What is 2/40 plus 2/5? (Answer: 9/20)

Exact Answer

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Problem: What is 2/40 plus 2/5?
Formula / Expression: 2/40 + 2/5
Final Answer: 9/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 40 is an exact multiple of 5 (5 × 8 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.
Working: LCD(40, 5) = 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 2/5 by 8 so both fractions share the common base 40.
Working: 2 × 1/40 × 1 = 2/40 and 2 × 8/5 × 8 = 16/40

Step 3: Add the Numerators
Now add the numerators (2 + 16 = 18) and keep the common denominator 40 unchanged.
Working: 2 + 16/40 = 18/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 40, which is 2. Divide both the numerator and denominator by 2.
Working: 18 ÷ 2/40 ÷ 2 = 9/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).
Working: 9 ÷ 20 = 0.45 (45%)

Key Values:
- Simplified Fraction: 9/20
- Mixed Number Form: 9/20
- Decimal Value: 0.45
- Percentage: 45%

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2/40 + 2/5 = 9/20

Simplified Fraction

9/20

Mixed Number

Proper (9/20)

Decimal Value

0.45

Percentage

45%

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Step-by-Step Solution: 2/40 + 2/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 40 is an exact multiple of 5 (5 × 8 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.

LCD(40, 5) = 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 2/5 by 8 so both fractions share the common base 40.

2 × 1/40 × 1 = 2/40 and 2 × 8/5 × 8 = 16/40

Step 3

Add the Numerators

Now add the numerators (2 + 16 = 18) and keep the common denominator 40 unchanged.

2 + 16/40 = 18/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 40, which is 2. Divide both the numerator and denominator by 2.

18 ÷ 2/40 ÷ 2 = 9/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).

9 ÷ 20 = 0.45 (45%)

Visual Representation

The diagram below illustrates 2/40 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/20`
Mixed Number Form	`9/20`
Decimal Form	`0.45`
Percentage	`45%`

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Frequently Asked Questions

What is 2/40 plus 2/5 as a fraction?

2/40 + 2/5 in simplest fraction form is 9/20.

What is 2/40 plus 2/5 as a decimal?

2/40 + 2/5 converted to a decimal is 0.45.

What is 2/40 plus 2/5 as a percentage?

2/40 + 2/5 expressed as a percentage is 45%.

Does 2/40 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.45) because the denominator in simplest terms contains only prime factors 2 and/or 5.