What is 2/11 plus 9/10? (Answer: 119/110)

Exact Answer

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Problem: What is 2/11 plus 9/10?
Formula / Expression: 2/11 + 9/10
Final Answer: 1 9/110 (119/110)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 10 = 110.
Working: LCD(11, 10) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 2/11 by 10, and multiply the numerator and denominator of 9/10 by 11 so both fractions share the common base 110.
Working: 2 × 10/11 × 10 = 20/110 and 9 × 11/10 × 11 = 99/110

Step 3: Add the Numerators
Now add the numerators (20 + 99 = 119) and keep the common denominator 110 unchanged.
Working: 20 + 99/110 = 119/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 119 and 110 is 1, confirming that 119/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 119/110

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (119) is greater than the denominator (110), divide 119 by 110: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/110.
Working: 119/110 = 1 9/110

Step 6: Decimal & Percentage Representation
Dividing the numerator 119 by denominator 110 produces a repeating decimal (approximately 1.081818, or 108.1818%).
Working: 119 ÷ 110 = 1.081818 (108.1818%)

Key Values:
- Simplified Fraction: 119/110
- Mixed Number Form: 1 9/110
- Decimal Value: 1.081818
- Percentage: 108.1818%

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Solved with FractionsCalc:
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2/11 + 9/10 = 119/110

Simplified Fraction

119/110

Mixed Number

1 9/110

Decimal Value

1.081818

Percentage

108.1818%

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Step-by-Step Solution: 2/11 + 9/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 10 = 110.

LCD(11, 10) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 2/11 by 10, and multiply the numerator and denominator of 9/10 by 11 so both fractions share the common base 110.

2 × 10/11 × 10 = 20/110 and 9 × 11/10 × 11 = 99/110

Step 3

Add the Numerators

Now add the numerators (20 + 99 = 119) and keep the common denominator 110 unchanged.

20 + 99/110 = 119/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 119 and 110 is 1, confirming that 119/110 cannot be reduced further—it is already in its simplest irreducible form.

119/110

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (119) is greater than the denominator (110), divide 119 by 110: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/110.

119/110 = 19/110

Step 6

Decimal & Percentage Representation

Dividing the numerator 119 by denominator 110 produces a repeating decimal (approximately 1.081818, or 108.1818%).

119 ÷ 110 = 1.081818 (108.1818%)

Visual Representation

The diagram below illustrates 2/11 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`119/110`
Mixed Number Form	`1 9/110`
Decimal Form	`1.081818`
Percentage	`108.1818%`

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Frequently Asked Questions

What is 2/11 plus 9/10 as a fraction?

2/11 + 9/10 in simplest fraction form is 119/110 (or 1 9/110 as a mixed number).

What is 2/11 plus 9/10 as a decimal?

2/11 + 9/10 converted to a decimal is 1.081818.

What is 2/11 plus 9/10 as a percentage?

2/11 + 9/10 expressed as a percentage is 108.1818%.

How do you write 2/11 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 119/110 can be written as the mixed number 1 9/110.

Does 2/11 plus 9/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.081818...) because the denominator contains prime factors other than 2 and 5.