5.4 Solving Proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you set up a proportion to solve for an unknown?

Back

To set up a proportion, you can use the formula \( \frac{a}{b} = \frac{c}{d} \), where a and b are known values, and c is the known value while d is the unknown.

Front

If Manuel can paint 5 pictures in 12.5 hours, how do you express the rate of painting in a proportion?

Back

The rate can be expressed as \( \frac{5}{12.5} \).

Front

What is the formula to find the time taken if distance and speed are known?

Back

The formula is: Time = Distance ÷ Speed.

Front

If a car travels 120 miles in 3 hours, what is its speed?

Back

Speed = Distance ÷ Time = \( \frac{120}{3} = 40 \) miles per hour.

Front

How do you find the number of tablespoons needed for a different amount of water using proportions?

Back

Set up a proportion based on the known ratio of tablespoons to quarts.

Front

What is the relationship between the quantities in a proportion?

Back

In a proportion, the cross products are equal, meaning \( a \times d = b \times c \).

Front

If Kevin mixes 8 ounces of yellow paint for every 3 ounces of white paint, how do you find the amount of white paint for a different amount of yellow?

Back

Set up the proportion \( \frac{8}{3} = \frac{24}{x} \) and solve for x.

Front

What is the first step in solving a proportion?

Back

The first step is to cross-multiply the terms.

Front

How do you solve the proportion \( \frac{8}{12} = \frac{x}{18} \)?

Back

Cross-multiply to get \( 8 \times 18 = 12 \times x \), then solve for x.