Cross Multiplication Review

Front

What is cross multiplication?

Back

Cross multiplication is a method used to solve equations involving fractions. It involves multiplying the numerator of one fraction by the denominator of the other fraction.

Front

How do you solve the equation \( \frac{a}{b} = \frac{c}{d} \) using cross multiplication?

Back

To solve \( \frac{a}{b} = \frac{c}{d} \), cross multiply to get \( a \cdot d = b \cdot c \). Then, solve for the variable.

Front

If \( \frac{x}{3} = \frac{6}{9} \), what is x?

Back

x = 2. Cross multiply to get \( 9x = 18 \), then divide by 9.

Front

What is the first step in solving \( \frac{2}{5} = \frac{x}{15} \)?

Back

Cross multiply to get \( 2 \cdot 15 = 5 \cdot x \), which simplifies to \( 30 = 5x \).

Front

If \( \frac{4}{x} = \frac{8}{12} \), how do you find x?

Back

Cross multiply to get \( 4 \cdot 12 = 8 \cdot x \). This simplifies to \( 48 = 8x \), so x = 6.

Front

What does it mean if two fractions are equivalent?

Back

Two fractions are equivalent if they represent the same value, meaning their cross products are equal.

Front

How can you check if your solution for x is correct?

Back

Substitute your value of x back into the original equation and verify that both sides are equal.

Front

If \( \frac{5}{x} = \frac{10}{20} \), what is x?

Back

x = 10. Cross multiply to get \( 5 \cdot 20 = 10 \cdot x \), which simplifies to \( 100 = 10x \).

Front

What is the relationship between the cross products in a proportion?

Back

In a proportion, the cross products are equal, meaning \( a \cdot d = b \cdot c \) for \( \frac{a}{b} = \frac{c}{d} \).

Front

If \( \frac{x}{4} = \frac{3}{12} \), how do you solve for x?

Back

Cross multiply to get \( 12x = 4 \cdot 3 \). This simplifies to \( 12x = 12 \), so x = 1.