Review: SAT ratios and proportions

What is a ratio?

A ratio compares two quantities, showing the relative size of one quantity to another.

Fill in the blank: 3:5 is a ______.

ratio

True or false: Ratios can only involve whole numbers.

False, because ratios can involve fractions or decimals.

What is a proportion?

A proportion states that two ratios are equal, often written as $\displaystyle \frac{a}{b} = \frac{c}{d}$.

Difference between ratio and proportion

A ratio compares two numbers; a proportion states that two ratios are equal.

If 4 pens cost $8, what is the unit rate?

$2 per pen

What does the term 'cross-multiplication' refer to?

Cross-multiplication is used to solve proportions by multiplying diagonally.

True or false: 6:2 and 3:1 are equivalent ratios.

True, because both simplify to the same ratio.

Example of a real-life proportion problem.

If 3 apples cost $1.50, how much do 5 apples cost?

What is the proportion of 8 to 12 in simplest form?

The simplest form is $\displaystyle \frac{2}{3}$.

If $\displaystyle \frac{a}{b} = \frac{c}{d}$, what is $\displaystyle b$?

Multiply $\displaystyle a$ by $\displaystyle d$ and divide by $\displaystyle c$: $\displaystyle b = \frac{ad}{c}$.

True or false: All proportions can be solved by scaling.

True, because you can multiply or divide both sides by the same number.

If a recipe uses a ratio of 2:3 for sugar to flour, how much flour for 4 cups sugar?

6 cups flour (maintaining the ratio).

What is the missing value? $\displaystyle \frac{3}{x} = \frac{9}{12}$

Cross-multiply to find $\displaystyle x = 4$.

If you drive 150 miles in 3 hours, what is your speed?

Your speed is 50 miles per hour.

True or false: A ratio can be expressed as a fraction.

True, because ratios can be written as $\displaystyle \frac{a}{b}$.

What is the ratio of 10 to 20 in simplest form?

The simplest form is $\displaystyle \frac{1}{2}$.

If a map has a scale of 1:100, how many meters does 2 cm represent?

200 meters (2 cm × 100).

Which is NOT a valid ratio?

Zero cannot be in the denominator of a ratio.

Find x if $\displaystyle \frac{5}{x} = \frac{15}{45}$.

Cross-multiply to find $\displaystyle x = 15$.

If the ratio of boys to girls is 3:4, how many boys in 28 students?

12 boys (3 out of 7 parts).

What is the unit rate of 60 miles in 1.5 hours?

40 miles per hour.