What is 1/9 plus 2/10? (Answer: 14/45)

Exact Answer

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Problem: What is 1/9 plus 2/10?
Formula / Expression: 1/9 + 2/10
Final Answer: 14/45
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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 1/9 by 10, and multiply the numerator and denominator of 2/10 by 9 so both fractions share the common base 90.
Working: 1 × 10/9 × 10 = 10/90 and 2 × 9/10 × 9 = 18/90

Step 3: Add the Numerators
Now add the numerators (10 + 18 = 28) and keep the common denominator 90 unchanged.
Working: 10 + 18/90 = 28/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 28 ÷ 2/90 ÷ 2 = 14/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 45 produces a repeating decimal (approximately 0.311111, or 31.1111%).
Working: 14 ÷ 45 = 0.311111 (31.1111%)

Key Values:
- Simplified Fraction: 14/45
- Mixed Number Form: 14/45
- Decimal Value: 0.311111
- Percentage: 31.1111%

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Solved with FractionsCalc:
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1/9 + 2/10 = 14/45

Simplified Fraction

14/45

Mixed Number

Proper (14/45)

Decimal Value

0.311111

Percentage

31.1111%

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Step-by-Step Solution: 1/9 + 2/10

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 1/9 by 10, and multiply the numerator and denominator of 2/10 by 9 so both fractions share the common base 90.

1 × 10/9 × 10 = 10/90 and 2 × 9/10 × 9 = 18/90

Step 3

Add the Numerators

Now add the numerators (10 + 18 = 28) and keep the common denominator 90 unchanged.

10 + 18/90 = 28/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 90, which is 2. Divide both the numerator and denominator by 2.

28 ÷ 2/90 ÷ 2 = 14/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 45 produces a repeating decimal (approximately 0.311111, or 31.1111%).

14 ÷ 45 = 0.311111 (31.1111%)

Visual Representation

The diagram below illustrates 1/9 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/45`
Mixed Number Form	`14/45`
Decimal Form	`0.311111`
Percentage	`31.1111%`

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Frequently Asked Questions

What is 1/9 plus 2/10 as a fraction?

1/9 + 2/10 in simplest fraction form is 14/45.

What is 1/9 plus 2/10 as a decimal?

1/9 + 2/10 converted to a decimal is 0.311111.

What is 1/9 plus 2/10 as a percentage?

1/9 + 2/10 expressed as a percentage is 31.1111%.

Does 1/9 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.311111...) because the denominator contains prime factors other than 2 and 5.