What is 2/9 plus 5/10? (Answer: 13/18)

Exact Answer

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Problem: What is 2/9 plus 5/10?
Formula / Expression: 2/9 + 5/10
Final Answer: 13/18
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 10 = 90.
Working: LCD(9, 10) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/9 by 10, and multiply the numerator and denominator of 5/10 by 9 so both fractions share the common base 90.
Working: 2 × 10/9 × 10 = 20/90 and 5 × 9/10 × 9 = 45/90

Step 3: Add the Numerators
Now add the numerators (20 + 45 = 65) and keep the common denominator 90 unchanged.
Working: 20 + 45/90 = 65/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 65 and 90, which is 5. Divide both the numerator and denominator by 5.
Working: 65 ÷ 5/90 ÷ 5 = 13/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 18 produces a repeating decimal (approximately 0.722222, or 72.2222%).
Working: 13 ÷ 18 = 0.722222 (72.2222%)

Key Values:
- Simplified Fraction: 13/18
- Mixed Number Form: 13/18
- Decimal Value: 0.722222
- Percentage: 72.2222%

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Solved with FractionsCalc:
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2/9 + 5/10 = 13/18

Simplified Fraction

13/18

Mixed Number

Proper (13/18)

Decimal Value

0.722222

Percentage

72.2222%

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Step-by-Step Solution: 2/9 + 5/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 10 = 90.

LCD(9, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/9 by 10, and multiply the numerator and denominator of 5/10 by 9 so both fractions share the common base 90.

2 × 10/9 × 10 = 20/90 and 5 × 9/10 × 9 = 45/90

Step 3

Add the Numerators

Now add the numerators (20 + 45 = 65) and keep the common denominator 90 unchanged.

20 + 45/90 = 65/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 65 and 90, which is 5. Divide both the numerator and denominator by 5.

65 ÷ 5/90 ÷ 5 = 13/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 18 produces a repeating decimal (approximately 0.722222, or 72.2222%).

13 ÷ 18 = 0.722222 (72.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 5/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/18`
Mixed Number Form	`13/18`
Decimal Form	`0.722222`
Percentage	`72.2222%`

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Frequently Asked Questions

What is 2/9 plus 5/10 as a fraction?

2/9 + 5/10 in simplest fraction form is 13/18.

What is 2/9 plus 5/10 as a decimal?

2/9 + 5/10 converted to a decimal is 0.722222.

What is 2/9 plus 5/10 as a percentage?

2/9 + 5/10 expressed as a percentage is 72.2222%.

Does 2/9 plus 5/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.722222...) because the denominator contains prime factors other than 2 and 5.