What is 10/22 plus 2/3? (Answer: 37/33)

Exact Answer

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Problem: What is 10/22 plus 2/3?
Formula / Expression: 10/22 + 2/3
Final Answer: 1 4/33 (37/33)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 3 = 66.
Working: LCD(22, 3) = 66

Step 2: Convert to Equivalent Fractions with Common Denominator 66
Multiply the numerator and denominator of 10/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.
Working: 10 × 3/22 × 3 = 30/66 and 2 × 22/3 × 22 = 44/66

Step 3: Add the Numerators
Now add the numerators (30 + 44 = 74) and keep the common denominator 66 unchanged.
Working: 30 + 44/66 = 74/66

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 66, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/66 ÷ 2 = 37/33

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (33), divide 37 by 33: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/33.
Working: 37/33 = 1 4/33

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 33 produces a repeating decimal (approximately 1.121212, or 112.1212%).
Working: 37 ÷ 33 = 1.121212 (112.1212%)

Key Values:
- Simplified Fraction: 37/33
- Mixed Number Form: 1 4/33
- Decimal Value: 1.121212
- Percentage: 112.1212%

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Solved with FractionsCalc:
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10/22 + 2/3 = 37/33

Simplified Fraction

37/33

Mixed Number

1 4/33

Decimal Value

1.121212

Percentage

112.1212%

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Step-by-Step Solution: 10/22 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 3 = 66.

LCD(22, 3) = 66

Step 2

Convert to Equivalent Fractions with Common Denominator 66

Multiply the numerator and denominator of 10/22 by 3, and multiply the numerator and denominator of 2/3 by 22 so both fractions share the common base 66.

10 × 3/22 × 3 = 30/66 and 2 × 22/3 × 22 = 44/66

Step 3

Add the Numerators

Now add the numerators (30 + 44 = 74) and keep the common denominator 66 unchanged.

30 + 44/66 = 74/66

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 66, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/66 ÷ 2 = 37/33

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (33), divide 37 by 33: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/33.

37/33 = 14/33

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 33 produces a repeating decimal (approximately 1.121212, or 112.1212%).

37 ÷ 33 = 1.121212 (112.1212%)

Visual Representation

The diagram below illustrates 10/22 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/33`
Mixed Number Form	`1 4/33`
Decimal Form	`1.121212`
Percentage	`112.1212%`

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Frequently Asked Questions

What is 10/22 plus 2/3 as a fraction?

10/22 + 2/3 in simplest fraction form is 37/33 (or 1 4/33 as a mixed number).

What is 10/22 plus 2/3 as a decimal?

10/22 + 2/3 converted to a decimal is 1.121212.

What is 10/22 plus 2/3 as a percentage?

10/22 + 2/3 expressed as a percentage is 112.1212%.

How do you write 10/22 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 37/33 can be written as the mixed number 1 4/33.

Does 10/22 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.121212...) because the denominator contains prime factors other than 2 and 5.