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While it''s common to encounter linear equations with multiple operations, some linear equations can be solved with a single operation. Let''s take a look at the process of solving one-step linear equations that involve subtraction and mixed numbers.

Before outlining the process of solving a one-step linear equation with subtraction, let''s go over the mixed number.

A mixed number is expressed as the sum of a whole number and a fraction (ex. 2 1/5). While mixed numbers give a better idea of the size of a number, making calculations is easier with improper fractions. For this reason, we''ll convert mixed numbers into improper fractions to solve one-step linear equations that involve subtraction.

Let''s get started!

Solve the following one-step linear equation:

x − 2 1/4 = 1/4

First, convert the mixed number into an improper fraction by writing the mixed number as a sum of a whole number and proper fraction. Then, write those parts with common denominators.

2 1/4 = 2 + 1/4 = 8/4 + 1/4 = 9/4

Your new linear equation is:

x − 9/4 = 1/4

Now, we''ll use the inverse operation of subtraction to solve. Use the addition property of equality to add

9/4

to both sides.x − 9/4 + 9/4 = 1/4 + 9/4

Simplify.

x = 10/4

Divide the numerator and the denominator by the greatest common factor, 2 to put the fraction in lowest terms.

p = 5/2 or 2 1/2

a. Solve:

y − 1 2/3 = 7/3

Turn the mixed number into an improper fraction.

1 + 2/3 = 3/3 + 2/3 = 5/3

New equation:

y − 5/3 = 7/3

Use the inverse operation to solve.

y − 5/3 + 5/3 = 7/3 + 5/3

Simplify.

y = 12/3

Divide the numerator and the denominator by the greatest common factor, 3.

Answer:

y = 4

b. Solve:

x − 2 3/4 = 3/4

Turn the mixed number into an improper fraction.

2 + 3/4 = 8/4 + 3/4 = 11/4

New equation:

x − 11/4 = 3/4

Use the inverse operation to solve.

x − 11/4 + 11/4 = 3/4 + 11/4

Simplify.

x = 14/4

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

Answer:

x = 7/2

or 3 1/2

Subtracting Fractions with Like Denominators

Adding and Subtracting Rational Expressions with Unlike Denominators

Common Core: 5th Grade Math Flashcards

MAP 5th Grade Math Practice Tests

Common Core: 5th Grade Math Diagnostic Tests

Solving one-step linear equations that involve mixed numbers and subtraction can be challenging, particularly for students who are new to inverse operations or need a refresher on mixed numbers. Whether your student is struggling with this topic or needs homework or test prep help, tutoring can make a major difference. Contact the Educational Directors at Varsity Tutors today to learn more about the benefits of working with a private tutor.

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