What is 10/13 plus 4/5? (Answer: 102/65)

Exact Answer

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Problem: What is 10/13 plus 4/5?
Formula / Expression: 10/13 + 4/5
Final Answer: 1 37/65 (102/65)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.
Working: LCD(13, 5) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 10/13 by 5, and multiply the numerator and denominator of 4/5 by 13 so both fractions share the common base 65.
Working: 10 × 5/13 × 5 = 50/65 and 4 × 13/5 × 13 = 52/65

Step 3: Add the Numerators
Now add the numerators (50 + 52 = 102) and keep the common denominator 65 unchanged.
Working: 50 + 52/65 = 102/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 102 and 65 is 1, confirming that 102/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 102/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (102) is greater than the denominator (65), divide 102 by 65: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/65.
Working: 102/65 = 1 37/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 102 by denominator 65 produces a repeating decimal (approximately 1.569231, or 156.9231%).
Working: 102 ÷ 65 = 1.569231 (156.9231%)

Key Values:
- Simplified Fraction: 102/65
- Mixed Number Form: 1 37/65
- Decimal Value: 1.569231
- Percentage: 156.9231%

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10/13 + 4/5 = 102/65

Simplified Fraction

102/65

Mixed Number

1 37/65

Decimal Value

1.569231

Percentage

156.9231%

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Step-by-Step Solution: 10/13 + 4/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 5 = 65.

LCD(13, 5) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 10/13 by 5, and multiply the numerator and denominator of 4/5 by 13 so both fractions share the common base 65.

10 × 5/13 × 5 = 50/65 and 4 × 13/5 × 13 = 52/65

Step 3

Add the Numerators

Now add the numerators (50 + 52 = 102) and keep the common denominator 65 unchanged.

50 + 52/65 = 102/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 102 and 65 is 1, confirming that 102/65 cannot be reduced further—it is already in its simplest irreducible form.

102/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (102) is greater than the denominator (65), divide 102 by 65: it goes in 1 whole time(s) with a remainder of 37, giving the mixed number 1 37/65.

102/65 = 137/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 102 by denominator 65 produces a repeating decimal (approximately 1.569231, or 156.9231%).

102 ÷ 65 = 1.569231 (156.9231%)

Visual Representation

The diagram below illustrates 10/13 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`102/65`
Mixed Number Form	`1 37/65`
Decimal Form	`1.569231`
Percentage	`156.9231%`

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Frequently Asked Questions

What is 10/13 plus 4/5 as a fraction?

10/13 + 4/5 in simplest fraction form is 102/65 (or 1 37/65 as a mixed number).

What is 10/13 plus 4/5 as a decimal?

10/13 + 4/5 converted to a decimal is 1.569231.

What is 10/13 plus 4/5 as a percentage?

10/13 + 4/5 expressed as a percentage is 156.9231%.

How do you write 10/13 plus 4/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 102/65 can be written as the mixed number 1 37/65.

Does 10/13 plus 4/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.569231...) because the denominator contains prime factors other than 2 and 5.