What is 2/24 plus 2/22? (Answer: 23/132)

Exact Answer

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Problem: What is 2/24 plus 2/22?
Formula / Expression: 2/24 + 2/22
Final Answer: 23/132
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 264 (which is smaller than their product 24 × 22 = 528, keeping the calculation simpler).
Working: LCD(24, 22) = 264

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 2/24 by 11, and multiply the numerator and denominator of 2/22 by 12 so both fractions share the common base 264.
Working: 2 × 11/24 × 11 = 22/264 and 2 × 12/22 × 12 = 24/264

Step 3: Add the Numerators
Now add the numerators (22 + 24 = 46) and keep the common denominator 264 unchanged.
Working: 22 + 24/264 = 46/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 264, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/264 ÷ 2 = 23/132

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 132 produces a repeating decimal (approximately 0.174242, or 17.4242%).
Working: 23 ÷ 132 = 0.174242 (17.4242%)

Key Values:
- Simplified Fraction: 23/132
- Mixed Number Form: 23/132
- Decimal Value: 0.174242
- Percentage: 17.4242%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-24-plus-2-22/
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2/24 + 2/22 = 23/132

Simplified Fraction

23/132

Mixed Number

Proper (23/132)

Decimal Value

0.174242

Percentage

17.4242%

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Step-by-Step Solution: 2/24 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 264 (which is smaller than their product 24 × 22 = 528, keeping the calculation simpler).

LCD(24, 22) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 2/24 by 11, and multiply the numerator and denominator of 2/22 by 12 so both fractions share the common base 264.

2 × 11/24 × 11 = 22/264 and 2 × 12/22 × 12 = 24/264

Step 3

Add the Numerators

Now add the numerators (22 + 24 = 46) and keep the common denominator 264 unchanged.

22 + 24/264 = 46/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 264, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/264 ÷ 2 = 23/132

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 132 produces a repeating decimal (approximately 0.174242, or 17.4242%).

23 ÷ 132 = 0.174242 (17.4242%)

Visual Representation

The diagram below illustrates 2/24 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/132`
Mixed Number Form	`23/132`
Decimal Form	`0.174242`
Percentage	`17.4242%`

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Frequently Asked Questions

What is 2/24 plus 2/22 as a fraction?

2/24 + 2/22 in simplest fraction form is 23/132.

What is 2/24 plus 2/22 as a decimal?

2/24 + 2/22 converted to a decimal is 0.174242.

What is 2/24 plus 2/22 as a percentage?

2/24 + 2/22 expressed as a percentage is 17.4242%.

Does 2/24 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.174242...) because the denominator contains prime factors other than 2 and 5.