What is 4/9 plus 6/13?
4/9 plus 6/13 equals 106/117 (or 0.905983 in decimal form). Learn the step-by-step solution to add 4/9 and 6/13 using Least Common Denominator and simplification.
Exact Answer
4/9 + 6/13 = 106/117
Simplified Fraction
106/117
Mixed Number
Proper (106/117)
Decimal Value
0.905983
Percentage
90.5983%
Step-by-Step Solution: 4/9 + 6/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.
LCD(9, 13) = 117
Step 2
Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 4/9 by 13, and multiply the numerator and denominator of 6/13 by 9 so both fractions share the common base 117.
4 × 13/9 × 13 = 52/117 and 6 × 9/13 × 9 = 54/117
Step 3
Add the Numerators
Now add the numerators (52 + 54 = 106) and keep the common denominator 117 unchanged.
52 + 54/117 = 106/117
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 106 and 117 is 1, confirming that 106/117 cannot be reduced further—it is already in its simplest irreducible form.
106/117
Step 5
Decimal & Percentage Representation
Dividing the numerator 106 by denominator 117 produces a repeating decimal (approximately 0.905983, or 90.5983%).
106 ÷ 117 = 0.905983 (90.5983%)
Visual Representation
The diagram below illustrates 4/9 plus 6/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 106/117 |
| Mixed Number Form | 106/117 |
| Decimal Form | 0.905983 |
| Percentage | 90.5983% |
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Frequently Asked Questions
What is 4/9 plus 6/13 as a fraction?
4/9 + 6/13 in simplest fraction form is 106/117.
What is 4/9 plus 6/13 as a decimal?
4/9 + 6/13 converted to a decimal is 0.905983.
What is 4/9 plus 6/13 as a percentage?
4/9 + 6/13 expressed as a percentage is 90.5983%.
Does 4/9 plus 6/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.905983...) because the denominator contains prime factors other than 2 and 5.