What is 4/7 plus 10/13? (Answer: 122/91)

Exact Answer

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Problem: What is 4/7 plus 10/13?
Formula / Expression: 4/7 + 10/13
Final Answer: 1 31/91 (122/91)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 13 = 91.
Working: LCD(7, 13) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 4/7 by 13, and multiply the numerator and denominator of 10/13 by 7 so both fractions share the common base 91.
Working: 4 × 13/7 × 13 = 52/91 and 10 × 7/13 × 7 = 70/91

Step 3: Add the Numerators
Now add the numerators (52 + 70 = 122) and keep the common denominator 91 unchanged.
Working: 52 + 70/91 = 122/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 122 and 91 is 1, confirming that 122/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 122/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (122) is greater than the denominator (91), divide 122 by 91: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/91.
Working: 122/91 = 1 31/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 122 by denominator 91 produces a repeating decimal (approximately 1.340659, or 134.0659%).
Working: 122 ÷ 91 = 1.340659 (134.0659%)

Key Values:
- Simplified Fraction: 122/91
- Mixed Number Form: 1 31/91
- Decimal Value: 1.340659
- Percentage: 134.0659%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-7-plus-10-13/
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4/7 + 10/13 = 122/91

Simplified Fraction

122/91

Mixed Number

1 31/91

Decimal Value

1.340659

Percentage

134.0659%

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Step-by-Step Solution: 4/7 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 13 = 91.

LCD(7, 13) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 4/7 by 13, and multiply the numerator and denominator of 10/13 by 7 so both fractions share the common base 91.

4 × 13/7 × 13 = 52/91 and 10 × 7/13 × 7 = 70/91

Step 3

Add the Numerators

Now add the numerators (52 + 70 = 122) and keep the common denominator 91 unchanged.

52 + 70/91 = 122/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 122 and 91 is 1, confirming that 122/91 cannot be reduced further—it is already in its simplest irreducible form.

122/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (122) is greater than the denominator (91), divide 122 by 91: it goes in 1 whole time(s) with a remainder of 31, giving the mixed number 1 31/91.

122/91 = 131/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 122 by denominator 91 produces a repeating decimal (approximately 1.340659, or 134.0659%).

122 ÷ 91 = 1.340659 (134.0659%)

Visual Representation

The diagram below illustrates 4/7 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`122/91`
Mixed Number Form	`1 31/91`
Decimal Form	`1.340659`
Percentage	`134.0659%`

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Frequently Asked Questions

What is 4/7 plus 10/13 as a fraction?

4/7 + 10/13 in simplest fraction form is 122/91 (or 1 31/91 as a mixed number).

What is 4/7 plus 10/13 as a decimal?

4/7 + 10/13 converted to a decimal is 1.340659.

What is 4/7 plus 10/13 as a percentage?

4/7 + 10/13 expressed as a percentage is 134.0659%.

How do you write 4/7 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 122/91 can be written as the mixed number 1 31/91.

Does 4/7 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.340659...) because the denominator contains prime factors other than 2 and 5.