What is 7/24 plus 10/13?
7/24 plus 10/13 equals 331/312 (or 1 19/312 as a mixed number) (or 1.060897 in decimal form). Learn the step-by-step solution to add 7/24 and 10/13 using Least Common Denominator and simplification.
Exact Answer
7/24 + 10/13 = 331/312
Simplified Fraction
331/312
Mixed Number
1 19/312
Decimal Value
1.060897
Percentage
106.0897%
Step-by-Step Solution: 7/24 + 10/13
Step 1
Find the Least Common Denominator (LCD)
The denominators 24 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 24 × 13 = 312.
LCD(24, 13) = 312
Step 2
Convert to Equivalent Fractions with Common Denominator 312
Multiply the numerator and denominator of 7/24 by 13, and multiply the numerator and denominator of 10/13 by 24 so both fractions share the common base 312.
7 × 13/24 × 13 = 91/312 and 10 × 24/13 × 24 = 240/312
Step 3
Add the Numerators
Now add the numerators (91 + 240 = 331) and keep the common denominator 312 unchanged.
91 + 240/312 = 331/312
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 331 and 312 is 1, confirming that 331/312 cannot be reduced further—it is already in its simplest irreducible form.
331/312
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (331) is greater than the denominator (312), divide 331 by 312: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/312.
331/312 = 119/312
Step 6
Decimal & Percentage Representation
Dividing the numerator 331 by denominator 312 produces a repeating decimal (approximately 1.060897, or 106.0897%).
331 ÷ 312 = 1.060897 (106.0897%)
Visual Representation
The diagram below illustrates 7/24 plus 10/13 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 331/312 |
| Mixed Number Form | 1 19/312 |
| Decimal Form | 1.060897 |
| Percentage | 106.0897% |
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Frequently Asked Questions
What is 7/24 plus 10/13 as a fraction?
7/24 + 10/13 in simplest fraction form is 331/312 (or 1 19/312 as a mixed number).
What is 7/24 plus 10/13 as a decimal?
7/24 + 10/13 converted to a decimal is 1.060897.
What is 7/24 plus 10/13 as a percentage?
7/24 + 10/13 expressed as a percentage is 106.0897%.
How do you write 7/24 plus 10/13 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 331/312 can be written as the mixed number 1 19/312.
Does 7/24 plus 10/13 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.060897...) because the denominator contains prime factors other than 2 and 5.