What is 27/48 plus 9/13? (Answer: 261/208)

Exact Answer

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Problem: What is 27/48 plus 9/13?
Formula / Expression: 27/48 + 9/13
Final Answer: 1 53/208 (261/208)
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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 27/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.
Working: 27 × 13/48 × 13 = 351/624 and 9 × 48/13 × 48 = 432/624

Step 3: Add the Numerators
Now add the numerators (351 + 432 = 783) and keep the common denominator 624 unchanged.
Working: 351 + 432/624 = 783/624

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 783 and 624, which is 3. Divide both the numerator and denominator by 3.
Working: 783 ÷ 3/624 ÷ 3 = 261/208

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (261) is greater than the denominator (208), divide 261 by 208: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/208.
Working: 261/208 = 1 53/208

Step 6: Decimal & Percentage Representation
Dividing the numerator 261 by denominator 208 produces a repeating decimal (approximately 1.254808, or 125.4808%).
Working: 261 ÷ 208 = 1.254808 (125.4808%)

Key Values:
- Simplified Fraction: 261/208
- Mixed Number Form: 1 53/208
- Decimal Value: 1.254808
- Percentage: 125.4808%

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Solved with FractionsCalc:
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27/48 + 9/13 = 261/208

Simplified Fraction

261/208

Mixed Number

1 53/208

Decimal Value

1.254808

Percentage

125.4808%

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Step-by-Step Solution: 27/48 + 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 27/48 by 13, and multiply the numerator and denominator of 9/13 by 48 so both fractions share the common base 624.

27 × 13/48 × 13 = 351/624 and 9 × 48/13 × 48 = 432/624

Step 3

Add the Numerators

Now add the numerators (351 + 432 = 783) and keep the common denominator 624 unchanged.

351 + 432/624 = 783/624

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 783 and 624, which is 3. Divide both the numerator and denominator by 3.

783 ÷ 3/624 ÷ 3 = 261/208

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (261) is greater than the denominator (208), divide 261 by 208: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/208.

261/208 = 153/208

Step 6

Decimal & Percentage Representation

Dividing the numerator 261 by denominator 208 produces a repeating decimal (approximately 1.254808, or 125.4808%).

261 ÷ 208 = 1.254808 (125.4808%)

Visual Representation

The diagram below illustrates 27/48 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`261/208`
Mixed Number Form	`1 53/208`
Decimal Form	`1.254808`
Percentage	`125.4808%`

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Frequently Asked Questions

What is 27/48 plus 9/13 as a fraction?

27/48 + 9/13 in simplest fraction form is 261/208 (or 1 53/208 as a mixed number).

What is 27/48 plus 9/13 as a decimal?

27/48 + 9/13 converted to a decimal is 1.254808.

What is 27/48 plus 9/13 as a percentage?

27/48 + 9/13 expressed as a percentage is 125.4808%.

How do you write 27/48 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 261/208 can be written as the mixed number 1 53/208.

Does 27/48 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.254808...) because the denominator contains prime factors other than 2 and 5.