What is 3/20 plus 2/8? (Answer: 2/5)

Exact Answer

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Problem: What is 3/20 plus 2/8?
Formula / Expression: 3/20 + 2/8
Final Answer: 2/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 8 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 20 × 8 = 160, keeping the calculation simpler).
Working: LCD(20, 8) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/20 by 2, and multiply the numerator and denominator of 2/8 by 5 so both fractions share the common base 40.
Working: 3 × 2/20 × 2 = 6/40 and 2 × 5/8 × 5 = 10/40

Step 3: Add the Numerators
Now add the numerators (6 + 10 = 16) and keep the common denominator 40 unchanged.
Working: 6 + 10/40 = 16/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 16 and 40, which is 8. Divide both the numerator and denominator by 8.
Working: 16 ÷ 8/40 ÷ 8 = 2/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).
Working: 2 ÷ 5 = 0.4 (40%)

Key Values:
- Simplified Fraction: 2/5
- Mixed Number Form: 2/5
- Decimal Value: 0.4
- Percentage: 40%

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Solved with FractionsCalc:
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3/20 + 2/8 = 2/5

Simplified Fraction

2/5

Mixed Number

Proper (2/5)

Decimal Value

0.4

Percentage

40%

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Step-by-Step Solution: 3/20 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 8 share a common factor (GCD = 4). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 20 × 8 = 160, keeping the calculation simpler).

LCD(20, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 3/20 by 2, and multiply the numerator and denominator of 2/8 by 5 so both fractions share the common base 40.

3 × 2/20 × 2 = 6/40 and 2 × 5/8 × 5 = 10/40

Step 3

Add the Numerators

Now add the numerators (6 + 10 = 16) and keep the common denominator 40 unchanged.

6 + 10/40 = 16/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 16 and 40, which is 8. Divide both the numerator and denominator by 8.

16 ÷ 8/40 ÷ 8 = 2/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 5 yields an exact terminating decimal of 0.4 (or 40%).

2 ÷ 5 = 0.4 (40%)

Visual Representation

The diagram below illustrates 3/20 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/5`
Mixed Number Form	`2/5`
Decimal Form	`0.4`
Percentage	`40%`

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Frequently Asked Questions

What is 3/20 plus 2/8 as a fraction?

3/20 + 2/8 in simplest fraction form is 2/5.

What is 3/20 plus 2/8 as a decimal?

3/20 + 2/8 converted to a decimal is 0.4.

What is 3/20 plus 2/8 as a percentage?

3/20 + 2/8 expressed as a percentage is 40%.

Does 3/20 plus 2/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.4) because the denominator in simplest terms contains only prime factors 2 and/or 5.