What is 17/24 plus 15/21?
17/24 plus 15/21 equals 239/168 (or 1 71/168 as a mixed number) (or 1.422619 in decimal form). Learn the step-by-step solution to add 17/24 and 15/21 using Least Common Denominator and simplification.
Exact Answer
17/24 + 15/21 = 239/168
Simplified Fraction
239/168
Mixed Number
1 71/168
Decimal Value
1.422619
Percentage
142.2619%
Step-by-Step Solution: 17/24 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).
LCD(24, 21) = 168
Step 2
Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 17/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.
17 × 7/24 × 7 = 119/168 and 15 × 8/21 × 8 = 120/168
Step 3
Add the Numerators
Now add the numerators (119 + 120 = 239) and keep the common denominator 168 unchanged.
119 + 120/168 = 239/168
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 239 and 168 is 1, confirming that 239/168 cannot be reduced further—it is already in its simplest irreducible form.
239/168
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (239) is greater than the denominator (168), divide 239 by 168: it goes in 1 whole time(s) with a remainder of 71, giving the mixed number 1 71/168.
239/168 = 171/168
Step 6
Decimal & Percentage Representation
Dividing the numerator 239 by denominator 168 produces a repeating decimal (approximately 1.422619, or 142.2619%).
239 ÷ 168 = 1.422619 (142.2619%)
Visual Representation
The diagram below illustrates 17/24 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 239/168 |
| Mixed Number Form | 1 71/168 |
| Decimal Form | 1.422619 |
| Percentage | 142.2619% |
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Frequently Asked Questions
What is 17/24 plus 15/21 as a fraction?
17/24 + 15/21 in simplest fraction form is 239/168 (or 1 71/168 as a mixed number).
What is 17/24 plus 15/21 as a decimal?
17/24 + 15/21 converted to a decimal is 1.422619.
What is 17/24 plus 15/21 as a percentage?
17/24 + 15/21 expressed as a percentage is 142.2619%.
How do you write 17/24 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 239/168 can be written as the mixed number 1 71/168.
Does 17/24 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.422619...) because the denominator contains prime factors other than 2 and 5.