What is 1/2 plus 10/11? (Answer: 31/22)

Exact Answer

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Problem: What is 1/2 plus 10/11?
Formula / Expression: 1/2 + 10/11
Final Answer: 1 9/22 (31/22)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 11 = 22.
Working: LCD(2, 11) = 22

Step 2: Convert to Equivalent Fractions with Common Denominator 22
Multiply the numerator and denominator of 1/2 by 11, and multiply the numerator and denominator of 10/11 by 2 so both fractions share the common base 22.
Working: 1 × 11/2 × 11 = 11/22 and 10 × 2/11 × 2 = 20/22

Step 3: Add the Numerators
Now add the numerators (11 + 20 = 31) and keep the common denominator 22 unchanged.
Working: 11 + 20/22 = 31/22

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 22 is 1, confirming that 31/22 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/22

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (22), divide 31 by 22: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/22.
Working: 31/22 = 1 9/22

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 22 produces a repeating decimal (approximately 1.409091, or 140.9091%).
Working: 31 ÷ 22 = 1.409091 (140.9091%)

Key Values:
- Simplified Fraction: 31/22
- Mixed Number Form: 1 9/22
- Decimal Value: 1.409091
- Percentage: 140.9091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-10-11/
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1/2 + 10/11 = 31/22

Simplified Fraction

31/22

Mixed Number

1 9/22

Decimal Value

1.409091

Percentage

140.9091%

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Step-by-Step Solution: 1/2 + 10/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 11 = 22.

LCD(2, 11) = 22

Step 2

Convert to Equivalent Fractions with Common Denominator 22

Multiply the numerator and denominator of 1/2 by 11, and multiply the numerator and denominator of 10/11 by 2 so both fractions share the common base 22.

1 × 11/2 × 11 = 11/22 and 10 × 2/11 × 2 = 20/22

Step 3

Add the Numerators

Now add the numerators (11 + 20 = 31) and keep the common denominator 22 unchanged.

11 + 20/22 = 31/22

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 22 is 1, confirming that 31/22 cannot be reduced further—it is already in its simplest irreducible form.

31/22

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (22), divide 31 by 22: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/22.

31/22 = 19/22

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 22 produces a repeating decimal (approximately 1.409091, or 140.9091%).

31 ÷ 22 = 1.409091 (140.9091%)

Visual Representation

The diagram below illustrates 1/2 plus 10/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/22`
Mixed Number Form	`1 9/22`
Decimal Form	`1.409091`
Percentage	`140.9091%`

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Frequently Asked Questions

What is 1/2 plus 10/11 as a fraction?

1/2 + 10/11 in simplest fraction form is 31/22 (or 1 9/22 as a mixed number).

What is 1/2 plus 10/11 as a decimal?

1/2 + 10/11 converted to a decimal is 1.409091.

What is 1/2 plus 10/11 as a percentage?

1/2 + 10/11 expressed as a percentage is 140.9091%.

How do you write 1/2 plus 10/11 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/22 can be written as the mixed number 1 9/22.

Does 1/2 plus 10/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.409091...) because the denominator contains prime factors other than 2 and 5.