Adding and Subtracting Mixed Numbers With Different Denominators
Learning Outcomes
- Add and subtract mixed numbers with unlike denominators
To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we have learned for adding or subtracting fractions with like denominators.
In our first video, we show the process of adding mixed numbers with different denominators using pattern blocks.
https://youtu.be/SngHXtqs_UE Now let's try adding mixed numbers with different denominators without the help of pattern blocks.Example
Add: [latex]2\frac{1}{2}+5\frac{2}{3}[/latex] Solution: Since the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, [latex]6[/latex]. Then we will add and simplify. We write the answer as a mixed number because we were given mixed numbers in the problem.Try It
[ohm_question]146566[/ohm_question]Example
Subtract: [latex]4\frac{3}{4}-2\frac{7}{8}[/latex]Answer: Solution Since the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD [latex]8[/latex]. Once in that form, we will subtract. But we will need to borrow [latex]1[/latex] first. We were given mixed numbers, so we leave the answer as a mixed number.
Try It
[ohm_question]146396[/ohm_question]Example
Subtract: [latex]3\frac{5}{11}-4\frac{3}{4}[/latex]Answer: Solution: We can see the answer will be negative since we are subtracting [latex]4[/latex] from [latex]3[/latex]. Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.
[latex]3\frac{5}{11}-4\frac{3}{4}[/latex] | |
Change to equivalent fractions with the LCD. | [latex]3\frac{5\cdot 4}{11\cdot 4}-4\frac{3\cdot 11}{4\cdot 11}[/latex] [latex]3\frac{20}{44}-4\frac{33}{44}[/latex] |
Rewrite as improper fractions. | [latex]\frac{152}{44}-\frac{209}{44}[/latex] |
Subtract. | [latex]-\frac{57}{44}[/latex] |
Rewrite as a mixed number. | [latex]-1\frac{13}{44}[/latex] |
Try It
[ohm_question]146367[/ohm_question]Licenses & Attributions
CC licensed content, Shared previously
- Ex: Add and Subtract Mixed Numbers Using Improper Fractions. Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.
- Ex: Find the Sum of Two Mixed Numbers Using Pattern Blocks. 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].