac56=9:10$, multiplying both parts by $12$. Also $1.2\text{ m}:45\text{ cm}=120:45=8:3$.

To divide $\$660$ in the ratio $8:3$, there are $11$ equal parts. One part is $\dfrac{660}{11}=\$60$; the shares are $\$480$ and $\$180$.

In $A:B=8:3$, $A$ is $\dfrac8{11}$ of the total, not $\dfrac83$ of the total.

Equivalent ratios and proportional shares

Equivalent ratios and proportional shares