What is 4/12 plus 9/13?
4/12 plus 9/13 equals 40/39 (or 1 1/39 as a mixed number) (or 1.025641 in decimal form). Learn the step-by-step solution to add 4/12 and 9/13 using Least Common Denominator and simplification.
Exact Answer
4/12 + 9/13 = 40/39
Simplified Fraction
40/39
Mixed Number
1 1/39
Decimal Value
1.025641
Percentage
102.5641%
Step-by-Step Solution: 4/12 + 9/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 12 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 13 = 156.
LCD(12, 13) = 156
Step 2
Convert to Equivalent Fractions with Common Denominator 156
Multiply the numerator and denominator of 4/12 by 13, and multiply the numerator and denominator of 9/13 by 12 so both fractions share the common base 156.
4 × 13/12 × 13 = 52/156 and 9 × 12/13 × 12 = 108/156
Step 3
Add the Numerators
Now add the numerators (52 + 108 = 160) and keep the common denominator 156 unchanged.
52 + 108/156 = 160/156
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 160 and 156, which is 4. Divide both the numerator and denominator by 4.
160 ÷ 4/156 ÷ 4 = 40/39
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (40) is greater than the denominator (39), divide 40 by 39: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/39.
40/39 = 11/39
Step 6
Decimal & Percentage Representation
Dividing the numerator 40 by denominator 39 produces a repeating decimal (approximately 1.025641, or 102.5641%).
40 ÷ 39 = 1.025641 (102.5641%)
Visual Representation
The diagram below illustrates 4/12 plus 9/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 40/39 |
| Mixed Number Form | 1 1/39 |
| Decimal Form | 1.025641 |
| Percentage | 102.5641% |
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Frequently Asked Questions
What is 4/12 plus 9/13 as a fraction?
4/12 + 9/13 in simplest fraction form is 40/39 (or 1 1/39 as a mixed number).
What is 4/12 plus 9/13 as a decimal?
4/12 + 9/13 converted to a decimal is 1.025641.
What is 4/12 plus 9/13 as a percentage?
4/12 + 9/13 expressed as a percentage is 102.5641%.
How do you write 4/12 plus 9/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 40/39 can be written as the mixed number 1 1/39.
Does 4/12 plus 9/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.025641...) because the denominator contains prime factors other than 2 and 5.