# How to Cross Multiply

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Cross multiplication involves the multiplication of two fractions set equal to each other and is used to solve for an unknown number. If the fraction a/b is set equal to x/y, the "b" and "x" can be multiplied together, as can the "a" and "y." This works because multiplying a fraction's numerator and denominator by the same number doesn't change the value of the fraction. For example, a * y / b * y is equal to a / b. And x * b / y * b is the same as x / y. But now both fractions have the same denominator (b * y), which can be discarded since the same operation was being done to both sides. That leaves you with the a * y = x * b.

Cross-multiply the fractions 8/9 = 4/x. Begin by multiplying the numerator of the first fraction by the denominator of the second: 8 * x. Move on to multiply the numerator of the second fraction by the denomination of the first: 9 * 4. Set the numbers equal to each other: 8 * x = 9 * 4. Simplify: 8x = 36. Divide both sides by 8 to get your answer: x = 4.5.

Cross-multiply x/10 = 5/20. Multiply the numerator of the first number by the denominator of the second: x * 20. Multiply the numerator of the second number by the denominator of the first: 5 * 10. Set the terms equal to each other: x * 20 = 5 * 10 or 20x = 50. Divide both sides by 20 to get your answer: x = 5/2.

Cross-multiply 20/ x = 10/8. Multiply the numerator of the first number by the denominator of the second, then the numerator of the second and denominator of the first and set the terms equal to each other: 20 * 8 = 10 * x or 160 = 10x. Divide both sides by 10 to get your answer: 16 = x.