What is 5/16 plus 9/13? (Answer: 209/208)

Exact Answer

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Problem: What is 5/16 plus 9/13?
Formula / Expression: 5/16 + 9/13
Final Answer: 1 1/208 (209/208)
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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 5/16 by 13, and multiply the numerator and denominator of 9/13 by 16 so both fractions share the common base 208.
Working: 5 × 13/16 × 13 = 65/208 and 9 × 16/13 × 16 = 144/208

Step 3: Add the Numerators
Now add the numerators (65 + 144 = 209) and keep the common denominator 208 unchanged.
Working: 65 + 144/208 = 209/208

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 208 is 1, confirming that 209/208 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/208

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (209) is greater than the denominator (208), divide 209 by 208: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/208.
Working: 209/208 = 1 1/208

Step 6: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 208 produces a repeating decimal (approximately 1.004808, or 100.4808%).
Working: 209 ÷ 208 = 1.004808 (100.4808%)

Key Values:
- Simplified Fraction: 209/208
- Mixed Number Form: 1 1/208
- Decimal Value: 1.004808
- Percentage: 100.4808%

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Solved with FractionsCalc:
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5/16 + 9/13 = 209/208

Simplified Fraction

209/208

Mixed Number

1 1/208

Decimal Value

1.004808

Percentage

100.4808%

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Step-by-Step Solution: 5/16 + 9/13

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 5/16 by 13, and multiply the numerator and denominator of 9/13 by 16 so both fractions share the common base 208.

5 × 13/16 × 13 = 65/208 and 9 × 16/13 × 16 = 144/208

Step 3

Add the Numerators

Now add the numerators (65 + 144 = 209) and keep the common denominator 208 unchanged.

65 + 144/208 = 209/208

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 208 is 1, confirming that 209/208 cannot be reduced further—it is already in its simplest irreducible form.

209/208

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (209) is greater than the denominator (208), divide 209 by 208: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/208.

209/208 = 11/208

Step 6

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 208 produces a repeating decimal (approximately 1.004808, or 100.4808%).

209 ÷ 208 = 1.004808 (100.4808%)

Visual Representation

The diagram below illustrates 5/16 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/208`
Mixed Number Form	`1 1/208`
Decimal Form	`1.004808`
Percentage	`100.4808%`

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Frequently Asked Questions

What is 5/16 plus 9/13 as a fraction?

5/16 + 9/13 in simplest fraction form is 209/208 (or 1 1/208 as a mixed number).

What is 5/16 plus 9/13 as a decimal?

5/16 + 9/13 converted to a decimal is 1.004808.

What is 5/16 plus 9/13 as a percentage?

5/16 + 9/13 expressed as a percentage is 100.4808%.

How do you write 5/16 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 209/208 can be written as the mixed number 1 1/208.

Does 5/16 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.004808...) because the denominator contains prime factors other than 2 and 5.