What is 3/10 plus 11/13? (Answer: 149/130)

Exact Answer

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Problem: What is 3/10 plus 11/13?
Formula / Expression: 3/10 + 11/13
Final Answer: 1 19/130 (149/130)
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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 3/10 by 13, and multiply the numerator and denominator of 11/13 by 10 so both fractions share the common base 130.
Working: 3 × 13/10 × 13 = 39/130 and 11 × 10/13 × 10 = 110/130

Step 3: Add the Numerators
Now add the numerators (39 + 110 = 149) and keep the common denominator 130 unchanged.
Working: 39 + 110/130 = 149/130

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 149 and 130 is 1, confirming that 149/130 cannot be reduced further—it is already in its simplest irreducible form.
Working: 149/130

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (149) is greater than the denominator (130), divide 149 by 130: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/130.
Working: 149/130 = 1 19/130

Step 6: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 130 produces a repeating decimal (approximately 1.146154, or 114.6154%).
Working: 149 ÷ 130 = 1.146154 (114.6154%)

Key Values:
- Simplified Fraction: 149/130
- Mixed Number Form: 1 19/130
- Decimal Value: 1.146154
- Percentage: 114.6154%

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Solved with FractionsCalc:
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3/10 + 11/13 = 149/130

Simplified Fraction

149/130

Mixed Number

1 19/130

Decimal Value

1.146154

Percentage

114.6154%

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Step-by-Step Solution: 3/10 + 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 3/10 by 13, and multiply the numerator and denominator of 11/13 by 10 so both fractions share the common base 130.

3 × 13/10 × 13 = 39/130 and 11 × 10/13 × 10 = 110/130

Step 3

Add the Numerators

Now add the numerators (39 + 110 = 149) and keep the common denominator 130 unchanged.

39 + 110/130 = 149/130

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 149 and 130 is 1, confirming that 149/130 cannot be reduced further—it is already in its simplest irreducible form.

149/130

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (149) is greater than the denominator (130), divide 149 by 130: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/130.

149/130 = 119/130

Step 6

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 130 produces a repeating decimal (approximately 1.146154, or 114.6154%).

149 ÷ 130 = 1.146154 (114.6154%)

Visual Representation

The diagram below illustrates 3/10 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/130`
Mixed Number Form	`1 19/130`
Decimal Form	`1.146154`
Percentage	`114.6154%`

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Frequently Asked Questions

What is 3/10 plus 11/13 as a fraction?

3/10 + 11/13 in simplest fraction form is 149/130 (or 1 19/130 as a mixed number).

What is 3/10 plus 11/13 as a decimal?

3/10 + 11/13 converted to a decimal is 1.146154.

What is 3/10 plus 11/13 as a percentage?

3/10 + 11/13 expressed as a percentage is 114.6154%.

How do you write 3/10 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 149/130 can be written as the mixed number 1 19/130.

Does 3/10 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.146154...) because the denominator contains prime factors other than 2 and 5.