What is 3/10 plus 10/13? (Answer: 139/130)

Exact Answer

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Problem: What is 3/10 plus 10/13?
Formula / Expression: 3/10 + 10/13
Final Answer: 1 9/130 (139/130)
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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 10/13 by 10 so both fractions share the common base 130.
Working: 3 × 13/10 × 13 = 39/130 and 10 × 10/13 × 10 = 100/130

Step 3: Add the Numerators
Now add the numerators (39 + 100 = 139) and keep the common denominator 130 unchanged.
Working: 39 + 100/130 = 139/130

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 130 is 1, confirming that 139/130 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/130

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (139) is greater than the denominator (130), divide 139 by 130: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/130.
Working: 139/130 = 1 9/130

Step 6: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 130 produces a repeating decimal (approximately 1.069231, or 106.9231%).
Working: 139 ÷ 130 = 1.069231 (106.9231%)

Key Values:
- Simplified Fraction: 139/130
- Mixed Number Form: 1 9/130
- Decimal Value: 1.069231
- Percentage: 106.9231%

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3/10 + 10/13 = 139/130

Simplified Fraction

139/130

Mixed Number

1 9/130

Decimal Value

1.069231

Percentage

106.9231%

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Step-by-Step Solution: 3/10 + 10/13

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 10/13 by 10 so both fractions share the common base 130.

3 × 13/10 × 13 = 39/130 and 10 × 10/13 × 10 = 100/130

Step 3

Add the Numerators

Now add the numerators (39 + 100 = 139) and keep the common denominator 130 unchanged.

39 + 100/130 = 139/130

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 130 is 1, confirming that 139/130 cannot be reduced further—it is already in its simplest irreducible form.

139/130

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (139) is greater than the denominator (130), divide 139 by 130: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/130.

139/130 = 19/130

Step 6

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 130 produces a repeating decimal (approximately 1.069231, or 106.9231%).

139 ÷ 130 = 1.069231 (106.9231%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/130`
Mixed Number Form	`1 9/130`
Decimal Form	`1.069231`
Percentage	`106.9231%`

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Frequently Asked Questions

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

3/10 + 10/13 in simplest fraction form is 139/130 (or 1 9/130 as a mixed number).

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

3/10 + 10/13 converted to a decimal is 1.069231.

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

3/10 + 10/13 expressed as a percentage is 106.9231%.

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

Because the numerator is greater than the denominator, the improper fraction 139/130 can be written as the mixed number 1 9/130.

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

It results in a repeating decimal (approximately 1.069231...) because the denominator contains prime factors other than 2 and 5.