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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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Learn more about adding one-step linear equations with mixed numbers

If your student is learning how to solve one-step linear equations that involve mixed numbers and addition for the first time, they might struggle with the inverse operation or have questions about turning mixed numbers into improper fractions. A private tutor can go over any concept giving your student trouble and also help with homework and test preparations. Get more information about the perks of tutoring by reaching out to the Educational Directors at Varsity Tutors.

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