Solving Proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you solve a proportion?

Back

To solve a proportion, you can use cross-multiplication. If a/b = c/d, then a*d = b*c.

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve proportions by multiplying the numerator of one ratio by the denominator of the other ratio.

Front

If 3/4 = x/12, what is x?

Back

x = 9. (Cross-multiply: 3*12 = 4*x, so 36 = 4x, and x = 36/4 = 9.)

Front

What is the first step in solving the proportion 5/x = 15/20?

Back

The first step is to cross-multiply: 5*20 = 15*x.

Front

What does it mean if two ratios are equivalent?

Back

Two ratios are equivalent if they represent the same relationship between numbers, meaning they simplify to the same fraction.

Front

How can you check if your solution to a proportion is correct?

Back

You can check your solution by substituting it back into the original proportion to see if both sides are equal.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions show that two ratios are equal.

Front

If a recipe calls for 2 cups of flour for every 3 cups of sugar, what is the ratio of flour to sugar?

Back

The ratio of flour to sugar is 2:3.

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, such as miles per hour.