What is 2/40 plus 2/20? (Answer: 3/20)

Exact Answer

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Problem: What is 2/40 plus 2/20?
Formula / Expression: 2/40 + 2/20
Final Answer: 3/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 40 is an exact multiple of 20 (20 × 2 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.
Working: LCD(40, 20) = 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 2/20 by 2 so both fractions share the common base 40.
Working: 2 × 1/40 × 1 = 2/40 and 2 × 2/20 × 2 = 4/40

Step 3: Add the Numerators
Now add the numerators (2 + 4 = 6) and keep the common denominator 40 unchanged.
Working: 2 + 4/40 = 6/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 40, which is 2. Divide both the numerator and denominator by 2.
Working: 6 ÷ 2/40 ÷ 2 = 3/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 20 yields an exact terminating decimal of 0.15 (or 15%).
Working: 3 ÷ 20 = 0.15 (15%)

Key Values:
- Simplified Fraction: 3/20
- Mixed Number Form: 3/20
- Decimal Value: 0.15
- Percentage: 15%

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2/40 + 2/20 = 3/20

Simplified Fraction

3/20

Mixed Number

Proper (3/20)

Decimal Value

0.15

Percentage

15%

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Step-by-Step Solution: 2/40 + 2/20

Step 1

Find the Least Common Denominator (LCD)

Notice that 40 is an exact multiple of 20 (20 × 2 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.

LCD(40, 20) = 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 2/20 by 2 so both fractions share the common base 40.

2 × 1/40 × 1 = 2/40 and 2 × 2/20 × 2 = 4/40

Step 3

Add the Numerators

Now add the numerators (2 + 4 = 6) and keep the common denominator 40 unchanged.

2 + 4/40 = 6/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 6 and 40, which is 2. Divide both the numerator and denominator by 2.

6 ÷ 2/40 ÷ 2 = 3/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 20 yields an exact terminating decimal of 0.15 (or 15%).

3 ÷ 20 = 0.15 (15%)

Visual Representation

The diagram below illustrates 2/40 plus 2/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/20`
Mixed Number Form	`3/20`
Decimal Form	`0.15`
Percentage	`15%`

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Frequently Asked Questions

What is 2/40 plus 2/20 as a fraction?

2/40 + 2/20 in simplest fraction form is 3/20.

What is 2/40 plus 2/20 as a decimal?

2/40 + 2/20 converted to a decimal is 0.15.

What is 2/40 plus 2/20 as a percentage?

2/40 + 2/20 expressed as a percentage is 15%.

Does 2/40 plus 2/20 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.15) because the denominator in simplest terms contains only prime factors 2 and/or 5.