Add or subtract the fractions below and simplify your result. 5 9 − 1 6 \frac59-\frac16

This problem asks us to add or subtract the fractions below and simplify our result. So we have 5/9 minus 1/6, and how can I go about solving this? Well, when we have situations where we do not have a common denominator, what we have to do is make these fractions have a common denominator. So we want to rewrite them as equivalent fractions with the same denominator so we can add or subtract them properly. Now, my first step is finding the least common denominator, which I can find for 9 and 6. Now, what I can recognize is that 9 breaks down into 3 x 3 using prime factorization and 6 breaks down into 2 x 3. Now, I can recognize that we have 2 3s for the 9, and so I don't need to include this 13 that we have in the 6, but I do need to include the 2. So what we end up getting is our LCD is 2 times 3 times 3, which means that our least common denominator is 18 using prime factorization. Now that I've found the least common denominator of 18, well, that means that my fractions are each going to have denominators of 18. When we get them to be equivalent fractions with the same denominator, and if I think about it, 9 times 2 gives me 18. So I can multiply this 2 in the numerator as well, giving me 2 times 5, which is 10. Now, 3 times 6 gives me 18, and I can multiply this numerator by 3 as well to give me, well, 3. And now all I need to do from here is subtract these fractions and simplify my result. So we get 10. -3. All over the common denominator of 18 and 10 minus 3 is 7. So we get 7/18, and we actually can't simplify this any farther since 7 is a prime number. So that means 7/ 18 is the solution to this problem.

Table of contents

Skip topic navigation

1. Whole Numbers2h 43m

Adding Whole Numbers
27m

Subtracting Whole Numbers
21m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving1h 11m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
41m

Translating Sentences to Algebraic Equations
9m

4. Fractions3h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

Adding And Subtracting Fractions
31m

Finding The Least Common Denominator
33m

Adding And Subtracting Unlike Fractions
34m

Ordering Fractions
19m

5. Decimals1h 20m

Introduction to Decimals
26m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 1m

Ratios and Rates
35m

Proportions
33m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics31m

Tables
3m

Bar Graphs
3m

Frequency Distributions and Histograms
5m

Line Graphs
14m

Circle Graphs
4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 29m

The Distributive Property
17m

Evaluating Expressions
15m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations and Inequalities4h 58m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
57m

Function Notation
15m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
38m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 40m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

16. Roots and Radicals2h 46m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
46m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

17. Quadratic Equations1h 55m

The Square Root Property
17m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
30m

4. Fractions

Adding And Subtracting Unlike Fractions

Prealgebra & Beginning Algebra

4. Fractions

Adding And Subtracting Unlike Fractions

Previous problemNext problem

Struggling with Prealgebra & Beginning Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Add or subtract the fractions below and simplify your result.
$\frac{5}{9} - \frac{1}{6}$

$\frac{7}{18}$

$\frac{13}{18}$

$$\frac$13$

$$\frac$49$

0 Comments

Previous problemNext problem

6:08m

Watch next

Master Adding And Subtracting Unlike Fractions Example 2 with a bite sized video explanation from Jennifer Canizales

Struggling with Prealgebra & Beginning Algebra?

Add or subtract the fractions below and simplify your result.59−16\(\frac\)59-\(\frac\)16

Watch next

Add or subtract the fractions below and simplify your result.
$\frac{5}{9} - \frac{1}{6}$