What is 2/40 plus 2/3? (Answer: 43/60)

Exact Answer

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Problem: What is 2/40 plus 2/3?
Formula / Expression: 2/40 + 2/3
Final Answer: 43/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 3 = 120.
Working: LCD(40, 3) = 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 2/3 by 40 so both fractions share the common base 120.
Working: 2 × 3/40 × 3 = 6/120 and 2 × 40/3 × 40 = 80/120

Step 3: Add the Numerators
Now add the numerators (6 + 80 = 86) and keep the common denominator 120 unchanged.
Working: 6 + 80/120 = 86/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/120 ÷ 2 = 43/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 60 produces a repeating decimal (approximately 0.716667, or 71.6667%).
Working: 43 ÷ 60 = 0.716667 (71.6667%)

Key Values:
- Simplified Fraction: 43/60
- Mixed Number Form: 43/60
- Decimal Value: 0.716667
- Percentage: 71.6667%

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2/40 + 2/3 = 43/60

Simplified Fraction

43/60

Mixed Number

Proper (43/60)

Decimal Value

0.716667

Percentage

71.6667%

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Step-by-Step Solution: 2/40 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 3 = 120.

LCD(40, 3) = 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 2/3 by 40 so both fractions share the common base 120.

2 × 3/40 × 3 = 6/120 and 2 × 40/3 × 40 = 80/120

Step 3

Add the Numerators

Now add the numerators (6 + 80 = 86) and keep the common denominator 120 unchanged.

6 + 80/120 = 86/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 120, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/120 ÷ 2 = 43/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 60 produces a repeating decimal (approximately 0.716667, or 71.6667%).

43 ÷ 60 = 0.716667 (71.6667%)

Visual Representation

The diagram below illustrates 2/40 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/60`
Mixed Number Form	`43/60`
Decimal Form	`0.716667`
Percentage	`71.6667%`

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Frequently Asked Questions

What is 2/40 plus 2/3 as a fraction?

2/40 + 2/3 in simplest fraction form is 43/60.

What is 2/40 plus 2/3 as a decimal?

2/40 + 2/3 converted to a decimal is 0.716667.

What is 2/40 plus 2/3 as a percentage?

2/40 + 2/3 expressed as a percentage is 71.6667%.

Does 2/40 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.716667...) because the denominator contains prime factors other than 2 and 5.