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Study Guides > Prealgebra

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. There are three vertical addition problems. The first shows 2 and 1 half plus 5 and 2 thirds. There is an arrow pointing to the next. This one shows 2 and 1 times a red 3 over 2 times a red 3, with an arrow pointing to the top red 3 that says, 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. There are four vertical subtraction problems. The first shows 4 and 3 fourths minus 2 and 7 eighths. There is an arrow pointing to the next. This shows 4 and 3 times a red 2 over 4 times a red 2, with an arrow above saying, 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]
In teh following video we show four more examples of adding and subtracting mixed numbers that have both like and unlike denominators. The method used for these examples employs improper fractions. https://youtu.be/jgvJWbUDTno

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