What is 2/5 plus 9/20? (Answer: 17/20)

Exact Answer

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Problem: What is 2/5 plus 9/20?
Formula / Expression: 2/5 + 9/20
Final Answer: 17/20
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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(5, 20) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 2/5 by 4, and multiply the numerator and denominator of 9/20 by 1 so both fractions share the common base 20.
Working: 2 × 4/5 × 4 = 8/20 and 9 × 1/20 × 1 = 9/20

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 20 unchanged.
Working: 8 + 9/20 = 17/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 20 is 1, confirming that 17/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 20 yields an exact terminating decimal of 0.85 (or 85%).
Working: 17 ÷ 20 = 0.85 (85%)

Key Values:
- Simplified Fraction: 17/20
- Mixed Number Form: 17/20
- Decimal Value: 0.85
- Percentage: 85%

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Solved with FractionsCalc:
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2/5 + 9/20 = 17/20

Simplified Fraction

17/20

Mixed Number

Proper (17/20)

Decimal Value

0.85

Percentage

85%

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Step-by-Step Solution: 2/5 + 9/20

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(5, 20) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 2/5 by 4, and multiply the numerator and denominator of 9/20 by 1 so both fractions share the common base 20.

2 × 4/5 × 4 = 8/20 and 9 × 1/20 × 1 = 9/20

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 20 unchanged.

8 + 9/20 = 17/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 20 is 1, confirming that 17/20 cannot be reduced further—it is already in its simplest irreducible form.

17/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 20 yields an exact terminating decimal of 0.85 (or 85%).

17 ÷ 20 = 0.85 (85%)

Visual Representation

The diagram below illustrates 2/5 plus 9/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/20`
Mixed Number Form	`17/20`
Decimal Form	`0.85`
Percentage	`85%`

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Frequently Asked Questions

What is 2/5 plus 9/20 as a fraction?

2/5 + 9/20 in simplest fraction form is 17/20.

What is 2/5 plus 9/20 as a decimal?

2/5 + 9/20 converted to a decimal is 0.85.

What is 2/5 plus 9/20 as a percentage?

2/5 + 9/20 expressed as a percentage is 85%.

Does 2/5 plus 9/20 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.85) because the denominator in simplest terms contains only prime factors 2 and/or 5.