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Solving One-Step Linear Equations with Mixed Numbers: Addition

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.

Some linear equations can be solved with a single operation. For this type of equation, use the inverse operation to solve. The easiest type involves only an addition or a subtraction.

Example :


3 4 + p = 1 1 4

Rewrite the mixed number as an improper fraction.

3 4 + p = 5 4

The inverse operation of addition is subtraction. Use the subtraction property of equality to subtract 3 4 from both sides.

3 4 + p 3 4 = 5 4 3 4


p = 2 4

Divide the numerator and the denominator by the GCF, 2 .

p = 1 2