Solving One-Step Linear Equations with Mixed Numbers: Subtraction
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.
How to subtract one-step linear equations with 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
Practice questions on subtracting one-step linear equations with mixed numbers
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
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Delve deeper into one-step linear equations with mixed numbers: subtraction
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.