What is 2/40 plus 2/8? (Answer: 3/10)

Exact Answer

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

Step 3: Add the Numerators
Now add the numerators (2 + 10 = 12) and keep the common denominator 40 unchanged.
Working: 2 + 10/40 = 12/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 40, which is 4. Divide both the numerator and denominator by 4.
Working: 12 ÷ 4/40 ÷ 4 = 3/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 10 yields an exact terminating decimal of 0.3 (or 30%).
Working: 3 ÷ 10 = 0.3 (30%)

Key Values:
- Simplified Fraction: 3/10
- Mixed Number Form: 3/10
- Decimal Value: 0.3
- Percentage: 30%

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Solved with FractionsCalc:
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2/40 + 2/8 = 3/10

Simplified Fraction

3/10

Mixed Number

Proper (3/10)

Decimal Value

0.3

Percentage

30%

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Step-by-Step Solution: 2/40 + 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 2/40 by 1, and multiply the numerator and denominator of 2/8 by 5 so both fractions share the common base 40.

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

Step 3

Add the Numerators

Now add the numerators (2 + 10 = 12) and keep the common denominator 40 unchanged.

2 + 10/40 = 12/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 40, which is 4. Divide both the numerator and denominator by 4.

12 ÷ 4/40 ÷ 4 = 3/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 10 yields an exact terminating decimal of 0.3 (or 30%).

3 ÷ 10 = 0.3 (30%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/10`
Mixed Number Form	`3/10`
Decimal Form	`0.3`
Percentage	`30%`

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Frequently Asked Questions

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

2/40 + 2/8 in simplest fraction form is 3/10.

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

2/40 + 2/8 converted to a decimal is 0.3.

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

2/40 + 2/8 expressed as a percentage is 30%.

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

It results in an exact terminating decimal (0.3) because the denominator in simplest terms contains only prime factors 2 and/or 5.