What is 3/13 plus 4/7? (Answer: 73/91)

Exact Answer

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Problem: What is 3/13 plus 4/7?
Formula / Expression: 3/13 + 4/7
Final Answer: 73/91
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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 3/13 by 7, and multiply the numerator and denominator of 4/7 by 13 so both fractions share the common base 91.
Working: 3 × 7/13 × 7 = 21/91 and 4 × 13/7 × 13 = 52/91

Step 3: Add the Numerators
Now add the numerators (21 + 52 = 73) and keep the common denominator 91 unchanged.
Working: 21 + 52/91 = 73/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 91 is 1, confirming that 73/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 91 produces a repeating decimal (approximately 0.802198, or 80.2198%).
Working: 73 ÷ 91 = 0.802198 (80.2198%)

Key Values:
- Simplified Fraction: 73/91
- Mixed Number Form: 73/91
- Decimal Value: 0.802198
- Percentage: 80.2198%

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Solved with FractionsCalc:
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3/13 + 4/7 = 73/91

Simplified Fraction

73/91

Mixed Number

Proper (73/91)

Decimal Value

0.802198

Percentage

80.2198%

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

3 × 7/13 × 7 = 21/91 and 4 × 13/7 × 13 = 52/91

Step 3

Add the Numerators

Now add the numerators (21 + 52 = 73) and keep the common denominator 91 unchanged.

21 + 52/91 = 73/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 91 is 1, confirming that 73/91 cannot be reduced further—it is already in its simplest irreducible form.

73/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 91 produces a repeating decimal (approximately 0.802198, or 80.2198%).

73 ÷ 91 = 0.802198 (80.2198%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/91`
Mixed Number Form	`73/91`
Decimal Form	`0.802198`
Percentage	`80.2198%`

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Frequently Asked Questions

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

3/13 + 4/7 in simplest fraction form is 73/91.

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

3/13 + 4/7 converted to a decimal is 0.802198.

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

3/13 + 4/7 expressed as a percentage is 80.2198%.

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

It results in a repeating decimal (approximately 0.802198...) because the denominator contains prime factors other than 2 and 5.