What is 4/13 plus 3/7? (Answer: 67/91)

Exact Answer

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Problem: What is 4/13 plus 3/7?
Formula / Expression: 4/13 + 3/7
Final Answer: 67/91
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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 4/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.
Working: 4 × 7/13 × 7 = 28/91 and 3 × 13/7 × 13 = 39/91

Step 3: Add the Numerators
Now add the numerators (28 + 39 = 67) and keep the common denominator 91 unchanged.
Working: 28 + 39/91 = 67/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 91 is 1, confirming that 67/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 91 produces a repeating decimal (approximately 0.736264, or 73.6264%).
Working: 67 ÷ 91 = 0.736264 (73.6264%)

Key Values:
- Simplified Fraction: 67/91
- Mixed Number Form: 67/91
- Decimal Value: 0.736264
- Percentage: 73.6264%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-13-plus-3-7/
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4/13 + 3/7 = 67/91

Simplified Fraction

67/91

Mixed Number

Proper (67/91)

Decimal Value

0.736264

Percentage

73.6264%

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Step-by-Step Solution: 4/13 + 3/7

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 4/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.

4 × 7/13 × 7 = 28/91 and 3 × 13/7 × 13 = 39/91

Step 3

Add the Numerators

Now add the numerators (28 + 39 = 67) and keep the common denominator 91 unchanged.

28 + 39/91 = 67/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 91 is 1, confirming that 67/91 cannot be reduced further—it is already in its simplest irreducible form.

67/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 91 produces a repeating decimal (approximately 0.736264, or 73.6264%).

67 ÷ 91 = 0.736264 (73.6264%)

Visual Representation

The diagram below illustrates 4/13 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/91`
Mixed Number Form	`67/91`
Decimal Form	`0.736264`
Percentage	`73.6264%`

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Frequently Asked Questions

What is 4/13 plus 3/7 as a fraction?

4/13 + 3/7 in simplest fraction form is 67/91.

What is 4/13 plus 3/7 as a decimal?

4/13 + 3/7 converted to a decimal is 0.736264.

What is 4/13 plus 3/7 as a percentage?

4/13 + 3/7 expressed as a percentage is 73.6264%.

Does 4/13 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.736264...) because the denominator contains prime factors other than 2 and 5.