What is 24/48 plus 9/13? (Answer: 31/26)

Exact Answer

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Problem: What is 24/48 plus 9/13?
Formula / Expression: 24/48 + 9/13
Final Answer: 1 5/26 (31/26)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.
Working: LCD(48, 13) = 624

Step 2: Convert to Equivalent Fractions with Common Denominator 624
Multiply the numerator and denominator of 24/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.
Working: 24 × 13/48 × 13 = 312/624 and 9 × 48/13 × 48 = 432/624

Step 3: Add the Numerators
Now add the numerators (312 + 432 = 744) and keep the common denominator 624 unchanged.
Working: 312 + 432/624 = 744/624

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 744 and 624, which is 24. Divide both the numerator and denominator by 24.
Working: 744 ÷ 24/624 ÷ 24 = 31/26

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (26), divide 31 by 26: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/26.
Working: 31/26 = 1 5/26

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 26 produces a repeating decimal (approximately 1.192308, or 119.2308%).
Working: 31 ÷ 26 = 1.192308 (119.2308%)

Key Values:
- Simplified Fraction: 31/26
- Mixed Number Form: 1 5/26
- Decimal Value: 1.192308
- Percentage: 119.2308%

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Solved with FractionsCalc:
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24/48 + 9/13 = 31/26

Simplified Fraction

31/26

Mixed Number

1 5/26

Decimal Value

1.192308

Percentage

119.2308%

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Step-by-Step Solution: 24/48 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 48 × 13 = 624.

LCD(48, 13) = 624

Step 2

Convert to Equivalent Fractions with Common Denominator 624

Multiply the numerator and denominator of 24/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.

24 × 13/48 × 13 = 312/624 and 9 × 48/13 × 48 = 432/624

Step 3

Add the Numerators

Now add the numerators (312 + 432 = 744) and keep the common denominator 624 unchanged.

312 + 432/624 = 744/624

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 744 and 624, which is 24. Divide both the numerator and denominator by 24.

744 ÷ 24/624 ÷ 24 = 31/26

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (26), divide 31 by 26: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/26.

31/26 = 15/26

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 26 produces a repeating decimal (approximately 1.192308, or 119.2308%).

31 ÷ 26 = 1.192308 (119.2308%)

Visual Representation

The diagram below illustrates 24/48 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/26`
Mixed Number Form	`1 5/26`
Decimal Form	`1.192308`
Percentage	`119.2308%`

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Frequently Asked Questions

What is 24/48 plus 9/13 as a fraction?

24/48 + 9/13 in simplest fraction form is 31/26 (or 1 5/26 as a mixed number).

What is 24/48 plus 9/13 as a decimal?

24/48 + 9/13 converted to a decimal is 1.192308.

What is 24/48 plus 9/13 as a percentage?

24/48 + 9/13 expressed as a percentage is 119.2308%.

How do you write 24/48 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/26 can be written as the mixed number 1 5/26.

Does 24/48 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.192308...) because the denominator contains prime factors other than 2 and 5.