Solving One-Step Linear Equations with Mixed Numbers: Addition

The process of solving one-step linear equations that involve mixed numbers and addition might seem a bit intimidating. But it''s easier than you might think. We''ll explore how to convert mixed numbers into improper fractions and use the inverse operation to make solving one-step linear equations simple.

How to add one-step linear equations with mixed numbers

A mixed number, which is a number expressed as the sum of a whole number and a fraction, can also be written as an improper fraction (ex. 1 1/4 = 5/4). While mixed numbers offer a better idea of the size of a number, improper fractions often make calculations easier. For this reason, we''ll turn mixed numbers into improper fractions to solve one-step linear equations.

Now, let''s solve the following equation:

1/4 + p = 1 3/4

First, we''ll convert the mixed number into an improper fraction. Write the mixed number as a sum of a whole number and proper fraction, and then write those parts with common denominators.

1 3/4 = 1 + 3/4 = 4/4 + 3/4 = 7/4

Your new linear equation is:

1/4 + p = 7/4

Now, let''s use the inverse operation to solve. The inverse operation of addition is subtraction, so we''ll use the subtraction property of equality to subtract 1/4 from both sides.

1/4 + p − 1/4 = 7/4 − 1/4

Simplify.

p = 6/4

Divide the numerator and the denominator by the greatest common factor, 2.

p = 3/2 or 1 1/2

Practice questions on adding one-step linear equations with mixed numbers

a. Solve:

3/5 + y = 2 1/5

Turn the mixed number into an improper fraction.

2 + 1/5 = 10/5 + 1/5 = 11/5

New equation:

3/5 + y = 11/5

Use the inverse operation to solve.

3/5 + y − 3/5 = 11/5 − 3/5

Simplify.

y = 8/5 or 1 3/5

b. Solve:

1 9/8 + 2 1/3

First, convert each mixed number into an improper fraction.
For:

1 9/8:

1 (whole number) = 1 * 8 (denominator) = 8

8 + 9 (numerator) = 17

So:

1 9/8 = 17/8

For:

2 1/3:

2 (whole number) = 2 * 3 (denominator) = 6

6 + 1 (numerator) = 7

So:

2 1/3 = 7/3

Now, add the improper fractions. To do this, find a common denominator. In this case, the common denominator is 24 (the least common multiple of 8 and 3).

For:

17/8:

17/8 * (3/3) = (17 * 3) / (8 * 3) = 51/24

For:

7/3:

7/3 * (8/8) = (7 * 8) / (3 * 8) = 56/24

Add the two fractions:

51/24 + 56/24 = (51 + 56) / 24 = 107/24

Convert the improper fraction back into a mixed number:

107 ÷ 24 = 4 (whole number) with a remainder of 11

So:

107/24 = 4 11/24

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