Cross multiplication

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 and setting the two products equal to each other.

Front

When can you use cross multiplication?

Back

Cross multiplication can be used when you have an equation in the form of \( \frac{a}{b} = \frac{c}{d} \). It allows you to eliminate the fractions and solve for the unknown.

Front

What is the first step in cross multiplication?

Back

The first step is to set up the equation in the form of two fractions equal to each other, such as \( \frac{a}{b} = \frac{c}{d} \).

Front

How do you set up the equation for cross multiplication?

Back

To set up the equation, write it as \( a \cdot d = b \cdot c \). This means you multiply the numerator of the first fraction by the denominator of the second fraction and vice versa.

Front

What is the result of cross multiplying \( \frac{2}{3} = \frac{x}{6} \)?

Back

Cross multiplying gives you \( 2 \cdot 6 = 3 \cdot x \), which simplifies to \( 12 = 3x \).

Front

How do you solve for x in the equation \( 12 = 3x \)?

Back

To solve for x, divide both sides by 3: \( x = \frac{12}{3} = 4 \).

Front

What is the value of x in the equation \( \frac{5}{x} = \frac{10}{15} \)?

Back

Cross multiplying gives you \( 5 \cdot 15 = 10 \cdot x \), which simplifies to \( 75 = 10x \). Dividing both sides by 10 gives \( x = 7.5 \).

Front

What does it mean to multiply out after cross multiplication?

Back

Multiplying out means to distribute and simplify the equation after cross multiplication to isolate the variable.

Front

What is the correct setup for the equation \( 5(x+2) = 2x(3x+8) \)?

Back

This equation is already set up correctly for cross multiplication.

Front

What is the correct setup for the equation \( 8(a+4) = 2(a-2) \)?

Back

This equation is also set up correctly for cross multiplication.