What is 2/40 plus 2/12? (Answer: 13/60)

Exact Answer

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Problem: What is 2/40 plus 2/12?
Formula / Expression: 2/40 + 2/12
Final Answer: 13/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 12 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 40 × 12 = 480, keeping the calculation simpler).
Working: LCD(40, 12) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 2/40 by 3, and multiply the numerator and denominator of 2/12 by 10 so both fractions share the common base 120.
Working: 2 × 3/40 × 3 = 6/120 and 2 × 10/12 × 10 = 20/120

Step 3: Add the Numerators
Now add the numerators (6 + 20 = 26) and keep the common denominator 120 unchanged.
Working: 6 + 20/120 = 26/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/120 ÷ 2 = 13/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 60 produces a repeating decimal (approximately 0.216667, or 21.6667%).
Working: 13 ÷ 60 = 0.216667 (21.6667%)

Key Values:
- Simplified Fraction: 13/60
- Mixed Number Form: 13/60
- Decimal Value: 0.216667
- Percentage: 21.6667%

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2/40 + 2/12 = 13/60

Simplified Fraction

13/60

Mixed Number

Proper (13/60)

Decimal Value

0.216667

Percentage

21.6667%

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Step-by-Step Solution: 2/40 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 12 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 40 × 12 = 480, keeping the calculation simpler).

LCD(40, 12) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 2/40 by 3, and multiply the numerator and denominator of 2/12 by 10 so both fractions share the common base 120.

2 × 3/40 × 3 = 6/120 and 2 × 10/12 × 10 = 20/120

Step 3

Add the Numerators

Now add the numerators (6 + 20 = 26) and keep the common denominator 120 unchanged.

6 + 20/120 = 26/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 120, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/120 ÷ 2 = 13/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 60 produces a repeating decimal (approximately 0.216667, or 21.6667%).

13 ÷ 60 = 0.216667 (21.6667%)

Visual Representation

The diagram below illustrates 2/40 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/60`
Mixed Number Form	`13/60`
Decimal Form	`0.216667`
Percentage	`21.6667%`

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Frequently Asked Questions

What is 2/40 plus 2/12 as a fraction?

2/40 + 2/12 in simplest fraction form is 13/60.

What is 2/40 plus 2/12 as a decimal?

2/40 + 2/12 converted to a decimal is 0.216667.

What is 2/40 plus 2/12 as a percentage?

2/40 + 2/12 expressed as a percentage is 21.6667%.

Does 2/40 plus 2/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.216667...) because the denominator contains prime factors other than 2 and 5.