What is 23/49 plus 9/13? (Answer: 740/637)

Exact Answer

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Problem: What is 23/49 plus 9/13?
Formula / Expression: 23/49 + 9/13
Final Answer: 1 103/637 (740/637)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 13 = 637.
Working: LCD(49, 13) = 637

Step 2: Convert to Equivalent Fractions with Common Denominator 637
Multiply the numerator and denominator of 23/49 by 13, and multiply the numerator and denominator of 9/13 by 49 so both fractions share the common base 637.
Working: 23 × 13/49 × 13 = 299/637 and 9 × 49/13 × 49 = 441/637

Step 3: Add the Numerators
Now add the numerators (299 + 441 = 740) and keep the common denominator 637 unchanged.
Working: 299 + 441/637 = 740/637

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 740 and 637 is 1, confirming that 740/637 cannot be reduced further—it is already in its simplest irreducible form.
Working: 740/637

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (740) is greater than the denominator (637), divide 740 by 637: it goes in 1 whole time(s) with a remainder of 103, giving the mixed number 1 103/637.
Working: 740/637 = 1 103/637

Step 6: Decimal & Percentage Representation
Dividing the numerator 740 by denominator 637 produces a repeating decimal (approximately 1.161695, or 116.1695%).
Working: 740 ÷ 637 = 1.161695 (116.1695%)

Key Values:
- Simplified Fraction: 740/637
- Mixed Number Form: 1 103/637
- Decimal Value: 1.161695
- Percentage: 116.1695%

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23/49 + 9/13 = 740/637

Simplified Fraction

740/637

Mixed Number

1 103/637

Decimal Value

1.161695

Percentage

116.1695%

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Step-by-Step Solution: 23/49 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 49 × 13 = 637.

LCD(49, 13) = 637

Step 2

Convert to Equivalent Fractions with Common Denominator 637

Multiply the numerator and denominator of 23/49 by 13, and multiply the numerator and denominator of 9/13 by 49 so both fractions share the common base 637.

23 × 13/49 × 13 = 299/637 and 9 × 49/13 × 49 = 441/637

Step 3

Add the Numerators

Now add the numerators (299 + 441 = 740) and keep the common denominator 637 unchanged.

299 + 441/637 = 740/637

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 740 and 637 is 1, confirming that 740/637 cannot be reduced further—it is already in its simplest irreducible form.

740/637

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (740) is greater than the denominator (637), divide 740 by 637: it goes in 1 whole time(s) with a remainder of 103, giving the mixed number 1 103/637.

740/637 = 1103/637

Step 6

Decimal & Percentage Representation

Dividing the numerator 740 by denominator 637 produces a repeating decimal (approximately 1.161695, or 116.1695%).

740 ÷ 637 = 1.161695 (116.1695%)

Visual Representation

The diagram below illustrates 23/49 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`740/637`
Mixed Number Form	`1 103/637`
Decimal Form	`1.161695`
Percentage	`116.1695%`

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Frequently Asked Questions

What is 23/49 plus 9/13 as a fraction?

23/49 + 9/13 in simplest fraction form is 740/637 (or 1 103/637 as a mixed number).

What is 23/49 plus 9/13 as a decimal?

23/49 + 9/13 converted to a decimal is 1.161695.

What is 23/49 plus 9/13 as a percentage?

23/49 + 9/13 expressed as a percentage is 116.1695%.

How do you write 23/49 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 740/637 can be written as the mixed number 1 103/637.

Does 23/49 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.161695...) because the denominator contains prime factors other than 2 and 5.