What is 10/18 plus 10/13? (Answer: 155/117)

Exact Answer

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Problem: What is 10/18 plus 10/13?
Formula / Expression: 10/18 + 10/13
Final Answer: 1 38/117 (155/117)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 13 = 234.
Working: LCD(18, 13) = 234

Step 2: Convert to Equivalent Fractions with Common Denominator 234
Multiply the numerator and denominator of 10/18 by 13, and multiply the numerator and denominator of 10/13 by 18 so both fractions share the common base 234.
Working: 10 × 13/18 × 13 = 130/234 and 10 × 18/13 × 18 = 180/234

Step 3: Add the Numerators
Now add the numerators (130 + 180 = 310) and keep the common denominator 234 unchanged.
Working: 130 + 180/234 = 310/234

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 310 and 234, which is 2. Divide both the numerator and denominator by 2.
Working: 310 ÷ 2/234 ÷ 2 = 155/117

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (155) is greater than the denominator (117), divide 155 by 117: it goes in 1 whole time(s) with a remainder of 38, giving the mixed number 1 38/117.
Working: 155/117 = 1 38/117

Step 6: Decimal & Percentage Representation
Dividing the numerator 155 by denominator 117 produces a repeating decimal (approximately 1.324786, or 132.4786%).
Working: 155 ÷ 117 = 1.324786 (132.4786%)

Key Values:
- Simplified Fraction: 155/117
- Mixed Number Form: 1 38/117
- Decimal Value: 1.324786
- Percentage: 132.4786%

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10/18 + 10/13 = 155/117

Simplified Fraction

155/117

Mixed Number

1 38/117

Decimal Value

1.324786

Percentage

132.4786%

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Step-by-Step Solution: 10/18 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 18 × 13 = 234.

LCD(18, 13) = 234

Step 2

Convert to Equivalent Fractions with Common Denominator 234

Multiply the numerator and denominator of 10/18 by 13, and multiply the numerator and denominator of 10/13 by 18 so both fractions share the common base 234.

10 × 13/18 × 13 = 130/234 and 10 × 18/13 × 18 = 180/234

Step 3

Add the Numerators

Now add the numerators (130 + 180 = 310) and keep the common denominator 234 unchanged.

130 + 180/234 = 310/234

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 310 and 234, which is 2. Divide both the numerator and denominator by 2.

310 ÷ 2/234 ÷ 2 = 155/117

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (155) is greater than the denominator (117), divide 155 by 117: it goes in 1 whole time(s) with a remainder of 38, giving the mixed number 1 38/117.

155/117 = 138/117

Step 6

Decimal & Percentage Representation

Dividing the numerator 155 by denominator 117 produces a repeating decimal (approximately 1.324786, or 132.4786%).

155 ÷ 117 = 1.324786 (132.4786%)

Visual Representation

The diagram below illustrates 10/18 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`155/117`
Mixed Number Form	`1 38/117`
Decimal Form	`1.324786`
Percentage	`132.4786%`

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Frequently Asked Questions

What is 10/18 plus 10/13 as a fraction?

10/18 + 10/13 in simplest fraction form is 155/117 (or 1 38/117 as a mixed number).

What is 10/18 plus 10/13 as a decimal?

10/18 + 10/13 converted to a decimal is 1.324786.

What is 10/18 plus 10/13 as a percentage?

10/18 + 10/13 expressed as a percentage is 132.4786%.

How do you write 10/18 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 155/117 can be written as the mixed number 1 38/117.

Does 10/18 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.324786...) because the denominator contains prime factors other than 2 and 5.