3 Ratios and Proportions Free Online FlashCards

What does a ratio compare?

A ratio compares two quantities.

How can the ratio of 8 apples to 12 oranges be written?

The ratio of 8 apples to 12 oranges can be written as $8:12$, “8 to 12,” or $\frac{8}{12}$.

Why does the order of quantities matter in a ratio?

Keep the quantities in the same order: apples to oranges is not the same comparison as oranges to apples.

What two kinds of comparisons can a ratio describe?

A ratio can compare parts of a group, such as apples to oranges, or a part to the whole, such as apples to all the fruit.

How do you simplify the ratio $18:24$?

Divide both terms by the same positive common factor: $18:24=3:4$, because both terms are divided by $6$.

How do you simplify a ratio with different units?

Convert to compatible units first: $1\text{ m}:50\text{ cm}=100\text{ cm}:50\text{ cm}=2:1$.

How can you create an equivalent ratio?

Multiply or divide both terms by the same nonzero number. For example, $3:5=6:10=9:15$.

What is a proportion?

A proportion is an equation stating that two ratios are equivalent.

Solve $\frac{3}{5}=\frac{x}{20}$ by scaling.

Since $5$ is multiplied by $4$ to get $20$, multiply $3$ by $4$: $x=12$.

What equation results from cross-multiplying $\frac{a}{b}=\frac{c}{d}$?

If $\frac{a}{b}=\frac{c}{d}$, where $b\ne0$ and $d\ne0$, cross-multiplication gives $ad=bc$.

How can you check the solution $x=12$ for $\frac{3}{5}=\frac{x}{20}$?

Substitute the result and confirm the ratios are equal: $\frac{12}{20}=\frac{3}{5}$.

What distinguishes a rate from a ratio of like quantities?

A rate compares quantities with different units, such as miles and hours.