Solving Proportions

Front

What is a proportion?

Back

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

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and then isolate the variable.

Front

What is cross-multiplication in proportions?

Back

Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio.

Front

If a/b = c/d, what is the cross-multiplication result?

Back

The result is ad = bc.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the first step in solving the proportion 3/x = 6/12?

Back

The first step is to cross-multiply: 3 * 12 = 6 * x.

Front

What is the solution to the proportion 4/x = 8/16?

Back

The solution is x = 2.

Front

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

Back

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

Front

What is the relationship between direct and inverse proportions?

Back

In direct proportions, as one quantity increases, the other also increases; in inverse proportions, as one quantity increases, the other decreases.

Front

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

Back

An example is using proportions to adjust a recipe based on the number of servings needed.