What is 2/18 plus 9/10? (Answer: 91/90)

Exact Answer

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Problem: What is 2/18 plus 9/10?
Formula / Expression: 2/18 + 9/10
Final Answer: 1 1/90 (91/90)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 18 × 10 = 180, keeping the calculation simpler).
Working: LCD(18, 10) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/18 by 5, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.
Working: 2 × 5/18 × 5 = 10/90 and 9 × 9/10 × 9 = 81/90

Step 3: Add the Numerators
Now add the numerators (10 + 81 = 91) and keep the common denominator 90 unchanged.
Working: 10 + 81/90 = 91/90

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 91 and 90 is 1, confirming that 91/90 cannot be reduced further—it is already in its simplest irreducible form.
Working: 91/90

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (91) is greater than the denominator (90), divide 91 by 90: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/90.
Working: 91/90 = 1 1/90

Step 6: Decimal & Percentage Representation
Dividing the numerator 91 by denominator 90 produces a repeating decimal (approximately 1.011111, or 101.1111%).
Working: 91 ÷ 90 = 1.011111 (101.1111%)

Key Values:
- Simplified Fraction: 91/90
- Mixed Number Form: 1 1/90
- Decimal Value: 1.011111
- Percentage: 101.1111%

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Solved with FractionsCalc:
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2/18 + 9/10 = 91/90

Simplified Fraction

91/90

Mixed Number

1 1/90

Decimal Value

1.011111

Percentage

101.1111%

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Step-by-Step Solution: 2/18 + 9/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 18 × 10 = 180, keeping the calculation simpler).

LCD(18, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/18 by 5, and multiply the numerator and denominator of 9/10 by 9 so both fractions share the common base 90.

2 × 5/18 × 5 = 10/90 and 9 × 9/10 × 9 = 81/90

Step 3

Add the Numerators

Now add the numerators (10 + 81 = 91) and keep the common denominator 90 unchanged.

10 + 81/90 = 91/90

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 91 and 90 is 1, confirming that 91/90 cannot be reduced further—it is already in its simplest irreducible form.

91/90

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (91) is greater than the denominator (90), divide 91 by 90: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/90.

91/90 = 11/90

Step 6

Decimal & Percentage Representation

Dividing the numerator 91 by denominator 90 produces a repeating decimal (approximately 1.011111, or 101.1111%).

91 ÷ 90 = 1.011111 (101.1111%)

Visual Representation

The diagram below illustrates 2/18 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`91/90`
Mixed Number Form	`1 1/90`
Decimal Form	`1.011111`
Percentage	`101.1111%`

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Frequently Asked Questions

What is 2/18 plus 9/10 as a fraction?

2/18 + 9/10 in simplest fraction form is 91/90 (or 1 1/90 as a mixed number).

What is 2/18 plus 9/10 as a decimal?

2/18 + 9/10 converted to a decimal is 1.011111.

What is 2/18 plus 9/10 as a percentage?

2/18 + 9/10 expressed as a percentage is 101.1111%.

How do you write 2/18 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 91/90 can be written as the mixed number 1 1/90.

Does 2/18 plus 9/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.011111...) because the denominator contains prime factors other than 2 and 5.