What is 3/40 plus 2/8? (Answer: 13/40)

Exact Answer

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Problem: What is 3/40 plus 2/8?
Formula / Expression: 3/40 + 2/8
Final Answer: 13/40
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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 3/40 by 1, and multiply the numerator and denominator of 2/8 by 5 so both fractions share the common base 40.
Working: 3 × 1/40 × 1 = 3/40 and 2 × 5/8 × 5 = 10/40

Step 3: Add the Numerators
Now add the numerators (3 + 10 = 13) and keep the common denominator 40 unchanged.
Working: 3 + 10/40 = 13/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 40 is 1, confirming that 13/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 40 yields an exact terminating decimal of 0.325 (or 32.5%).
Working: 13 ÷ 40 = 0.325 (32.5%)

Key Values:
- Simplified Fraction: 13/40
- Mixed Number Form: 13/40
- Decimal Value: 0.325
- Percentage: 32.5%

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3/40 + 2/8 = 13/40

Simplified Fraction

13/40

Mixed Number

Proper (13/40)

Decimal Value

0.325

Percentage

32.5%

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

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

3 × 1/40 × 1 = 3/40 and 2 × 5/8 × 5 = 10/40

Step 3

Add the Numerators

Now add the numerators (3 + 10 = 13) and keep the common denominator 40 unchanged.

3 + 10/40 = 13/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 40 is 1, confirming that 13/40 cannot be reduced further—it is already in its simplest irreducible form.

13/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 40 yields an exact terminating decimal of 0.325 (or 32.5%).

13 ÷ 40 = 0.325 (32.5%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/40`
Mixed Number Form	`13/40`
Decimal Form	`0.325`
Percentage	`32.5%`

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Frequently Asked Questions

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

3/40 + 2/8 in simplest fraction form is 13/40.

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

3/40 + 2/8 converted to a decimal is 0.325.

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

3/40 + 2/8 expressed as a percentage is 32.5%.

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

It results in an exact terminating decimal (0.325) because the denominator in simplest terms contains only prime factors 2 and/or 5.