What is 3/4 plus 10/13?
3/4 plus 10/13 equals 79/52 (or 1 27/52 as a mixed number) (or 1.519231 in decimal form). Learn the step-by-step solution to add 3/4 and 10/13 using Least Common Denominator and simplification.
Exact Answer
3/4 + 10/13 = 79/52
Simplified Fraction
79/52
Mixed Number
1 27/52
Decimal Value
1.519231
Percentage
151.9231%
Step-by-Step Solution: 3/4 + 10/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.
LCD(4, 13) = 52
Step 2
Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 3/4 by 13, and multiply the numerator and denominator of 10/13 by 4 so both fractions share the common base 52.
3 × 13/4 × 13 = 39/52 and 10 × 4/13 × 4 = 40/52
Step 3
Add the Numerators
Now add the numerators (39 + 40 = 79) and keep the common denominator 52 unchanged.
39 + 40/52 = 79/52
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 52 is 1, confirming that 79/52 cannot be reduced further—it is already in its simplest irreducible form.
79/52
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (52), divide 79 by 52: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/52.
79/52 = 127/52
Step 6
Decimal & Percentage Representation
Dividing the numerator 79 by denominator 52 produces a repeating decimal (approximately 1.519231, or 151.9231%).
79 ÷ 52 = 1.519231 (151.9231%)
Visual Representation
The diagram below illustrates 3/4 plus 10/13 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 79/52 |
| Mixed Number Form | 1 27/52 |
| Decimal Form | 1.519231 |
| Percentage | 151.9231% |
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Frequently Asked Questions
What is 3/4 plus 10/13 as a fraction?
3/4 + 10/13 in simplest fraction form is 79/52 (or 1 27/52 as a mixed number).
What is 3/4 plus 10/13 as a decimal?
3/4 + 10/13 converted to a decimal is 1.519231.
What is 3/4 plus 10/13 as a percentage?
3/4 + 10/13 expressed as a percentage is 151.9231%.
How do you write 3/4 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 79/52 can be written as the mixed number 1 27/52.
Does 3/4 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.519231...) because the denominator contains prime factors other than 2 and 5.