What is 2/33 plus 2/23? (Answer: 112/759)

Exact Answer

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Problem: What is 2/33 plus 2/23?
Formula / Expression: 2/33 + 2/23
Final Answer: 112/759
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 23 = 759.
Working: LCD(33, 23) = 759

Step 2: Convert to Equivalent Fractions with Common Denominator 759
Multiply the numerator and denominator of 2/33 by 23, and multiply the numerator and denominator of 2/23 by 33 so both fractions share the common base 759.
Working: 2 × 23/33 × 23 = 46/759 and 2 × 33/23 × 33 = 66/759

Step 3: Add the Numerators
Now add the numerators (46 + 66 = 112) and keep the common denominator 759 unchanged.
Working: 46 + 66/759 = 112/759

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 112 and 759 is 1, confirming that 112/759 cannot be reduced further—it is already in its simplest irreducible form.
Working: 112/759

Step 5: Decimal & Percentage Representation
Dividing the numerator 112 by denominator 759 produces a repeating decimal (approximately 0.147563, or 14.7563%).
Working: 112 ÷ 759 = 0.147563 (14.7563%)

Key Values:
- Simplified Fraction: 112/759
- Mixed Number Form: 112/759
- Decimal Value: 0.147563
- Percentage: 14.7563%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-33-plus-2-23/
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2/33 + 2/23 = 112/759

Simplified Fraction

112/759

Mixed Number

Proper (112/759)

Decimal Value

0.147563

Percentage

14.7563%

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Step-by-Step Solution: 2/33 + 2/23

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 23 = 759.

LCD(33, 23) = 759

Step 2

Convert to Equivalent Fractions with Common Denominator 759

Multiply the numerator and denominator of 2/33 by 23, and multiply the numerator and denominator of 2/23 by 33 so both fractions share the common base 759.

2 × 23/33 × 23 = 46/759 and 2 × 33/23 × 33 = 66/759

Step 3

Add the Numerators

Now add the numerators (46 + 66 = 112) and keep the common denominator 759 unchanged.

46 + 66/759 = 112/759

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 112 and 759 is 1, confirming that 112/759 cannot be reduced further—it is already in its simplest irreducible form.

112/759

Step 5

Decimal & Percentage Representation

Dividing the numerator 112 by denominator 759 produces a repeating decimal (approximately 0.147563, or 14.7563%).

112 ÷ 759 = 0.147563 (14.7563%)

Visual Representation

The diagram below illustrates 2/33 plus 2/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`112/759`
Mixed Number Form	`112/759`
Decimal Form	`0.147563`
Percentage	`14.7563%`

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Frequently Asked Questions

What is 2/33 plus 2/23 as a fraction?

2/33 + 2/23 in simplest fraction form is 112/759.

What is 2/33 plus 2/23 as a decimal?

2/33 + 2/23 converted to a decimal is 0.147563.

What is 2/33 plus 2/23 as a percentage?

2/33 + 2/23 expressed as a percentage is 14.7563%.

Does 2/33 plus 2/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.147563...) because the denominator contains prime factors other than 2 and 5.