What is 3/20 plus 2/5? (Answer: 11/20)

Exact Answer

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Problem: What is 3/20 plus 2/5?
Formula / Expression: 3/20 + 2/5
Final Answer: 11/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 20 is an exact multiple of 5 (5 × 4 = 20). The Least Common Denominator (LCD) is simply 20, meaning we only need to scale one fraction.
Working: LCD(20, 5) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 3/20 by 1, and multiply the numerator and denominator of 2/5 by 4 so both fractions share the common base 20.
Working: 3 × 1/20 × 1 = 3/20 and 2 × 4/5 × 4 = 8/20

Step 3: Add the Numerators
Now add the numerators (3 + 8 = 11) and keep the common denominator 20 unchanged.
Working: 3 + 8/20 = 11/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 20 is 1, confirming that 11/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 20 yields an exact terminating decimal of 0.55 (or 55%).
Working: 11 ÷ 20 = 0.55 (55%)

Key Values:
- Simplified Fraction: 11/20
- Mixed Number Form: 11/20
- Decimal Value: 0.55
- Percentage: 55%

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Solved with FractionsCalc:
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3/20 + 2/5 = 11/20

Simplified Fraction

11/20

Mixed Number

Proper (11/20)

Decimal Value

0.55

Percentage

55%

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Step-by-Step Solution: 3/20 + 2/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 20 is an exact multiple of 5 (5 × 4 = 20). The Least Common Denominator (LCD) is simply 20, meaning we only need to scale one fraction.

LCD(20, 5) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 3/20 by 1, and multiply the numerator and denominator of 2/5 by 4 so both fractions share the common base 20.

3 × 1/20 × 1 = 3/20 and 2 × 4/5 × 4 = 8/20

Step 3

Add the Numerators

Now add the numerators (3 + 8 = 11) and keep the common denominator 20 unchanged.

3 + 8/20 = 11/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 20 is 1, confirming that 11/20 cannot be reduced further—it is already in its simplest irreducible form.

11/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 20 yields an exact terminating decimal of 0.55 (or 55%).

11 ÷ 20 = 0.55 (55%)

Visual Representation

The diagram below illustrates 3/20 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/20`
Mixed Number Form	`11/20`
Decimal Form	`0.55`
Percentage	`55%`

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Frequently Asked Questions

What is 3/20 plus 2/5 as a fraction?

3/20 + 2/5 in simplest fraction form is 11/20.

What is 3/20 plus 2/5 as a decimal?

3/20 + 2/5 converted to a decimal is 0.55.

What is 3/20 plus 2/5 as a percentage?

3/20 + 2/5 expressed as a percentage is 55%.

Does 3/20 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.55) because the denominator in simplest terms contains only prime factors 2 and/or 5.