Subtracting Mixed Numbers With a Common Denominator
Learning Outcomes
- Use a model to subtract mixed numbers with like denominators
- Subtract mixed numbers with like denominators using two different methods
Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half. We will use fraction circles (pizzas!) to help us visualize the process. Start with one whole.
Algebraically, you would write:Example
Use a model to subtract: [latex]1-\frac{1}{3}[/latex]. Solution:Try It
#146391 [ohm_question]146391[/ohm_question]Example
Use a model to subtract: [latex]2-\frac{3}{4}[/latex].Answer: Solution:
Try It
#146392 [ohm_question]146392[/ohm_question]Example
Use a model to subtract: [latex]2 - 1\frac{2}{5}[/latex].Answer: Solution:
try It
#146393 [ohm_question]146393[/ohm_question]Example
Use a model to subtract: [latex]1\frac{1}{4}-\frac{3}{4}[/latex]Answer: Solution:
Rewrite vertically. Start with one whole and one fourth. | [latex]\color{red}{1\frac{1}{4}}[/latex] [latex]--\frac{3}{4}[/latex] | |
Since the fractions have denominator 4, cut the whole into 4 pieces. You now have [latex]\frac{4}{4}[/latex] and [latex]\frac{1}{4}[/latex] which is [latex]\frac{5}{4}[/latex] . | [latex]\color{red}{\frac{5}{4}}[/latex] [latex]--\frac{3}{4}[/latex] | |
Take away [latex]\frac{3}{4}[/latex] . There is [latex]\frac{1}{2}[/latex] left. | [latex]\frac{5}{4}[/latex] [latex]\frac{\color{red}{--\frac{3}{4}}}{\frac{2}{4}=\frac{1}{2}}[/latex] |
Try It
Use a model to subtract. Draw a picture to illustrate your model. [latex-display]1\frac{1}{3}-\frac{2}{3}[/latex-display]Answer:
Use a model to subtract. Draw a picture to illustrate your model. [latex-display]1\frac{1}{5}-\frac{4}{5}[/latex-display]Answer:
Subtract mixed numbers with like denominators
Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.
Subtract mixed numbers with common denominators
- Rewrite the problem in vertical form.
- Compare the two fractions.
- If the top fraction is larger than the bottom fraction, go to Step 3.
- If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.
- Subtract the fractions.
- Subtract the whole numbers.
- Simplify, if possible.
Example
Find the difference: [latex]5\frac{3}{5}-2\frac{4}{5}[/latex] Solution:[latex]5\frac{3}{5}-2\frac{4}{5}[/latex] | |
Rewrite the problem in vertical form. | |
Since [latex]\frac{3}{5}[/latex] is less than [latex]\frac{4}{5}[/latex] , take 1 from the 5 and add it to the [latex]\frac{3}{5}:\left(\frac{5}{5}+\frac{3}{5}=\frac{8}{5}\right)[/latex] | |
Subtract the fractions. | |
Subtract the whole parts. The result is in simplest form. |
Try It
#146395 [ohm_question]146395[/ohm_question]Subtract mixed numbers with common denominators as improper fractions
Step 1. Rewrite the mixed numbers as improper fractions. Step 2. Subtract the numerators. Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible.Example
Find the difference by converting to improper fractions: [latex-display]9\frac{6}{11}-7\frac{10}{11}[/latex-display]Answer: Solution:
[latex]9\frac{6}{11}-7\frac{10}{11}[/latex] | |
Rewrite as improper fractions. | [latex]\frac{105}{11}-\frac{87}{11}[/latex] |
Subtract the numerators. | [latex]\frac{18}{11}[/latex] |
Rewrite as a mixed number. | [latex]1\frac{7}{11}[/latex] |
Try It
#146395 [ohm_question height="270"]146395[/ohm_question]Licenses & Attributions
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- Ex: Subtract Mixed Numbers 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].