What is 2/48 plus 2/22? (Answer: 35/264)

Exact Answer

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Problem: What is 2/48 plus 2/22?
Formula / Expression: 2/48 + 2/22
Final Answer: 35/264
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 528 (which is smaller than their product 48 × 22 = 1056, keeping the calculation simpler).
Working: LCD(48, 22) = 528

Step 2: Convert to Equivalent Fractions with Common Denominator 528
Multiply the numerator and denominator of 2/48 by 11, and multiply the numerator and denominator of 2/22 by 24 so both fractions share the common base 528.
Working: 2 × 11/48 × 11 = 22/528 and 2 × 24/22 × 24 = 48/528

Step 3: Add the Numerators
Now add the numerators (22 + 48 = 70) and keep the common denominator 528 unchanged.
Working: 22 + 48/528 = 70/528

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 528, which is 2. Divide both the numerator and denominator by 2.
Working: 70 ÷ 2/528 ÷ 2 = 35/264

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 264 produces a repeating decimal (approximately 0.132576, or 13.2576%).
Working: 35 ÷ 264 = 0.132576 (13.2576%)

Key Values:
- Simplified Fraction: 35/264
- Mixed Number Form: 35/264
- Decimal Value: 0.132576
- Percentage: 13.2576%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-48-plus-2-22/
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2/48 + 2/22 = 35/264

Simplified Fraction

35/264

Mixed Number

Proper (35/264)

Decimal Value

0.132576

Percentage

13.2576%

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Step-by-Step Solution: 2/48 + 2/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 528 (which is smaller than their product 48 × 22 = 1056, keeping the calculation simpler).

LCD(48, 22) = 528

Step 2

Convert to Equivalent Fractions with Common Denominator 528

Multiply the numerator and denominator of 2/48 by 11, and multiply the numerator and denominator of 2/22 by 24 so both fractions share the common base 528.

2 × 11/48 × 11 = 22/528 and 2 × 24/22 × 24 = 48/528

Step 3

Add the Numerators

Now add the numerators (22 + 48 = 70) and keep the common denominator 528 unchanged.

22 + 48/528 = 70/528

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 528, which is 2. Divide both the numerator and denominator by 2.

70 ÷ 2/528 ÷ 2 = 35/264

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 264 produces a repeating decimal (approximately 0.132576, or 13.2576%).

35 ÷ 264 = 0.132576 (13.2576%)

Visual Representation

The diagram below illustrates 2/48 plus 2/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/264`
Mixed Number Form	`35/264`
Decimal Form	`0.132576`
Percentage	`13.2576%`

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Frequently Asked Questions

What is 2/48 plus 2/22 as a fraction?

2/48 + 2/22 in simplest fraction form is 35/264.

What is 2/48 plus 2/22 as a decimal?

2/48 + 2/22 converted to a decimal is 0.132576.

What is 2/48 plus 2/22 as a percentage?

2/48 + 2/22 expressed as a percentage is 13.2576%.

Does 2/48 plus 2/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.132576...) because the denominator contains prime factors other than 2 and 5.