What is 2/33 plus 2/24? (Answer: 19/132)

Exact Answer

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Problem: What is 2/33 plus 2/24?
Formula / Expression: 2/33 + 2/24
Final Answer: 19/132
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 24 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 264 (which is smaller than their product 33 × 24 = 792, keeping the calculation simpler).
Working: LCD(33, 24) = 264

Step 2: Convert to Equivalent Fractions with Common Denominator 264
Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 2/24 by 11 so both fractions share the common base 264.
Working: 2 × 8/33 × 8 = 16/264 and 2 × 11/24 × 11 = 22/264

Step 3: Add the Numerators
Now add the numerators (16 + 22 = 38) and keep the common denominator 264 unchanged.
Working: 16 + 22/264 = 38/264

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 264, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/264 ÷ 2 = 19/132

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 132 produces a repeating decimal (approximately 0.143939, or 14.3939%).
Working: 19 ÷ 132 = 0.143939 (14.3939%)

Key Values:
- Simplified Fraction: 19/132
- Mixed Number Form: 19/132
- Decimal Value: 0.143939
- Percentage: 14.3939%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-2-24/
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2/33 + 2/24 = 19/132

Simplified Fraction

19/132

Mixed Number

Proper (19/132)

Decimal Value

0.143939

Percentage

14.3939%

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Step-by-Step Solution: 2/33 + 2/24

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 24 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 264 (which is smaller than their product 33 × 24 = 792, keeping the calculation simpler).

LCD(33, 24) = 264

Step 2

Convert to Equivalent Fractions with Common Denominator 264

Multiply the numerator and denominator of 2/33 by 8, and multiply the numerator and denominator of 2/24 by 11 so both fractions share the common base 264.

2 × 8/33 × 8 = 16/264 and 2 × 11/24 × 11 = 22/264

Step 3

Add the Numerators

Now add the numerators (16 + 22 = 38) and keep the common denominator 264 unchanged.

16 + 22/264 = 38/264

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 264, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/264 ÷ 2 = 19/132

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 132 produces a repeating decimal (approximately 0.143939, or 14.3939%).

19 ÷ 132 = 0.143939 (14.3939%)

Visual Representation

The diagram below illustrates 2/33 plus 2/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/132`
Mixed Number Form	`19/132`
Decimal Form	`0.143939`
Percentage	`14.3939%`

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Frequently Asked Questions

What is 2/33 plus 2/24 as a fraction?

2/33 + 2/24 in simplest fraction form is 19/132.

What is 2/33 plus 2/24 as a decimal?

2/33 + 2/24 converted to a decimal is 0.143939.

What is 2/33 plus 2/24 as a percentage?

2/33 + 2/24 expressed as a percentage is 14.3939%.

Does 2/33 plus 2/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.143939...) because the denominator contains prime factors other than 2 and 5.