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Adding Mixed Fractions

A mixed number can be explained as a fraction and a whole number. Any improper fraction could be expressed as mixed number and vice-versa. For changing a mixed number into an improper fraction, begin multiplying the whole number by the denominator and then add the numerator to get the result. In this article we will see about addition of mixed fractions. Examples for mixed fractions are: 5 `7/4`, 3 `11/3 ` etc.

Addiding Two Mixed Fractions

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How to Add Mixed Fractions

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The following are the steps for how to add mixed fractions:

Step 1: Change the given mixed fractions into improper fractions.

Step 2: If the denominators are different, then convert the fractions to fractions with a common denominator.

Step 3: Add the numerators and keep the denominator as same

Step 4: If the sum is an improper fraction, convert it to a mixed number.

Step 4: If possible, simplify the answer
.

Below are the solved examples based on adding mixed fractions

Solved Examples

Question 1: Add the mixed number 5 `1/2` , 11`1/2`
Solution:
Step 1: Change the mixed numbers into improper fractions

5$\frac{1}{2}$ $\frac{(5\times2)+5}{2}$

$\frac{1}{2}$

11$\frac{1}{2}$ = $\frac{(11\times2)+1}{2}$

$\frac{23}{2}$

The improper fractions are $\frac{11}{2}$$\frac{23}{2}$

Step 2: Here the denominators are same. So add the numerators

$\frac{11}{2}$ + $\frac{23}{2}$ = $\frac{11+23}{2}$

= $\frac{34}{2}$

Step 3: Simplify

$\frac{34}{2}$


Correct answer is 17
Question 2: Add the mixed fractions 7 `3/2` , 3 `1/4`
Solution:
Step 1: Change the mixed numbers into improper fractions

7$\frac{3}{2}$ = $\frac{(7\times2)+3}{2}$

= $\frac{17}{2}$

3$\frac{1}{4}$ = $\frac{(3\times4)+1}{4}$

= $\frac{13}{4}$

The improper fractions are $\frac{17}{2}$

Step 2: Here the denominators are different, take LCM

LCM of 2, 4 = 4

$\frac{17}{2}$ = $\frac{(17\times2)}{2\times2}$ = $\frac{34}{4}$

Step 3: Add the numerators

$\frac{17}{2}$ + $\frac{13}{4}$ = $\frac{34}{4}$ + $\frac{13}{4}$

= $\frac{34}{13}$

= $\frac{47}{4}$

Step 4: Simplify and Express the answer as a mixed number

$\frac{47}{4}$



Correct answer is 11$\frac{3}{4}$
Question 3: Add the mixed fractions 2 `8/12` , 5`1/2` , 11 `1/4`
Solution:
Step 1: change the mixed numbers into improper fractions

2$\frac{8}{12}$ = $\frac{(2\times12)+8}{12}$

= $\frac{32}{12}$

= $\frac{8}{3}$

5$\frac{1}{2}$ = $\frac{(5\times2)+1}{2}$

= $\frac{11}{2}$

11$\frac{1}{4}$ = $\frac{(11\times4)+1}{4}$

= $\frac{45}{4}$

Now the improper fractions are $\frac{8}{3}$, $\frac{11}{2}$, $\frac{45}{4}$

Step 2: Here the denominators are different, take LCM

LCM of 3, 2, 4 = 12

$\frac{8}{3}$ = $\frac{8\times4}{3\times4}$

= $\frac{32}{12}$

$\frac{11}{2}$ = $\frac{11\times6}{2\times6}$ = $\frac{66}{12}$

$\frac{45}{4}$ = $\frac{45\times3}{4\times3}$ = $\frac{135}{12}$

Step 3: Add the numerators

$\frac{32}{12}$ + $\frac{66}{12}$ + $\frac{135}{12}$ = $\frac{(32+66+135)}{12}$

Step 4: Simplify and Express the answer as a mixed number

 $\frac{233}{12}$


Correct answer is 19$\frac{5}{12}$
Question 4: Multiply the following fraction and the mixed number $\frac{3}{4}$ x 2$\frac{3}{5}$
Correct answer is 1$\frac{19}{20}$
Question 5: Multiply the following fraction and the mixed number $\frac{5}{6}$ x 4$\frac{5}{4}$
Correct answer is 4$\frac{9}{24}$
Question 6: Multiply the following fraction and the mixed number $\frac{6}{7}$ x 5$\frac{8}{5}$
Correct answer is $\frac{23}{35}$
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