Proportions Warm Up

Front

What is a proportion?

Back

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

Front

How do you determine if two ratios form a proportion?

Back

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

Front

What is the cross product of the ratios \( \frac{a}{b} \) and \( \frac{c}{d} \)?

Back

The cross product is \( a \times d \) and \( b \times c \). If \( a \times d = b \times c \), then the ratios form a proportion.

Front

Do the ratios \( \frac{5}{6} \) and \( \frac{20}{24} \) form a proportion?

Back

Yes, they form a proportion because \( 5 \times 24 = 6 \times 20 \).

Front

Do the ratios \( \frac{2}{3} \) and \( \frac{8}{15} \) form a proportion?

Back

No, they do not form a proportion because \( 2 \times 15 \neq 3 \times 8 \).

Front

Solve the proportion: \( \frac{16}{12} = \frac{x}{3} \).

Back

The answer is \( 4 \).

Front

Do the ratios \( \frac{15}{20} \) and \( \frac{42}{56} \) form a proportion?

Back

Yes, they form a proportion because \( 15 \times 56 = 20 \times 42 \).

Front

Solve the proportion: \( \frac{5}{6} = \frac{25}{h} \).

Back

The answer is \( 30 \).

Front

What is the first step to solve a proportion?

Back

The first step is to cross-multiply the two ratios.

Front

What does it mean if two ratios are equivalent?

Back

It means that they represent the same relationship or value.