What is 1/8 plus 2/5? (Answer: 21/40)

Exact Answer

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Problem: What is 1/8 plus 2/5?
Formula / Expression: 1/8 + 2/5
Final Answer: 21/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.
Working: LCD(8, 5) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 1/8 by 5, and multiply the numerator and denominator of 2/5 by 8 so both fractions share the common base 40.
Working: 1 × 5/8 × 5 = 5/40 and 2 × 8/5 × 8 = 16/40

Step 3: Add the Numerators
Now add the numerators (5 + 16 = 21) and keep the common denominator 40 unchanged.
Working: 5 + 16/40 = 21/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 40 is 1, confirming that 21/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 40 yields an exact terminating decimal of 0.525 (or 52.5%).
Working: 21 ÷ 40 = 0.525 (52.5%)

Key Values:
- Simplified Fraction: 21/40
- Mixed Number Form: 21/40
- Decimal Value: 0.525
- Percentage: 52.5%

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Solved with FractionsCalc:
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1/8 + 2/5 = 21/40

Simplified Fraction

21/40

Mixed Number

Proper (21/40)

Decimal Value

0.525

Percentage

52.5%

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Step-by-Step Solution: 1/8 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 5 = 40.

LCD(8, 5) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 1/8 by 5, and multiply the numerator and denominator of 2/5 by 8 so both fractions share the common base 40.

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

Step 3

Add the Numerators

Now add the numerators (5 + 16 = 21) and keep the common denominator 40 unchanged.

5 + 16/40 = 21/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 40 is 1, confirming that 21/40 cannot be reduced further—it is already in its simplest irreducible form.

21/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 40 yields an exact terminating decimal of 0.525 (or 52.5%).

21 ÷ 40 = 0.525 (52.5%)

Visual Representation

The diagram below illustrates 1/8 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/40`
Mixed Number Form	`21/40`
Decimal Form	`0.525`
Percentage	`52.5%`

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Frequently Asked Questions

What is 1/8 plus 2/5 as a fraction?

1/8 + 2/5 in simplest fraction form is 21/40.

What is 1/8 plus 2/5 as a decimal?

1/8 + 2/5 converted to a decimal is 0.525.

What is 1/8 plus 2/5 as a percentage?

1/8 + 2/5 expressed as a percentage is 52.5%.

Does 1/8 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.525) because the denominator in simplest terms contains only prime factors 2 and/or 5.