What is 2/40 plus 3/8? (Answer: 17/40)

Exact Answer

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Problem: What is 2/40 plus 3/8?
Formula / Expression: 2/40 + 3/8
Final Answer: 17/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 40 is an exact multiple of 8 (8 × 5 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.
Working: LCD(40, 8) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 2/40 by 1, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.
Working: 2 × 1/40 × 1 = 2/40 and 3 × 5/8 × 5 = 15/40

Step 3: Add the Numerators
Now add the numerators (2 + 15 = 17) and keep the common denominator 40 unchanged.
Working: 2 + 15/40 = 17/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 40 is 1, confirming that 17/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 40 yields an exact terminating decimal of 0.425 (or 42.5%).
Working: 17 ÷ 40 = 0.425 (42.5%)

Key Values:
- Simplified Fraction: 17/40
- Mixed Number Form: 17/40
- Decimal Value: 0.425
- Percentage: 42.5%

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2/40 + 3/8 = 17/40

Simplified Fraction

17/40

Mixed Number

Proper (17/40)

Decimal Value

0.425

Percentage

42.5%

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Step-by-Step Solution: 2/40 + 3/8

Step 1

Find the Least Common Denominator (LCD)

Notice that 40 is an exact multiple of 8 (8 × 5 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.

LCD(40, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 2/40 by 1, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.

2 × 1/40 × 1 = 2/40 and 3 × 5/8 × 5 = 15/40

Step 3

Add the Numerators

Now add the numerators (2 + 15 = 17) and keep the common denominator 40 unchanged.

2 + 15/40 = 17/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 40 is 1, confirming that 17/40 cannot be reduced further—it is already in its simplest irreducible form.

17/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 40 yields an exact terminating decimal of 0.425 (or 42.5%).

17 ÷ 40 = 0.425 (42.5%)

Visual Representation

The diagram below illustrates 2/40 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/40`
Mixed Number Form	`17/40`
Decimal Form	`0.425`
Percentage	`42.5%`

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Frequently Asked Questions

What is 2/40 plus 3/8 as a fraction?

2/40 + 3/8 in simplest fraction form is 17/40.

What is 2/40 plus 3/8 as a decimal?

2/40 + 3/8 converted to a decimal is 0.425.

What is 2/40 plus 3/8 as a percentage?

2/40 + 3/8 expressed as a percentage is 42.5%.

Does 2/40 plus 3/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.425) because the denominator in simplest terms contains only prime factors 2 and/or 5.