What is 17/27 plus 15/21?
17/27 plus 15/21 equals 254/189 (or 1 65/189 as a mixed number) (or 1.343915 in decimal form). Learn the step-by-step solution to add 17/27 and 15/21 using Least Common Denominator and simplification.
Exact Answer
17/27 + 15/21 = 254/189
Simplified Fraction
254/189
Mixed Number
1 65/189
Decimal Value
1.343915
Percentage
134.3915%
Step-by-Step Solution: 17/27 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
LCD(27, 21) = 189
Step 2
Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 17/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.
17 × 7/27 × 7 = 119/189 and 15 × 9/21 × 9 = 135/189
Step 3
Add the Numerators
Now add the numerators (119 + 135 = 254) and keep the common denominator 189 unchanged.
119 + 135/189 = 254/189
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 254 and 189 is 1, confirming that 254/189 cannot be reduced further—it is already in its simplest irreducible form.
254/189
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (254) is greater than the denominator (189), divide 254 by 189: it goes in 1 whole time(s) with a remainder of 65, giving the mixed number 1 65/189.
254/189 = 165/189
Step 6
Decimal & Percentage Representation
Dividing the numerator 254 by denominator 189 produces a repeating decimal (approximately 1.343915, or 134.3915%).
254 ÷ 189 = 1.343915 (134.3915%)
Visual Representation
The diagram below illustrates 17/27 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 254/189 |
| Mixed Number Form | 1 65/189 |
| Decimal Form | 1.343915 |
| Percentage | 134.3915% |
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Frequently Asked Questions
What is 17/27 plus 15/21 as a fraction?
17/27 + 15/21 in simplest fraction form is 254/189 (or 1 65/189 as a mixed number).
What is 17/27 plus 15/21 as a decimal?
17/27 + 15/21 converted to a decimal is 1.343915.
What is 17/27 plus 15/21 as a percentage?
17/27 + 15/21 expressed as a percentage is 134.3915%.
How do you write 17/27 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 254/189 can be written as the mixed number 1 65/189.
Does 17/27 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.343915...) because the denominator contains prime factors other than 2 and 5.