What is 8/13 plus 10/16? (Answer: 129/104)

Exact Answer

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Problem: What is 8/13 plus 10/16?
Formula / Expression: 8/13 + 10/16
Final Answer: 1 25/104 (129/104)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 208
Multiply the numerator and denominator of 8/13 by 16, and multiply the numerator and denominator of 10/16 by 13 so both fractions share the common base 208.
Working: 8 × 16/13 × 16 = 128/208 and 10 × 13/16 × 13 = 130/208

Step 3: Add the Numerators
Now add the numerators (128 + 130 = 258) and keep the common denominator 208 unchanged.
Working: 128 + 130/208 = 258/208

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 258 and 208, which is 2. Divide both the numerator and denominator by 2.
Working: 258 ÷ 2/208 ÷ 2 = 129/104

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (129) is greater than the denominator (104), divide 129 by 104: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/104.
Working: 129/104 = 1 25/104

Step 6: Decimal & Percentage Representation
Dividing the numerator 129 by denominator 104 produces a repeating decimal (approximately 1.240385, or 124.0385%).
Working: 129 ÷ 104 = 1.240385 (124.0385%)

Key Values:
- Simplified Fraction: 129/104
- Mixed Number Form: 1 25/104
- Decimal Value: 1.240385
- Percentage: 124.0385%

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8/13 + 10/16 = 129/104

Simplified Fraction

129/104

Mixed Number

1 25/104

Decimal Value

1.240385

Percentage

124.0385%

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Step-by-Step Solution: 8/13 + 10/16

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 16) = 208

Step 2

Convert to Equivalent Fractions with Common Denominator 208

Multiply the numerator and denominator of 8/13 by 16, and multiply the numerator and denominator of 10/16 by 13 so both fractions share the common base 208.

8 × 16/13 × 16 = 128/208 and 10 × 13/16 × 13 = 130/208

Step 3

Add the Numerators

Now add the numerators (128 + 130 = 258) and keep the common denominator 208 unchanged.

128 + 130/208 = 258/208

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 258 and 208, which is 2. Divide both the numerator and denominator by 2.

258 ÷ 2/208 ÷ 2 = 129/104

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (129) is greater than the denominator (104), divide 129 by 104: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/104.

129/104 = 125/104

Step 6

Decimal & Percentage Representation

Dividing the numerator 129 by denominator 104 produces a repeating decimal (approximately 1.240385, or 124.0385%).

129 ÷ 104 = 1.240385 (124.0385%)

Visual Representation

The diagram below illustrates 8/13 plus 10/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`129/104`
Mixed Number Form	`1 25/104`
Decimal Form	`1.240385`
Percentage	`124.0385%`

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Frequently Asked Questions

What is 8/13 plus 10/16 as a fraction?

8/13 + 10/16 in simplest fraction form is 129/104 (or 1 25/104 as a mixed number).

What is 8/13 plus 10/16 as a decimal?

8/13 + 10/16 converted to a decimal is 1.240385.

What is 8/13 plus 10/16 as a percentage?

8/13 + 10/16 expressed as a percentage is 124.0385%.

How do you write 8/13 plus 10/16 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 129/104 can be written as the mixed number 1 25/104.

Does 8/13 plus 10/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.240385...) because the denominator contains prime factors other than 2 and 5.