What is 2/40 plus 2/15? (Answer: 11/60)

Exact Answer

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Problem: What is 2/40 plus 2/15?
Formula / Expression: 2/40 + 2/15
Final Answer: 11/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 15 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 40 × 15 = 600, keeping the calculation simpler).
Working: LCD(40, 15) = 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 2/15 by 8 so both fractions share the common base 120.
Working: 2 × 3/40 × 3 = 6/120 and 2 × 8/15 × 8 = 16/120

Step 3: Add the Numerators
Now add the numerators (6 + 16 = 22) and keep the common denominator 120 unchanged.
Working: 6 + 16/120 = 22/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/120 ÷ 2 = 11/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 60 produces a repeating decimal (approximately 0.183333, or 18.3333%).
Working: 11 ÷ 60 = 0.183333 (18.3333%)

Key Values:
- Simplified Fraction: 11/60
- Mixed Number Form: 11/60
- Decimal Value: 0.183333
- Percentage: 18.3333%

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2/40 + 2/15 = 11/60

Simplified Fraction

11/60

Mixed Number

Proper (11/60)

Decimal Value

0.183333

Percentage

18.3333%

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Step-by-Step Solution: 2/40 + 2/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 15 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 40 × 15 = 600, keeping the calculation simpler).

LCD(40, 15) = 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 2/15 by 8 so both fractions share the common base 120.

2 × 3/40 × 3 = 6/120 and 2 × 8/15 × 8 = 16/120

Step 3

Add the Numerators

Now add the numerators (6 + 16 = 22) and keep the common denominator 120 unchanged.

6 + 16/120 = 22/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 120, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/120 ÷ 2 = 11/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 60 produces a repeating decimal (approximately 0.183333, or 18.3333%).

11 ÷ 60 = 0.183333 (18.3333%)

Visual Representation

The diagram below illustrates 2/40 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/60`
Mixed Number Form	`11/60`
Decimal Form	`0.183333`
Percentage	`18.3333%`

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Frequently Asked Questions

What is 2/40 plus 2/15 as a fraction?

2/40 + 2/15 in simplest fraction form is 11/60.

What is 2/40 plus 2/15 as a decimal?

2/40 + 2/15 converted to a decimal is 0.183333.

What is 2/40 plus 2/15 as a percentage?

2/40 + 2/15 expressed as a percentage is 18.3333%.

Does 2/40 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.183333...) because the denominator contains prime factors other than 2 and 5.