What is 1/9 plus 7/13? (Answer: 76/117)

Exact Answer

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Problem: What is 1/9 plus 7/13?
Formula / Expression: 1/9 + 7/13
Final Answer: 76/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.
Working: LCD(9, 13) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 1/9 by 13, and multiply the numerator and denominator of 7/13 by 9 so both fractions share the common base 117.
Working: 1 × 13/9 × 13 = 13/117 and 7 × 9/13 × 9 = 63/117

Step 3: Add the Numerators
Now add the numerators (13 + 63 = 76) and keep the common denominator 117 unchanged.
Working: 13 + 63/117 = 76/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 117 is 1, confirming that 76/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 117 produces a repeating decimal (approximately 0.649573, or 64.9573%).
Working: 76 ÷ 117 = 0.649573 (64.9573%)

Key Values:
- Simplified Fraction: 76/117
- Mixed Number Form: 76/117
- Decimal Value: 0.649573
- Percentage: 64.9573%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-7-13/
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1/9 + 7/13 = 76/117

Simplified Fraction

76/117

Mixed Number

Proper (76/117)

Decimal Value

0.649573

Percentage

64.9573%

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Step-by-Step Solution: 1/9 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 13 = 117.

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 1/9 by 13, and multiply the numerator and denominator of 7/13 by 9 so both fractions share the common base 117.

1 × 13/9 × 13 = 13/117 and 7 × 9/13 × 9 = 63/117

Step 3

Add the Numerators

Now add the numerators (13 + 63 = 76) and keep the common denominator 117 unchanged.

13 + 63/117 = 76/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 117 is 1, confirming that 76/117 cannot be reduced further—it is already in its simplest irreducible form.

76/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 117 produces a repeating decimal (approximately 0.649573, or 64.9573%).

76 ÷ 117 = 0.649573 (64.9573%)

Visual Representation

The diagram below illustrates 1/9 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/117`
Mixed Number Form	`76/117`
Decimal Form	`0.649573`
Percentage	`64.9573%`

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Frequently Asked Questions

What is 1/9 plus 7/13 as a fraction?

1/9 + 7/13 in simplest fraction form is 76/117.

What is 1/9 plus 7/13 as a decimal?

1/9 + 7/13 converted to a decimal is 0.649573.

What is 1/9 plus 7/13 as a percentage?

1/9 + 7/13 expressed as a percentage is 64.9573%.

Does 1/9 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.649573...) because the denominator contains prime factors other than 2 and 5.