Solving Proportions

Front

What is a proportion?

Back

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

Front

How can you determine if two ratios form a proportion?

Back

Two ratios form a proportion if the cross products are equal.

Front

What is the cross product of the ratios a/b and c/d?

Back

The cross product is ad and bc; if ad = bc, then a/b = c/d is a proportion.

Front

What is the first step in solving a proportion?

Back

The first step is to set the two ratios equal to each other.

Front

If 3/4 = x/12, how do you solve for x?

Back

Cross multiply to get 3 * 12 = 4 * x, which simplifies to 36 = 4x, then x = 9.

Front

What does it mean to solve a proportion?

Back

To solve a proportion means to find the unknown value that makes the two ratios equal.

Front

If a proportion is given as 5/x = 10/20, how do you solve for x?

Back

Cross multiply to get 5 * 20 = 10 * x, which simplifies to 100 = 10x, then x = 10.

Front

What is the value of k in the proportion 2/3 = k/9?

Back

Cross multiply to get 2 * 9 = 3 * k, which simplifies to 18 = 3k, then k = 6.

Front

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

Back

Substitute the value back into the original proportion to see if both sides are equal.

Front

What is an example of a real-world application of proportions?

Back

Proportions can be used in recipes to adjust ingredient amounts based on serving sizes.