What is 3/13 plus 7/9?
3/13 plus 7/9 equals 118/117 (or 1 1/117 as a mixed number) (or 1.008547 in decimal form). Learn the step-by-step solution to add 3/13 and 7/9 using Least Common Denominator and simplification.
Exact Answer
3/13 + 7/9 = 118/117
Simplified Fraction
118/117
Mixed Number
1 1/117
Decimal Value
1.008547
Percentage
100.8547%
Step-by-Step Solution: 3/13 + 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 3/13 by 9, and multiply the numerator and denominator of 7/9 by 13 so both fractions share the common base 117.
3 × 9/13 × 9 = 27/117 and 7 × 13/9 × 13 = 91/117
Step 3
Add the Numerators
Now add the numerators (27 + 91 = 118) and keep the common denominator 117 unchanged.
27 + 91/117 = 118/117
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 118 and 117 is 1, confirming that 118/117 cannot be reduced further—it is already in its simplest irreducible form.
118/117
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (118) is greater than the denominator (117), divide 118 by 117: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/117.
118/117 = 11/117
Step 6
Decimal & Percentage Representation
Dividing the numerator 118 by denominator 117 produces a repeating decimal (approximately 1.008547, or 100.8547%).
118 ÷ 117 = 1.008547 (100.8547%)
Visual Representation
The diagram below illustrates 3/13 plus 7/9 visually:
+
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 118/117 |
| Mixed Number Form | 1 1/117 |
| Decimal Form | 1.008547 |
| Percentage | 100.8547% |
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Frequently Asked Questions
What is 3/13 plus 7/9 as a fraction?
3/13 + 7/9 in simplest fraction form is 118/117 (or 1 1/117 as a mixed number).
What is 3/13 plus 7/9 as a decimal?
3/13 + 7/9 converted to a decimal is 1.008547.
What is 3/13 plus 7/9 as a percentage?
3/13 + 7/9 expressed as a percentage is 100.8547%.
How do you write 3/13 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 118/117 can be written as the mixed number 1 1/117.
Does 3/13 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.008547...) because the denominator contains prime factors other than 2 and 5.