What is 9/16 plus 10/13? (Answer: 277/208)

Exact Answer

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Problem: What is 9/16 plus 10/13?
Formula / Expression: 9/16 + 10/13
Final Answer: 1 69/208 (277/208)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 13 = 208.
Working: LCD(16, 13) = 208

Step 2: Convert to Equivalent Fractions with Common Denominator 208
Multiply the numerator and denominator of 9/16 by 13, and multiply the numerator and denominator of 10/13 by 16 so both fractions share the common base 208.
Working: 9 × 13/16 × 13 = 117/208 and 10 × 16/13 × 16 = 160/208

Step 3: Add the Numerators
Now add the numerators (117 + 160 = 277) and keep the common denominator 208 unchanged.
Working: 117 + 160/208 = 277/208

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 277 and 208 is 1, confirming that 277/208 cannot be reduced further—it is already in its simplest irreducible form.
Working: 277/208

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (277) is greater than the denominator (208), divide 277 by 208: it goes in 1 whole time(s) with a remainder of 69, giving the mixed number 1 69/208.
Working: 277/208 = 1 69/208

Step 6: Decimal & Percentage Representation
Dividing the numerator 277 by denominator 208 produces a repeating decimal (approximately 1.331731, or 133.1731%).
Working: 277 ÷ 208 = 1.331731 (133.1731%)

Key Values:
- Simplified Fraction: 277/208
- Mixed Number Form: 1 69/208
- Decimal Value: 1.331731
- Percentage: 133.1731%

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9/16 + 10/13 = 277/208

Simplified Fraction

277/208

Mixed Number

1 69/208

Decimal Value

1.331731

Percentage

133.1731%

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Step-by-Step Solution: 9/16 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 13 = 208.

LCD(16, 13) = 208

Step 2

Convert to Equivalent Fractions with Common Denominator 208

Multiply the numerator and denominator of 9/16 by 13, and multiply the numerator and denominator of 10/13 by 16 so both fractions share the common base 208.

9 × 13/16 × 13 = 117/208 and 10 × 16/13 × 16 = 160/208

Step 3

Add the Numerators

Now add the numerators (117 + 160 = 277) and keep the common denominator 208 unchanged.

117 + 160/208 = 277/208

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 277 and 208 is 1, confirming that 277/208 cannot be reduced further—it is already in its simplest irreducible form.

277/208

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (277) is greater than the denominator (208), divide 277 by 208: it goes in 1 whole time(s) with a remainder of 69, giving the mixed number 1 69/208.

277/208 = 169/208

Step 6

Decimal & Percentage Representation

Dividing the numerator 277 by denominator 208 produces a repeating decimal (approximately 1.331731, or 133.1731%).

277 ÷ 208 = 1.331731 (133.1731%)

Visual Representation

The diagram below illustrates 9/16 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`277/208`
Mixed Number Form	`1 69/208`
Decimal Form	`1.331731`
Percentage	`133.1731%`

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Frequently Asked Questions

What is 9/16 plus 10/13 as a fraction?

9/16 + 10/13 in simplest fraction form is 277/208 (or 1 69/208 as a mixed number).

What is 9/16 plus 10/13 as a decimal?

9/16 + 10/13 converted to a decimal is 1.331731.

What is 9/16 plus 10/13 as a percentage?

9/16 + 10/13 expressed as a percentage is 133.1731%.

How do you write 9/16 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 277/208 can be written as the mixed number 1 69/208.

Does 9/16 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.331731...) because the denominator contains prime factors other than 2 and 5.