What is 9/40 plus 2/5? (Answer: 5/8)

Exact Answer

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Problem: What is 9/40 plus 2/5?
Formula / Expression: 9/40 + 2/5
Final Answer: 5/8
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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 9/40 by 1, and multiply the numerator and denominator of 2/5 by 8 so both fractions share the common base 40.
Working: 9 × 1/40 × 1 = 9/40 and 2 × 8/5 × 8 = 16/40

Step 3: Add the Numerators
Now add the numerators (9 + 16 = 25) and keep the common denominator 40 unchanged.
Working: 9 + 16/40 = 25/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 25 and 40, which is 5. Divide both the numerator and denominator by 5.
Working: 25 ÷ 5/40 ÷ 5 = 5/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).
Working: 5 ÷ 8 = 0.625 (62.5%)

Key Values:
- Simplified Fraction: 5/8
- Mixed Number Form: 5/8
- Decimal Value: 0.625
- Percentage: 62.5%

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Solved with FractionsCalc:
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9/40 + 2/5 = 5/8

Simplified Fraction

5/8

Mixed Number

Proper (5/8)

Decimal Value

0.625

Percentage

62.5%

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Step-by-Step Solution: 9/40 + 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 9/40 by 1, and multiply the numerator and denominator of 2/5 by 8 so both fractions share the common base 40.

9 × 1/40 × 1 = 9/40 and 2 × 8/5 × 8 = 16/40

Step 3

Add the Numerators

Now add the numerators (9 + 16 = 25) and keep the common denominator 40 unchanged.

9 + 16/40 = 25/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 25 and 40, which is 5. Divide both the numerator and denominator by 5.

25 ÷ 5/40 ÷ 5 = 5/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).

5 ÷ 8 = 0.625 (62.5%)

Visual Representation

The diagram below illustrates 9/40 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/8`
Mixed Number Form	`5/8`
Decimal Form	`0.625`
Percentage	`62.5%`

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Frequently Asked Questions

What is 9/40 plus 2/5 as a fraction?

9/40 + 2/5 in simplest fraction form is 5/8.

What is 9/40 plus 2/5 as a decimal?

9/40 + 2/5 converted to a decimal is 0.625.

What is 9/40 plus 2/5 as a percentage?

9/40 + 2/5 expressed as a percentage is 62.5%.

Does 9/40 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.625) because the denominator in simplest terms contains only prime factors 2 and/or 5.