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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