What is 4/6 plus 10/13?
4/6 plus 10/13 equals 56/39 (or 1 17/39 as a mixed number) (or 1.435897 in decimal form). Learn the step-by-step solution to add 4/6 and 10/13 using Least Common Denominator and simplification.
Exact Answer
4/6 + 10/13 = 56/39
Simplified Fraction
56/39
Mixed Number
1 17/39
Decimal Value
1.435897
Percentage
143.5897%
Step-by-Step Solution: 4/6 + 10/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 6 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 13 = 78.
LCD(6, 13) = 78
Step 2
Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 4/6 by 13, and multiply the numerator and denominator of 10/13 by 6 so both fractions share the common base 78.
4 × 13/6 × 13 = 52/78 and 10 × 6/13 × 6 = 60/78
Step 3
Add the Numerators
Now add the numerators (52 + 60 = 112) and keep the common denominator 78 unchanged.
52 + 60/78 = 112/78
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 112 and 78, which is 2. Divide both the numerator and denominator by 2.
112 ÷ 2/78 ÷ 2 = 56/39
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (56) is greater than the denominator (39), divide 56 by 39: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/39.
56/39 = 117/39
Step 6
Decimal & Percentage Representation
Dividing the numerator 56 by denominator 39 produces a repeating decimal (approximately 1.435897, or 143.5897%).
56 ÷ 39 = 1.435897 (143.5897%)
Visual Representation
The diagram below illustrates 4/6 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 56/39 |
| Mixed Number Form | 1 17/39 |
| Decimal Form | 1.435897 |
| Percentage | 143.5897% |
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Frequently Asked Questions
What is 4/6 plus 10/13 as a fraction?
4/6 + 10/13 in simplest fraction form is 56/39 (or 1 17/39 as a mixed number).
What is 4/6 plus 10/13 as a decimal?
4/6 + 10/13 converted to a decimal is 1.435897.
What is 4/6 plus 10/13 as a percentage?
4/6 + 10/13 expressed as a percentage is 143.5897%.
How do you write 4/6 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 56/39 can be written as the mixed number 1 17/39.
Does 4/6 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.435897...) because the denominator contains prime factors other than 2 and 5.