What is 10/27 plus 15/21?
10/27 plus 15/21 equals 205/189 (or 1 16/189 as a mixed number) (or 1.084656 in decimal form). Learn the step-by-step solution to add 10/27 and 15/21 using Least Common Denominator and simplification.
Exact Answer
10/27 + 15/21 = 205/189
Simplified Fraction
205/189
Mixed Number
1 16/189
Decimal Value
1.084656
Percentage
108.4656%
Step-by-Step Solution: 10/27 + 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 10/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.
10 × 7/27 × 7 = 70/189 and 15 × 9/21 × 9 = 135/189
Step 3
Add the Numerators
Now add the numerators (70 + 135 = 205) and keep the common denominator 189 unchanged.
70 + 135/189 = 205/189
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 205 and 189 is 1, confirming that 205/189 cannot be reduced further—it is already in its simplest irreducible form.
205/189
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (205) is greater than the denominator (189), divide 205 by 189: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/189.
205/189 = 116/189
Step 6
Decimal & Percentage Representation
Dividing the numerator 205 by denominator 189 produces a repeating decimal (approximately 1.084656, or 108.4656%).
205 ÷ 189 = 1.084656 (108.4656%)
Visual Representation
The diagram below illustrates 10/27 plus 15/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 205/189 |
| Mixed Number Form | 1 16/189 |
| Decimal Form | 1.084656 |
| Percentage | 108.4656% |
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Frequently Asked Questions
What is 10/27 plus 15/21 as a fraction?
10/27 + 15/21 in simplest fraction form is 205/189 (or 1 16/189 as a mixed number).
What is 10/27 plus 15/21 as a decimal?
10/27 + 15/21 converted to a decimal is 1.084656.
What is 10/27 plus 15/21 as a percentage?
10/27 + 15/21 expressed as a percentage is 108.4656%.
How do you write 10/27 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 205/189 can be written as the mixed number 1 16/189.
Does 10/27 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.084656...) because the denominator contains prime factors other than 2 and 5.