What is 1/3 plus 10/13? (Answer: 43/39)

Exact Answer

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Problem: What is 1/3 plus 10/13?
Formula / Expression: 1/3 + 10/13
Final Answer: 1 4/39 (43/39)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 13 = 39.
Working: LCD(3, 13) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 1/3 by 13, and multiply the numerator and denominator of 10/13 by 3 so both fractions share the common base 39.
Working: 1 × 13/3 × 13 = 13/39 and 10 × 3/13 × 3 = 30/39

Step 3: Add the Numerators
Now add the numerators (13 + 30 = 43) and keep the common denominator 39 unchanged.
Working: 13 + 30/39 = 43/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 39 is 1, confirming that 43/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (39), divide 43 by 39: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/39.
Working: 43/39 = 1 4/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 39 produces a repeating decimal (approximately 1.102564, or 110.2564%).
Working: 43 ÷ 39 = 1.102564 (110.2564%)

Key Values:
- Simplified Fraction: 43/39
- Mixed Number Form: 1 4/39
- Decimal Value: 1.102564
- Percentage: 110.2564%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-3-plus-10-13/
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1/3 + 10/13 = 43/39

Simplified Fraction

43/39

Mixed Number

1 4/39

Decimal Value

1.102564

Percentage

110.2564%

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Step-by-Step Solution: 1/3 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 13 = 39.

LCD(3, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 1/3 by 13, and multiply the numerator and denominator of 10/13 by 3 so both fractions share the common base 39.

1 × 13/3 × 13 = 13/39 and 10 × 3/13 × 3 = 30/39

Step 3

Add the Numerators

Now add the numerators (13 + 30 = 43) and keep the common denominator 39 unchanged.

13 + 30/39 = 43/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 39 is 1, confirming that 43/39 cannot be reduced further—it is already in its simplest irreducible form.

43/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (39), divide 43 by 39: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/39.

43/39 = 14/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 39 produces a repeating decimal (approximately 1.102564, or 110.2564%).

43 ÷ 39 = 1.102564 (110.2564%)

Visual Representation

The diagram below illustrates 1/3 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/39`
Mixed Number Form	`1 4/39`
Decimal Form	`1.102564`
Percentage	`110.2564%`

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Frequently Asked Questions

What is 1/3 plus 10/13 as a fraction?

1/3 + 10/13 in simplest fraction form is 43/39 (or 1 4/39 as a mixed number).

What is 1/3 plus 10/13 as a decimal?

1/3 + 10/13 converted to a decimal is 1.102564.

What is 1/3 plus 10/13 as a percentage?

1/3 + 10/13 expressed as a percentage is 110.2564%.

How do you write 1/3 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 43/39 can be written as the mixed number 1 4/39.

Does 1/3 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.102564...) because the denominator contains prime factors other than 2 and 5.