What is 10/14 plus 15/21?
10/14 plus 15/21 equals 10/7 (or 1 3/7 as a mixed number) (or 1.428571 in decimal form). Learn the step-by-step solution to add 10/14 and 15/21 using Least Common Denominator and simplification.
Exact Answer
10/14 + 15/21 = 10/7
Simplified Fraction
10/7
Mixed Number
1 3/7
Decimal Value
1.428571
Percentage
142.8571%
Step-by-Step Solution: 10/14 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).
LCD(14, 21) = 42
Step 2
Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 10/14 by 3, and multiply the numerator and denominator of 15/21 by 2 so both fractions share the common base 42.
10 × 3/14 × 3 = 30/42 and 15 × 2/21 × 2 = 30/42
Step 3
Add the Numerators
Now add the numerators (30 + 30 = 60) and keep the common denominator 42 unchanged.
30 + 30/42 = 60/42
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 42, which is 6. Divide both the numerator and denominator by 6.
60 ÷ 6/42 ÷ 6 = 10/7
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (10) is greater than the denominator (7), divide 10 by 7: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/7.
10/7 = 13/7
Step 6
Decimal & Percentage Representation
Dividing the numerator 10 by denominator 7 produces a repeating decimal (approximately 1.428571, or 142.8571%).
10 ÷ 7 = 1.428571 (142.8571%)
Visual Representation
The diagram below illustrates 10/14 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 10/7 |
| Mixed Number Form | 1 3/7 |
| Decimal Form | 1.428571 |
| Percentage | 142.8571% |
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Frequently Asked Questions
What is 10/14 plus 15/21 as a fraction?
10/14 + 15/21 in simplest fraction form is 10/7 (or 1 3/7 as a mixed number).
What is 10/14 plus 15/21 as a decimal?
10/14 + 15/21 converted to a decimal is 1.428571.
What is 10/14 plus 15/21 as a percentage?
10/14 + 15/21 expressed as a percentage is 142.8571%.
How do you write 10/14 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 10/7 can be written as the mixed number 1 3/7.
Does 10/14 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.428571...) because the denominator contains prime factors other than 2 and 5.