What is 10/24 plus 9/13? (Answer: 173/156)

Exact Answer

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Problem: What is 10/24 plus 9/13?
Formula / Expression: 10/24 + 9/13
Final Answer: 1 17/156 (173/156)
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Step-by-Step Solution:

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.
Working: LCD(24, 13) = 312

Step 2: Convert to Equivalent Fractions with Common Denominator 312
Multiply the numerator and denominator of 10/24 by 13, and multiply the numerator and denominator of 9/13 by 24 so both fractions share the common base 312.
Working: 10 × 13/24 × 13 = 130/312 and 9 × 24/13 × 24 = 216/312

Step 3: Add the Numerators
Now add the numerators (130 + 216 = 346) and keep the common denominator 312 unchanged.
Working: 130 + 216/312 = 346/312

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 346 and 312, which is 2. Divide both the numerator and denominator by 2.
Working: 346 ÷ 2/312 ÷ 2 = 173/156

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (173) is greater than the denominator (156), divide 173 by 156: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/156.
Working: 173/156 = 1 17/156

Step 6: Decimal & Percentage Representation
Dividing the numerator 173 by denominator 156 produces a repeating decimal (approximately 1.108974, or 110.8974%).
Working: 173 ÷ 156 = 1.108974 (110.8974%)

Key Values:
- Simplified Fraction: 173/156
- Mixed Number Form: 1 17/156
- Decimal Value: 1.108974
- Percentage: 110.8974%

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Solved with FractionsCalc:
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10/24 + 9/13 = 173/156

Simplified Fraction

173/156

Mixed Number

1 17/156

Decimal Value

1.108974

Percentage

110.8974%

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Step-by-Step Solution: 10/24 + 9/13

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 10/24 by 13, and multiply the numerator and denominator of 9/13 by 24 so both fractions share the common base 312.

10 × 13/24 × 13 = 130/312 and 9 × 24/13 × 24 = 216/312

Step 3

Add the Numerators

Now add the numerators (130 + 216 = 346) and keep the common denominator 312 unchanged.

130 + 216/312 = 346/312

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 346 and 312, which is 2. Divide both the numerator and denominator by 2.

346 ÷ 2/312 ÷ 2 = 173/156

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (173) is greater than the denominator (156), divide 173 by 156: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/156.

173/156 = 117/156

Step 6

Decimal & Percentage Representation

Dividing the numerator 173 by denominator 156 produces a repeating decimal (approximately 1.108974, or 110.8974%).

173 ÷ 156 = 1.108974 (110.8974%)

Visual Representation

The diagram below illustrates 10/24 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`173/156`
Mixed Number Form	`1 17/156`
Decimal Form	`1.108974`
Percentage	`110.8974%`

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Frequently Asked Questions

What is 10/24 plus 9/13 as a fraction?

10/24 + 9/13 in simplest fraction form is 173/156 (or 1 17/156 as a mixed number).

What is 10/24 plus 9/13 as a decimal?

10/24 + 9/13 converted to a decimal is 1.108974.

What is 10/24 plus 9/13 as a percentage?

10/24 + 9/13 expressed as a percentage is 110.8974%.

How do you write 10/24 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 173/156 can be written as the mixed number 1 17/156.

Does 10/24 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.108974...) because the denominator contains prime factors other than 2 and 5.