What is 2/8 plus 10/13? (Answer: 53/52)

Exact Answer

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Problem: What is 2/8 plus 10/13?
Formula / Expression: 2/8 + 10/13
Final Answer: 1 1/52 (53/52)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.
Working: LCD(8, 13) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 2/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.
Working: 2 × 13/8 × 13 = 26/104 and 10 × 8/13 × 8 = 80/104

Step 3: Add the Numerators
Now add the numerators (26 + 80 = 106) and keep the common denominator 104 unchanged.
Working: 26 + 80/104 = 106/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 104, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/104 ÷ 2 = 53/52

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (52), divide 53 by 52: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/52.
Working: 53/52 = 1 1/52

Step 6: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 52 produces a repeating decimal (approximately 1.019231, or 101.9231%).
Working: 53 ÷ 52 = 1.019231 (101.9231%)

Key Values:
- Simplified Fraction: 53/52
- Mixed Number Form: 1 1/52
- Decimal Value: 1.019231
- Percentage: 101.9231%

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Solved with FractionsCalc:
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2/8 + 10/13 = 53/52

Simplified Fraction

53/52

Mixed Number

1 1/52

Decimal Value

1.019231

Percentage

101.9231%

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Step-by-Step Solution: 2/8 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 2/8 by 13, and multiply the numerator and denominator of 10/13 by 8 so both fractions share the common base 104.

2 × 13/8 × 13 = 26/104 and 10 × 8/13 × 8 = 80/104

Step 3

Add the Numerators

Now add the numerators (26 + 80 = 106) and keep the common denominator 104 unchanged.

26 + 80/104 = 106/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 104, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/104 ÷ 2 = 53/52

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (53) is greater than the denominator (52), divide 53 by 52: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/52.

53/52 = 11/52

Step 6

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 52 produces a repeating decimal (approximately 1.019231, or 101.9231%).

53 ÷ 52 = 1.019231 (101.9231%)

Visual Representation

The diagram below illustrates 2/8 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/52`
Mixed Number Form	`1 1/52`
Decimal Form	`1.019231`
Percentage	`101.9231%`

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Frequently Asked Questions

What is 2/8 plus 10/13 as a fraction?

2/8 + 10/13 in simplest fraction form is 53/52 (or 1 1/52 as a mixed number).

What is 2/8 plus 10/13 as a decimal?

2/8 + 10/13 converted to a decimal is 1.019231.

What is 2/8 plus 10/13 as a percentage?

2/8 + 10/13 expressed as a percentage is 101.9231%.

How do you write 2/8 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 53/52 can be written as the mixed number 1 1/52.

Does 2/8 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.019231...) because the denominator contains prime factors other than 2 and 5.