Subtracting Fractions With Common Denominators
Learning Outcomes
- Use fraction circles to find the difference between two fractions with like denominators
- Subtract fractions with a like denominator without fraction circles
- Subtract fractions with like denominators that contain variables
Model Fraction Subtraction
Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into [latex]12[/latex] slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or [latex]\frac{7}{12}[/latex] of the pizza) left in the box. If Leonardo eats [latex]2[/latex] of these remaining pieces (or [latex]\frac{2}{12}[/latex] of the pizza), how much is left? There would be [latex]5[/latex] pieces left (or [latex]\frac{5}{12}[/latex] of the pizza). [latex-display]\frac{7}{12}-\frac{2}{12}=\frac{5}{12}[/latex-display] Let’s use fraction circles to model the same example, [latex]\frac{7}{12}-\frac{2}{12}[/latex]. Start with seven [latex]\frac{1}{12}[/latex] pieces. Take away two [latex]\frac{1}{12}[/latex] pieces. How many twelfths are left? Again, we have five twelfths, [latex]\frac{5}{12}[/latex]. Doing the Manipulative Mathematics activity "Model Fraction Subtraction" will help you develop a better understanding of subtracting fractions.Example
Use fraction circles to find the difference: [latex]\frac{4}{5}-\frac{1}{5}[/latex] Solution: Start with four [latex]\frac{1}{5}[/latex] pieces. Take away one [latex]\frac{1}{5}[/latex] piece. Count how many fifths are left. There are three [latex]\frac{1}{5}[/latex] pieces left.Try It
#146190 [ohm_question height="270"]146190[/ohm_question]Subtract Fractions with a Common Denominator
We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.Fraction Subtraction
If [latex]a,b,\text{ and }c[/latex] are numbers where [latex]c\ne 0[/latex], then [latex-display]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/latex-display] To subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.Example
Find the difference: [latex]\frac{23}{24}-\frac{14}{24}[/latex]Answer: Solution:
[latex]\frac{23}{24}-\frac{14}{24}[/latex] | |
Subtract the numerators and place the difference over the common denominator. | [latex]\frac{23 - 14}{24}[/latex] |
Simplify the numerator. | [latex]\frac{9}{24}[/latex] |
Simplify the fraction by removing common factors. | [latex]\frac{3}{8}[/latex] |
Try It
#146191 [ohm_question height="270"]146191[/ohm_question]Example
Find the difference: [latex]\frac{y}{6}-\frac{1}{6}[/latex]Answer: Solution:
[latex]\frac{y}{6}-\frac{1}{6}[/latex] | |
Subtract the numerators and place the difference over the common denominator. | [latex]\frac{y - 1}{6}[/latex] |
Try it
#146192 [ohm_question height="270"]146192[/ohm_question]Example
Find the difference: [latex]-\frac{10}{x}-\frac{4}{x}[/latex]Answer: Solution: Remember, the fraction [latex]-\frac{10}{x}[/latex] can be written as [latex]\frac{-10}{x}[/latex].
[latex]-\frac{10}{x}-\frac{4}{x}[/latex] | |
Subtract the numerators. | [latex]\frac{-10 - 4}{x}[/latex] |
Simplify. | [latex]\frac{-14}{x}[/latex] |
Rewrite with the negative sign in front of the fraction. | [latex]-\frac{14}{x}[/latex] |
Try It
#146249 [ohm_question height="270"]146249[/ohm_question]Example
Simplify: [latex]\frac{3}{8}+\left(-\frac{5}{8}\right)-\frac{1}{8}[/latex]Answer: Solution:
[latex]\frac{3}{8}+\left(-\frac{5}{8}\right)-\frac{1}{8}[/latex] | |
Combine the numerators over the common denominator. | [latex]\frac{3+\left(-5\right)-1}{8}[/latex] |
Simplify the numerator, working left to right. | [latex]\frac{-2 - 1}{8}[/latex] |
Subtract the terms in the numerator. | [latex]\frac{-3}{8}[/latex] |
Rewrite with the negative sign in front of the fraction. | [latex]-\frac{3}{8}[/latex] |
Try It
#146250 [ohm_question height="270"]146250[/ohm_question]Licenses & Attributions
CC licensed content, Original
- Subtract Fractions with Variables and Common Denominators. Authored by: James Sousa (Mathispower4u.com) for Lumen Learning. License: CC BY: Attribution.
CC licensed content, Shared previously
- Ex: Subtract Fractions with Like Denominators. Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].