What is 1/9 plus 10/39? (Answer: 43/117)

Exact Answer

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Problem: What is 1/9 plus 10/39?
Formula / Expression: 1/9 + 10/39
Final Answer: 43/117
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 117 (which is smaller than their product 9 × 39 = 351, keeping the calculation simpler).
Working: LCD(9, 39) = 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 10/39 by 3 so both fractions share the common base 117.
Working: 1 × 13/9 × 13 = 13/117 and 10 × 3/39 × 3 = 30/117

Step 3: Add the Numerators
Now add the numerators (13 + 30 = 43) and keep the common denominator 117 unchanged.
Working: 13 + 30/117 = 43/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 117 is 1, confirming that 43/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 117 produces a repeating decimal (approximately 0.367521, or 36.7521%).
Working: 43 ÷ 117 = 0.367521 (36.7521%)

Key Values:
- Simplified Fraction: 43/117
- Mixed Number Form: 43/117
- Decimal Value: 0.367521
- Percentage: 36.7521%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-10-39/
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1/9 + 10/39 = 43/117

Simplified Fraction

43/117

Mixed Number

Proper (43/117)

Decimal Value

0.367521

Percentage

36.7521%

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Step-by-Step Solution: 1/9 + 10/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 117 (which is smaller than their product 9 × 39 = 351, keeping the calculation simpler).

LCD(9, 39) = 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 10/39 by 3 so both fractions share the common base 117.

1 × 13/9 × 13 = 13/117 and 10 × 3/39 × 3 = 30/117

Step 3

Add the Numerators

Now add the numerators (13 + 30 = 43) and keep the common denominator 117 unchanged.

13 + 30/117 = 43/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 117 is 1, confirming that 43/117 cannot be reduced further—it is already in its simplest irreducible form.

43/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 117 produces a repeating decimal (approximately 0.367521, or 36.7521%).

43 ÷ 117 = 0.367521 (36.7521%)

Visual Representation

The diagram below illustrates 1/9 plus 10/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/117`
Mixed Number Form	`43/117`
Decimal Form	`0.367521`
Percentage	`36.7521%`

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Frequently Asked Questions

What is 1/9 plus 10/39 as a fraction?

1/9 + 10/39 in simplest fraction form is 43/117.

What is 1/9 plus 10/39 as a decimal?

1/9 + 10/39 converted to a decimal is 0.367521.

What is 1/9 plus 10/39 as a percentage?

1/9 + 10/39 expressed as a percentage is 36.7521%.

Does 1/9 plus 10/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.367521...) because the denominator contains prime factors other than 2 and 5.