What is 2/32 plus 2/22? (Answer: 27/176)

Exact Answer

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Problem: What is 2/32 plus 2/22?
Formula / Expression: 2/32 + 2/22
Final Answer: 27/176
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 352 (which is smaller than their product 32 × 22 = 704, keeping the calculation simpler).
Working: LCD(32, 22) = 352

Step 2: Convert to Equivalent Fractions with Common Denominator 352
Multiply the numerator and denominator of 2/32 by 11, and multiply the numerator and denominator of 2/22 by 16 so both fractions share the common base 352.
Working: 2 × 11/32 × 11 = 22/352 and 2 × 16/22 × 16 = 32/352

Step 3: Add the Numerators
Now add the numerators (22 + 32 = 54) and keep the common denominator 352 unchanged.
Working: 22 + 32/352 = 54/352

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 352, which is 2. Divide both the numerator and denominator by 2.
Working: 54 ÷ 2/352 ÷ 2 = 27/176

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 176 produces a repeating decimal (approximately 0.153409, or 15.3409%).
Working: 27 ÷ 176 = 0.153409 (15.3409%)

Key Values:
- Simplified Fraction: 27/176
- Mixed Number Form: 27/176
- Decimal Value: 0.153409
- Percentage: 15.3409%

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Solved with FractionsCalc:
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2/32 + 2/22 = 27/176

Simplified Fraction

27/176

Mixed Number

Proper (27/176)

Decimal Value

0.153409

Percentage

15.3409%

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Step-by-Step Solution: 2/32 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 352 (which is smaller than their product 32 × 22 = 704, keeping the calculation simpler).

LCD(32, 22) = 352

Step 2

Convert to Equivalent Fractions with Common Denominator 352

Multiply the numerator and denominator of 2/32 by 11, and multiply the numerator and denominator of 2/22 by 16 so both fractions share the common base 352.

2 × 11/32 × 11 = 22/352 and 2 × 16/22 × 16 = 32/352

Step 3

Add the Numerators

Now add the numerators (22 + 32 = 54) and keep the common denominator 352 unchanged.

22 + 32/352 = 54/352

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 54 and 352, which is 2. Divide both the numerator and denominator by 2.

54 ÷ 2/352 ÷ 2 = 27/176

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 176 produces a repeating decimal (approximately 0.153409, or 15.3409%).

27 ÷ 176 = 0.153409 (15.3409%)

Visual Representation

The diagram below illustrates 2/32 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/176`
Mixed Number Form	`27/176`
Decimal Form	`0.153409`
Percentage	`15.3409%`

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Frequently Asked Questions

What is 2/32 plus 2/22 as a fraction?

2/32 + 2/22 in simplest fraction form is 27/176.

What is 2/32 plus 2/22 as a decimal?

2/32 + 2/22 converted to a decimal is 0.153409.

What is 2/32 plus 2/22 as a percentage?

2/32 + 2/22 expressed as a percentage is 15.3409%.

Does 2/32 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.153409...) because the denominator contains prime factors other than 2 and 5.