What is 4/10 plus 11/13? (Answer: 81/65)

Exact Answer

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Problem: What is 4/10 plus 11/13?
Formula / Expression: 4/10 + 11/13
Final Answer: 1 16/65 (81/65)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 13 = 130.
Working: LCD(10, 13) = 130

Step 2: Convert to Equivalent Fractions with Common Denominator 130
Multiply the numerator and denominator of 4/10 by 13, and multiply the numerator and denominator of 11/13 by 10 so both fractions share the common base 130.
Working: 4 × 13/10 × 13 = 52/130 and 11 × 10/13 × 10 = 110/130

Step 3: Add the Numerators
Now add the numerators (52 + 110 = 162) and keep the common denominator 130 unchanged.
Working: 52 + 110/130 = 162/130

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 162 and 130, which is 2. Divide both the numerator and denominator by 2.
Working: 162 ÷ 2/130 ÷ 2 = 81/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (81) is greater than the denominator (65), divide 81 by 65: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/65.
Working: 81/65 = 1 16/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 65 produces a repeating decimal (approximately 1.246154, or 124.6154%).
Working: 81 ÷ 65 = 1.246154 (124.6154%)

Key Values:
- Simplified Fraction: 81/65
- Mixed Number Form: 1 16/65
- Decimal Value: 1.246154
- Percentage: 124.6154%

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Solved with FractionsCalc:
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4/10 + 11/13 = 81/65

Simplified Fraction

81/65

Mixed Number

1 16/65

Decimal Value

1.246154

Percentage

124.6154%

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Step-by-Step Solution: 4/10 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 13 = 130.

LCD(10, 13) = 130

Step 2

Convert to Equivalent Fractions with Common Denominator 130

Multiply the numerator and denominator of 4/10 by 13, and multiply the numerator and denominator of 11/13 by 10 so both fractions share the common base 130.

4 × 13/10 × 13 = 52/130 and 11 × 10/13 × 10 = 110/130

Step 3

Add the Numerators

Now add the numerators (52 + 110 = 162) and keep the common denominator 130 unchanged.

52 + 110/130 = 162/130

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 162 and 130, which is 2. Divide both the numerator and denominator by 2.

162 ÷ 2/130 ÷ 2 = 81/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (81) is greater than the denominator (65), divide 81 by 65: it goes in 1 whole time(s) with a remainder of 16, giving the mixed number 1 16/65.

81/65 = 116/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 65 produces a repeating decimal (approximately 1.246154, or 124.6154%).

81 ÷ 65 = 1.246154 (124.6154%)

Visual Representation

The diagram below illustrates 4/10 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/65`
Mixed Number Form	`1 16/65`
Decimal Form	`1.246154`
Percentage	`124.6154%`

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Frequently Asked Questions

What is 4/10 plus 11/13 as a fraction?

4/10 + 11/13 in simplest fraction form is 81/65 (or 1 16/65 as a mixed number).

What is 4/10 plus 11/13 as a decimal?

4/10 + 11/13 converted to a decimal is 1.246154.

What is 4/10 plus 11/13 as a percentage?

4/10 + 11/13 expressed as a percentage is 124.6154%.

How do you write 4/10 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 81/65 can be written as the mixed number 1 16/65.

Does 4/10 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.246154...) because the denominator contains prime factors other than 2 and 5.