What is 2/3 plus 10/11? (Answer: 52/33)

Exact Answer

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Problem: What is 2/3 plus 10/11?
Formula / Expression: 2/3 + 10/11
Final Answer: 1 19/33 (52/33)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 11 = 33.
Working: LCD(3, 11) = 33

Step 2: Convert to Equivalent Fractions with Common Denominator 33
Multiply the numerator and denominator of 2/3 by 11, and multiply the numerator and denominator of 10/11 by 3 so both fractions share the common base 33.
Working: 2 × 11/3 × 11 = 22/33 and 10 × 3/11 × 3 = 30/33

Step 3: Add the Numerators
Now add the numerators (22 + 30 = 52) and keep the common denominator 33 unchanged.
Working: 22 + 30/33 = 52/33

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 33 is 1, confirming that 52/33 cannot be reduced further—it is already in its simplest irreducible form.
Working: 52/33

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (52) is greater than the denominator (33), divide 52 by 33: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/33.
Working: 52/33 = 1 19/33

Step 6: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 33 produces a repeating decimal (approximately 1.575758, or 157.5758%).
Working: 52 ÷ 33 = 1.575758 (157.5758%)

Key Values:
- Simplified Fraction: 52/33
- Mixed Number Form: 1 19/33
- Decimal Value: 1.575758
- Percentage: 157.5758%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-plus-10-11/
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2/3 + 10/11 = 52/33

Simplified Fraction

52/33

Mixed Number

1 19/33

Decimal Value

1.575758

Percentage

157.5758%

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Step-by-Step Solution: 2/3 + 10/11

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 11 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 11 = 33.

LCD(3, 11) = 33

Step 2

Convert to Equivalent Fractions with Common Denominator 33

Multiply the numerator and denominator of 2/3 by 11, and multiply the numerator and denominator of 10/11 by 3 so both fractions share the common base 33.

2 × 11/3 × 11 = 22/33 and 10 × 3/11 × 3 = 30/33

Step 3

Add the Numerators

Now add the numerators (22 + 30 = 52) and keep the common denominator 33 unchanged.

22 + 30/33 = 52/33

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 52 and 33 is 1, confirming that 52/33 cannot be reduced further—it is already in its simplest irreducible form.

52/33

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (52) is greater than the denominator (33), divide 52 by 33: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/33.

52/33 = 119/33

Step 6

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 33 produces a repeating decimal (approximately 1.575758, or 157.5758%).

52 ÷ 33 = 1.575758 (157.5758%)

Visual Representation

The diagram below illustrates 2/3 plus 10/11 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/33`
Mixed Number Form	`1 19/33`
Decimal Form	`1.575758`
Percentage	`157.5758%`

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Frequently Asked Questions

What is 2/3 plus 10/11 as a fraction?

2/3 + 10/11 in simplest fraction form is 52/33 (or 1 19/33 as a mixed number).

What is 2/3 plus 10/11 as a decimal?

2/3 + 10/11 converted to a decimal is 1.575758.

What is 2/3 plus 10/11 as a percentage?

2/3 + 10/11 expressed as a percentage is 157.5758%.

How do you write 2/3 plus 10/11 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 52/33 can be written as the mixed number 1 19/33.

Does 2/3 plus 10/11 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.575758...) because the denominator contains prime factors other than 2 and 5.