What is 24/46 plus 9/13? (Answer: 363/299)

Exact Answer

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Problem: What is 24/46 plus 9/13?
Formula / Expression: 24/46 + 9/13
Final Answer: 1 64/299 (363/299)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.
Working: LCD(46, 13) = 598

Step 2: Convert to Equivalent Fractions with Common Denominator 598
Multiply the numerator and denominator of 24/46 by 13, and multiply the numerator and denominator of 9/13 by 46 so both fractions share the common base 598.
Working: 24 × 13/46 × 13 = 312/598 and 9 × 46/13 × 46 = 414/598

Step 3: Add the Numerators
Now add the numerators (312 + 414 = 726) and keep the common denominator 598 unchanged.
Working: 312 + 414/598 = 726/598

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 726 and 598, which is 2. Divide both the numerator and denominator by 2.
Working: 726 ÷ 2/598 ÷ 2 = 363/299

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (363) is greater than the denominator (299), divide 363 by 299: it goes in 1 whole time(s) with a remainder of 64, giving the mixed number 1 64/299.
Working: 363/299 = 1 64/299

Step 6: Decimal & Percentage Representation
Dividing the numerator 363 by denominator 299 produces a repeating decimal (approximately 1.214047, or 121.4047%).
Working: 363 ÷ 299 = 1.214047 (121.4047%)

Key Values:
- Simplified Fraction: 363/299
- Mixed Number Form: 1 64/299
- Decimal Value: 1.214047
- Percentage: 121.4047%

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Solved with FractionsCalc:
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24/46 + 9/13 = 363/299

Simplified Fraction

363/299

Mixed Number

1 64/299

Decimal Value

1.214047

Percentage

121.4047%

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Step-by-Step Solution: 24/46 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.

LCD(46, 13) = 598

Step 2

Convert to Equivalent Fractions with Common Denominator 598

Multiply the numerator and denominator of 24/46 by 13, and multiply the numerator and denominator of 9/13 by 46 so both fractions share the common base 598.

24 × 13/46 × 13 = 312/598 and 9 × 46/13 × 46 = 414/598

Step 3

Add the Numerators

Now add the numerators (312 + 414 = 726) and keep the common denominator 598 unchanged.

312 + 414/598 = 726/598

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 726 and 598, which is 2. Divide both the numerator and denominator by 2.

726 ÷ 2/598 ÷ 2 = 363/299

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (363) is greater than the denominator (299), divide 363 by 299: it goes in 1 whole time(s) with a remainder of 64, giving the mixed number 1 64/299.

363/299 = 164/299

Step 6

Decimal & Percentage Representation

Dividing the numerator 363 by denominator 299 produces a repeating decimal (approximately 1.214047, or 121.4047%).

363 ÷ 299 = 1.214047 (121.4047%)

Visual Representation

The diagram below illustrates 24/46 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`363/299`
Mixed Number Form	`1 64/299`
Decimal Form	`1.214047`
Percentage	`121.4047%`

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Frequently Asked Questions

What is 24/46 plus 9/13 as a fraction?

24/46 + 9/13 in simplest fraction form is 363/299 (or 1 64/299 as a mixed number).

What is 24/46 plus 9/13 as a decimal?

24/46 + 9/13 converted to a decimal is 1.214047.

What is 24/46 plus 9/13 as a percentage?

24/46 + 9/13 expressed as a percentage is 121.4047%.

How do you write 24/46 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 363/299 can be written as the mixed number 1 64/299.

Does 24/46 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.214047...) because the denominator contains prime factors other than 2 and 5.