What is 2/40 plus 2/6? (Answer: 23/60)

Exact Answer

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Problem: What is 2/40 plus 2/6?
Formula / Expression: 2/40 + 2/6
Final Answer: 23/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 40 × 6 = 240, keeping the calculation simpler).
Working: LCD(40, 6) = 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 2/6 by 20 so both fractions share the common base 120.
Working: 2 × 3/40 × 3 = 6/120 and 2 × 20/6 × 20 = 40/120

Step 3: Add the Numerators
Now add the numerators (6 + 40 = 46) and keep the common denominator 120 unchanged.
Working: 6 + 40/120 = 46/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 46 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 46 ÷ 2/120 ÷ 2 = 23/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 60 produces a repeating decimal (approximately 0.383333, or 38.3333%).
Working: 23 ÷ 60 = 0.383333 (38.3333%)

Key Values:
- Simplified Fraction: 23/60
- Mixed Number Form: 23/60
- Decimal Value: 0.383333
- Percentage: 38.3333%

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Solved with FractionsCalc:
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2/40 + 2/6 = 23/60

Simplified Fraction

23/60

Mixed Number

Proper (23/60)

Decimal Value

0.383333

Percentage

38.3333%

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Step-by-Step Solution: 2/40 + 2/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 40 × 6 = 240, keeping the calculation simpler).

LCD(40, 6) = 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 2/6 by 20 so both fractions share the common base 120.

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

Step 3

Add the Numerators

Now add the numerators (6 + 40 = 46) and keep the common denominator 120 unchanged.

6 + 40/120 = 46/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 46 and 120, which is 2. Divide both the numerator and denominator by 2.

46 ÷ 2/120 ÷ 2 = 23/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 60 produces a repeating decimal (approximately 0.383333, or 38.3333%).

23 ÷ 60 = 0.383333 (38.3333%)

Visual Representation

The diagram below illustrates 2/40 plus 2/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/60`
Mixed Number Form	`23/60`
Decimal Form	`0.383333`
Percentage	`38.3333%`

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Frequently Asked Questions

What is 2/40 plus 2/6 as a fraction?

2/40 + 2/6 in simplest fraction form is 23/60.

What is 2/40 plus 2/6 as a decimal?

2/40 + 2/6 converted to a decimal is 0.383333.

What is 2/40 plus 2/6 as a percentage?

2/40 + 2/6 expressed as a percentage is 38.3333%.

Does 2/40 plus 2/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.383333...) because the denominator contains prime factors other than 2 and 5.