What is 2/48 plus 2/10? (Answer: 29/120)

Exact Answer

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Problem: What is 2/48 plus 2/10?
Formula / Expression: 2/48 + 2/10
Final Answer: 29/120
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 240 (which is smaller than their product 48 × 10 = 480, keeping the calculation simpler).
Working: LCD(48, 10) = 240

Step 2: Convert to Equivalent Fractions with Common Denominator 240
Multiply the numerator and denominator of 2/48 by 5, and multiply the numerator and denominator of 2/10 by 24 so both fractions share the common base 240.
Working: 2 × 5/48 × 5 = 10/240 and 2 × 24/10 × 24 = 48/240

Step 3: Add the Numerators
Now add the numerators (10 + 48 = 58) and keep the common denominator 240 unchanged.
Working: 10 + 48/240 = 58/240

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 240, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/240 ÷ 2 = 29/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 120 produces a repeating decimal (approximately 0.241667, or 24.1667%).
Working: 29 ÷ 120 = 0.241667 (24.1667%)

Key Values:
- Simplified Fraction: 29/120
- Mixed Number Form: 29/120
- Decimal Value: 0.241667
- Percentage: 24.1667%

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Solved with FractionsCalc:
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2/48 + 2/10 = 29/120

Simplified Fraction

29/120

Mixed Number

Proper (29/120)

Decimal Value

0.241667

Percentage

24.1667%

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Step-by-Step Solution: 2/48 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 240 (which is smaller than their product 48 × 10 = 480, keeping the calculation simpler).

LCD(48, 10) = 240

Step 2

Convert to Equivalent Fractions with Common Denominator 240

Multiply the numerator and denominator of 2/48 by 5, and multiply the numerator and denominator of 2/10 by 24 so both fractions share the common base 240.

2 × 5/48 × 5 = 10/240 and 2 × 24/10 × 24 = 48/240

Step 3

Add the Numerators

Now add the numerators (10 + 48 = 58) and keep the common denominator 240 unchanged.

10 + 48/240 = 58/240

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 240, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/240 ÷ 2 = 29/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 120 produces a repeating decimal (approximately 0.241667, or 24.1667%).

29 ÷ 120 = 0.241667 (24.1667%)

Visual Representation

The diagram below illustrates 2/48 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/120`
Mixed Number Form	`29/120`
Decimal Form	`0.241667`
Percentage	`24.1667%`

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Frequently Asked Questions

What is 2/48 plus 2/10 as a fraction?

2/48 + 2/10 in simplest fraction form is 29/120.

What is 2/48 plus 2/10 as a decimal?

2/48 + 2/10 converted to a decimal is 0.241667.

What is 2/48 plus 2/10 as a percentage?

2/48 + 2/10 expressed as a percentage is 24.1667%.

Does 2/48 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.241667...) because the denominator contains prime factors other than 2 and 5.