What is 1/10 plus 2/9? (Answer: 29/90)

Exact Answer

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Problem: What is 1/10 plus 2/9?
Formula / Expression: 1/10 + 2/9
Final Answer: 29/90
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 1/10 by 9, and multiply the numerator and denominator of 2/9 by 10 so both fractions share the common base 90.
Working: 1 × 9/10 × 9 = 9/90 and 2 × 10/9 × 10 = 20/90

Step 3: Add the Numerators
Now add the numerators (9 + 20 = 29) and keep the common denominator 90 unchanged.
Working: 9 + 20/90 = 29/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 29 and 90 is 1, confirming that 29/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 29/90

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 90 produces a repeating decimal (approximately 0.322222, or 32.2222%).
Working: 29 ÷ 90 = 0.322222 (32.2222%)

Key Values:
- Simplified Fraction: 29/90
- Mixed Number Form: 29/90
- Decimal Value: 0.322222
- Percentage: 32.2222%

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Solved with FractionsCalc:
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1/10 + 2/9 = 29/90

Simplified Fraction

29/90

Mixed Number

Proper (29/90)

Decimal Value

0.322222

Percentage

32.2222%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(10, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

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

1 × 9/10 × 9 = 9/90 and 2 × 10/9 × 10 = 20/90

Step 3

Add the Numerators

Now add the numerators (9 + 20 = 29) and keep the common denominator 90 unchanged.

9 + 20/90 = 29/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 29 and 90 is 1, confirming that 29/90 cannot be reduced further—it is already in its simplest irreducible form.

29/90

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 90 produces a repeating decimal (approximately 0.322222, or 32.2222%).

29 ÷ 90 = 0.322222 (32.2222%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/90`
Mixed Number Form	`29/90`
Decimal Form	`0.322222`
Percentage	`32.2222%`

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Frequently Asked Questions

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

1/10 + 2/9 in simplest fraction form is 29/90.

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

1/10 + 2/9 converted to a decimal is 0.322222.

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

1/10 + 2/9 expressed as a percentage is 32.2222%.

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

It results in a repeating decimal (approximately 0.322222...) because the denominator contains prime factors other than 2 and 5.