What is 3/7 plus 7/13? (Answer: 88/91)

Exact Answer

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Problem: What is 3/7 plus 7/13?
Formula / Expression: 3/7 + 7/13
Final Answer: 88/91
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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 3/7 by 13, and multiply the numerator and denominator of 7/13 by 7 so both fractions share the common base 91.
Working: 3 × 13/7 × 13 = 39/91 and 7 × 7/13 × 7 = 49/91

Step 3: Add the Numerators
Now add the numerators (39 + 49 = 88) and keep the common denominator 91 unchanged.
Working: 39 + 49/91 = 88/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 88 and 91 is 1, confirming that 88/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 88/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 88 by denominator 91 produces a repeating decimal (approximately 0.967033, or 96.7033%).
Working: 88 ÷ 91 = 0.967033 (96.7033%)

Key Values:
- Simplified Fraction: 88/91
- Mixed Number Form: 88/91
- Decimal Value: 0.967033
- Percentage: 96.7033%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-7-13/
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3/7 + 7/13 = 88/91

Simplified Fraction

88/91

Mixed Number

Proper (88/91)

Decimal Value

0.967033

Percentage

96.7033%

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Step-by-Step Solution: 3/7 + 7/13

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 3/7 by 13, and multiply the numerator and denominator of 7/13 by 7 so both fractions share the common base 91.

3 × 13/7 × 13 = 39/91 and 7 × 7/13 × 7 = 49/91

Step 3

Add the Numerators

Now add the numerators (39 + 49 = 88) and keep the common denominator 91 unchanged.

39 + 49/91 = 88/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 88 and 91 is 1, confirming that 88/91 cannot be reduced further—it is already in its simplest irreducible form.

88/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 88 by denominator 91 produces a repeating decimal (approximately 0.967033, or 96.7033%).

88 ÷ 91 = 0.967033 (96.7033%)

Visual Representation

The diagram below illustrates 3/7 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`88/91`
Mixed Number Form	`88/91`
Decimal Form	`0.967033`
Percentage	`96.7033%`

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Frequently Asked Questions

What is 3/7 plus 7/13 as a fraction?

3/7 + 7/13 in simplest fraction form is 88/91.

What is 3/7 plus 7/13 as a decimal?

3/7 + 7/13 converted to a decimal is 0.967033.

What is 3/7 plus 7/13 as a percentage?

3/7 + 7/13 expressed as a percentage is 96.7033%.

Does 3/7 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.967033...) because the denominator contains prime factors other than 2 and 5.