What is 5/13 plus 4/7? (Answer: 87/91)

Exact Answer

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Problem: What is 5/13 plus 4/7?
Formula / Expression: 5/13 + 4/7
Final Answer: 87/91
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 5/13 by 7, and multiply the numerator and denominator of 4/7 by 13 so both fractions share the common base 91.
Working: 5 × 7/13 × 7 = 35/91 and 4 × 13/7 × 13 = 52/91

Step 3: Add the Numerators
Now add the numerators (35 + 52 = 87) and keep the common denominator 91 unchanged.
Working: 35 + 52/91 = 87/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 87 and 91 is 1, confirming that 87/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 87/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 87 by denominator 91 produces a repeating decimal (approximately 0.956044, or 95.6044%).
Working: 87 ÷ 91 = 0.956044 (95.6044%)

Key Values:
- Simplified Fraction: 87/91
- Mixed Number Form: 87/91
- Decimal Value: 0.956044
- Percentage: 95.6044%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-13-plus-4-7/
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5/13 + 4/7 = 87/91

Simplified Fraction

87/91

Mixed Number

Proper (87/91)

Decimal Value

0.956044

Percentage

95.6044%

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Step-by-Step Solution: 5/13 + 4/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 5/13 by 7, and multiply the numerator and denominator of 4/7 by 13 so both fractions share the common base 91.

5 × 7/13 × 7 = 35/91 and 4 × 13/7 × 13 = 52/91

Step 3

Add the Numerators

Now add the numerators (35 + 52 = 87) and keep the common denominator 91 unchanged.

35 + 52/91 = 87/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 87 and 91 is 1, confirming that 87/91 cannot be reduced further—it is already in its simplest irreducible form.

87/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 87 by denominator 91 produces a repeating decimal (approximately 0.956044, or 95.6044%).

87 ÷ 91 = 0.956044 (95.6044%)

Visual Representation

The diagram below illustrates 5/13 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`87/91`
Mixed Number Form	`87/91`
Decimal Form	`0.956044`
Percentage	`95.6044%`

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Frequently Asked Questions

What is 5/13 plus 4/7 as a fraction?

5/13 + 4/7 in simplest fraction form is 87/91.

What is 5/13 plus 4/7 as a decimal?

5/13 + 4/7 converted to a decimal is 0.956044.

What is 5/13 plus 4/7 as a percentage?

5/13 + 4/7 expressed as a percentage is 95.6044%.

Does 5/13 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.956044...) because the denominator contains prime factors other than 2 and 5.