What is 2/13 plus 7/9?
2/13 plus 7/9 equals 109/117 (or 0.931624 in decimal form). Learn the step-by-step solution to add 2/13 and 7/9 using Least Common Denominator and simplification.
Exact Answer
2/13 + 7/9 = 109/117
Simplified Fraction
109/117
Mixed Number
Proper (109/117)
Decimal Value
0.931624
Percentage
93.1624%
Step-by-Step Solution: 2/13 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.
LCD(13, 9) = 117
Step 2
Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 2/13 by 9, and multiply the numerator and denominator of 7/9 by 13 so both fractions share the common base 117.
2 × 9/13 × 9 = 18/117 and 7 × 13/9 × 13 = 91/117
Step 3
Add the Numerators
Now add the numerators (18 + 91 = 109) and keep the common denominator 117 unchanged.
18 + 91/117 = 109/117
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 117 is 1, confirming that 109/117 cannot be reduced further—it is already in its simplest irreducible form.
109/117
Step 5
Decimal & Percentage Representation
Dividing the numerator 109 by denominator 117 produces a repeating decimal (approximately 0.931624, or 93.1624%).
109 ÷ 117 = 0.931624 (93.1624%)
Visual Representation
The diagram below illustrates 2/13 plus 7/9 visually:
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=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 109/117 |
| Mixed Number Form | 109/117 |
| Decimal Form | 0.931624 |
| Percentage | 93.1624% |
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Frequently Asked Questions
What is 2/13 plus 7/9 as a fraction?
2/13 + 7/9 in simplest fraction form is 109/117.
What is 2/13 plus 7/9 as a decimal?
2/13 + 7/9 converted to a decimal is 0.931624.
What is 2/13 plus 7/9 as a percentage?
2/13 + 7/9 expressed as a percentage is 93.1624%.
Does 2/13 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.931624...) because the denominator contains prime factors other than 2 and 5.