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Solving One-Step Linear Equations with Mixed Numbers: Division

A mixed number is a number expressed as the sum of a whole number and a fractions , such as 3 1 4 .

It is usually easier to do calculations with improper fractions than mixed numbers, but mixed numbers give a better idea of the size of a number. So you should know how to convert back and forth.

To solve an equation that has a mixed number coefficient, we convert the mixed number to an improper fraction as the first step.

We can solve linear equations when only multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of 1.

Example:

Solve.

x 6 = 5 5 12

Rewrite the mixed number as an improper fraction.

x 6 = 65 12

The inverse operation of division is multiplication.

To isolate the variable x (to get a coefficient of 1 ), multiply both sides by 6 .

x 6 × 6 = 65 12 × 6

Cancel the common factors and simplify.

x 6 1 × 6 1 = 65 12 2 × 6 1 x = 65 2

Convert the improper fraction into a mixed number.

65 2 = 32 1 2

Therefore, the solution is 32 1 2 .