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Mixed Simple Proper Improper
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Mixed fraction addition formula

a p q + b r s = ( ( ( a × q ) + p ) × s ) + ( ( ( b × s ) + r ) × q ) q × s

More about mixed fraction addition

Tricks

1. Add the whole numbers separately from the fractions.
2. If the denominators are already the same, then simply add the numerators and keep the denominator the same.
3. Combine the whole numbers sum with the sum of the fractions to obtain the final mixed number sum.

Rules

1. Ensure both fractions have the common denominator.
2. In mixed fraction, fraction always in a combination of a whole number and a fraction.
3. In the fraction part, the numerator is always less than the denominator.

Practise mixed fraction addition

Examples

Example 1: Find the mixed fraction addition of 3 1/2 + 2 3/4.
Solution: Convert into improper fractions i.e 3 1/2 = 7/2 and 2 3/4 = 11/4
Denominators are unlike, make the denominator same by finding LCM of denominators. i.e 14/4 and 11/4
Add both fractions then convert into mixed fraction i.e 14/4 + 11/4 = 25/4 = 6 1/4
Mixed fraction addition of 3 1/2 + 2 3/4 = 6 1/4.

Example 2: Find the mixed fraction addition of 4 6/7 + 1 3/9.
Solution: Convert into improper fractions i.e 4 6/7 = 34/7 and 1 3/9 = 4/3
Denominators are unlike, make the denominator same by finding LCM of denominators.
i.e 54/63 and 21/63
Add both fractions then convert into mixed fraction
i.e 54/63 + 21/63 = 75/63 = 6 4/21
Mixed fraction addition of 4 6/7 + 1 3/9 = 6 4/21.

Example 3: Find the mixed fraction addition of 5 10/22 + 2 7/11.
Solution: Convert into improper fractions i.e 5 10/22 = 120/22 and 2 7/11 = 29/11
Denominators are unlike, make the denominator same by finding LCM of denominators. i.e 120/22 and 58/22
Add both fractions then convert into mixed fraction
i.e 120/22 + 58/22 = 89/11 = 8 1/11
Mixed fraction addition of 5 10/22 + 2 7/11 = 8 1/11.

Example 4: Find the mixed fraction addition of 10 5/9 + 12 2/12.
Solution: Convert into improper fractions i.e 10 5/9 = 95/9 and 12 2/12 = 146/12
Denominators are unlike, make the denominator same by finding LCM of denominators. i.e 380/36 + 438/36
Add both fractions then convert into mixed fraction
i.e 380/36 + 438/36 = 409/18 = 22 13/18
Mixed fraction addition of 10 5/9 + 12 2/12 = 22 13/18.

Example 5: Find the mixed fraction addition of 6 1/4 + 4 3/5.
Solution: Convert into improper fractions i.e 6 1/4 = 25/4 and 4 3/5 = 23/5
Denominators are unlike, make the denominator same by finding LCM of denominators. i.e 125/20 and 92/20
Add both fractions then convert into mixed fraction
i.e 125/20 + 92/20 = 217/20 = 10 17/20
Mixed fraction addition of 6 1/4 + 4 3/5 = 10 17/20.

Exercise

1. 2 3/5 + 1 3/4 = 4 7/20
 2. 10 4/5 + 12 3/5 = 23 2/5
 3. 9 3/11 + 12 7/11 = 21 10/11
 4. 14 2/6 + 8 2/6 = 22 2/3
 5. 2 3/9 + 3 6/9 = 6 0/1
 6. 8 2/3 + 13 4/5 = 22 7/15
 7. 7 3/8 + 4 1/4 = 11 5/8
 8. 5 1/2 + 5 2/12 = 10 2/3
 9. 14 3/7 + 9 2/4 = 23 13/14
 10. 3 5/15 + 2 5/10 = 5 5/6

Add mixed fraction calculator FAQ

What is mixed fraction addition?
The mixed fraction addition involves combining two or more mixed numbers to form a single mixed number. This involves adding the whole numbers together, adding the fractions together, and then combining the whole number and fractional parts to obtain the final mixed number result.
Is it possible to add mixed fractions directly?
Yes, you can add mixed fractions or mixed numbers directly by converting them into improper fractions first, then following the same steps as with simple fractions.
What are the steps to find mixed fraction addition?
Step 1: Convert mixed numbers to improper fractions by multiplying the whole number by the denominator, then adding the numerator, while keeping the denominator the same.
Step 2: To add the improper fractions, they must have the like denominator. If they do not, find a common denominator, add the numerators together and the denominator remains the same.
Step 3: Convert the result to a mixed number by dividing the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.
Could you provide examples from real-life scenarios where the addition of mixed fractions is commonly applied?
Additon of mixed fractions is commonly applied in various fields like working hours, travel and distance, financial calculations, healthcare, sports and landscaping. For example, in measuments, if you are installing edging along the perimeter of your garden to define the flower beds. one side of the garden measures 15 1/2 feet, and the adjacent side measures an additional 12 3/4 feet. Adding these together gives a total length of 28 1/4 feet of edging needed to enclose the garden.
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