What is 10/13 plus 7/9? (Answer: 181/117)

Exact Answer

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Problem: What is 10/13 plus 7/9?
Formula / Expression: 10/13 + 7/9
Final Answer: 1 64/117 (181/117)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 10/13 by 9, and multiply the numerator and denominator of 7/9 by 13 so both fractions share the common base 117.
Working: 10 × 9/13 × 9 = 90/117 and 7 × 13/9 × 13 = 91/117

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 117 unchanged.
Working: 90 + 91/117 = 181/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 117 is 1, confirming that 181/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (181) is greater than the denominator (117), divide 181 by 117: it goes in 1 whole time(s) with a remainder of 64, giving the mixed number 1 64/117.
Working: 181/117 = 1 64/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 117 produces a repeating decimal (approximately 1.547009, or 154.7009%).
Working: 181 ÷ 117 = 1.547009 (154.7009%)

Key Values:
- Simplified Fraction: 181/117
- Mixed Number Form: 1 64/117
- Decimal Value: 1.547009
- Percentage: 154.7009%

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Solved with FractionsCalc:
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10/13 + 7/9 = 181/117

Simplified Fraction

181/117

Mixed Number

1 64/117

Decimal Value

1.547009

Percentage

154.7009%

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Step-by-Step Solution: 10/13 + 7/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(13, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 10/13 by 9, and multiply the numerator and denominator of 7/9 by 13 so both fractions share the common base 117.

10 × 9/13 × 9 = 90/117 and 7 × 13/9 × 13 = 91/117

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 117 unchanged.

90 + 91/117 = 181/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 117 is 1, confirming that 181/117 cannot be reduced further—it is already in its simplest irreducible form.

181/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (181) is greater than the denominator (117), divide 181 by 117: it goes in 1 whole time(s) with a remainder of 64, giving the mixed number 1 64/117.

181/117 = 164/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 117 produces a repeating decimal (approximately 1.547009, or 154.7009%).

181 ÷ 117 = 1.547009 (154.7009%)

Visual Representation

The diagram below illustrates 10/13 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/117`
Mixed Number Form	`1 64/117`
Decimal Form	`1.547009`
Percentage	`154.7009%`

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Frequently Asked Questions

What is 10/13 plus 7/9 as a fraction?

10/13 + 7/9 in simplest fraction form is 181/117 (or 1 64/117 as a mixed number).

What is 10/13 plus 7/9 as a decimal?

10/13 + 7/9 converted to a decimal is 1.547009.

What is 10/13 plus 7/9 as a percentage?

10/13 + 7/9 expressed as a percentage is 154.7009%.

How do you write 10/13 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 181/117 can be written as the mixed number 1 64/117.

Does 10/13 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.547009...) because the denominator contains prime factors other than 2 and 5.