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?

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 \( \frac{a}{b} = \frac{c}{d} \), what is the cross-multiplication result?

Back

The result is \( a \cdot d = b \cdot c \).

Front

What does it mean if two ratios are equivalent?

Back

It means that they represent the same relationship between quantities.

Front

How can you check if two ratios are in proportion?

Back

You can check by cross-multiplying and seeing if the products are equal.

Front

What is the value of \( r \) if \( \frac{r}{4} = \frac{1}{2} \)?

Back

The value of \( r \) is 2.

Front

Solve for \( b \): \( \frac{b}{3} = \frac{8}{12} \)

Back

The value of \( b \) is 6.

Front

If \( \frac{5}{x} = \frac{15}{9} \), what is \( x \)?

Back

The value of \( x \) is 3.

Front

What is the first step in solving the equation \( \frac{w+2}{5} = \frac{7}{5} \)?

Back

The first step is to cross-multiply to get \( w + 2 = 7 \).