What is 4/13 plus 4/9?
4/13 plus 4/9 equals 88/117 (or 0.752137 in decimal form). Learn the step-by-step solution to add 4/13 and 4/9 using Least Common Denominator and simplification.
Exact Answer
4/13 + 4/9 = 88/117
Simplified Fraction
88/117
Mixed Number
Proper (88/117)
Decimal Value
0.752137
Percentage
75.2137%
Step-by-Step Solution: 4/13 + 4/9
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 4/13 by 9, and multiply the numerator and denominator of 4/9 by 13 so both fractions share the common base 117.
4 × 9/13 × 9 = 36/117 and 4 × 13/9 × 13 = 52/117
Step 3
Add the Numerators
Now add the numerators (36 + 52 = 88) and keep the common denominator 117 unchanged.
36 + 52/117 = 88/117
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 88 and 117 is 1, confirming that 88/117 cannot be reduced further—it is already in its simplest irreducible form.
88/117
Step 5
Decimal & Percentage Representation
Dividing the numerator 88 by denominator 117 produces a repeating decimal (approximately 0.752137, or 75.2137%).
88 ÷ 117 = 0.752137 (75.2137%)
Visual Representation
The diagram below illustrates 4/13 plus 4/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 88/117 |
| Mixed Number Form | 88/117 |
| Decimal Form | 0.752137 |
| Percentage | 75.2137% |
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Frequently Asked Questions
What is 4/13 plus 4/9 as a fraction?
4/13 + 4/9 in simplest fraction form is 88/117.
What is 4/13 plus 4/9 as a decimal?
4/13 + 4/9 converted to a decimal is 0.752137.
What is 4/13 plus 4/9 as a percentage?
4/13 + 4/9 expressed as a percentage is 75.2137%.
Does 4/13 plus 4/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.752137...) because the denominator contains prime factors other than 2 and 5.