What is 1/5 plus 3/8? (Answer: 23/40)

Exact Answer

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Problem: What is 1/5 plus 3/8?
Formula / Expression: 1/5 + 3/8
Final Answer: 23/40
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 1/5 by 8, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.
Working: 1 × 8/5 × 8 = 8/40 and 3 × 5/8 × 5 = 15/40

Step 3: Add the Numerators
Now add the numerators (8 + 15 = 23) and keep the common denominator 40 unchanged.
Working: 8 + 15/40 = 23/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 40 is 1, confirming that 23/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 40 yields an exact terminating decimal of 0.575 (or 57.5%).
Working: 23 ÷ 40 = 0.575 (57.5%)

Key Values:
- Simplified Fraction: 23/40
- Mixed Number Form: 23/40
- Decimal Value: 0.575
- Percentage: 57.5%

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Solved with FractionsCalc:
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1/5 + 3/8 = 23/40

Simplified Fraction

23/40

Mixed Number

Proper (23/40)

Decimal Value

0.575

Percentage

57.5%

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Step-by-Step Solution: 1/5 + 3/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(5, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 1/5 by 8, and multiply the numerator and denominator of 3/8 by 5 so both fractions share the common base 40.

1 × 8/5 × 8 = 8/40 and 3 × 5/8 × 5 = 15/40

Step 3

Add the Numerators

Now add the numerators (8 + 15 = 23) and keep the common denominator 40 unchanged.

8 + 15/40 = 23/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 40 is 1, confirming that 23/40 cannot be reduced further—it is already in its simplest irreducible form.

23/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 40 yields an exact terminating decimal of 0.575 (or 57.5%).

23 ÷ 40 = 0.575 (57.5%)

Visual Representation

The diagram below illustrates 1/5 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/40`
Mixed Number Form	`23/40`
Decimal Form	`0.575`
Percentage	`57.5%`

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Frequently Asked Questions

What is 1/5 plus 3/8 as a fraction?

1/5 + 3/8 in simplest fraction form is 23/40.

What is 1/5 plus 3/8 as a decimal?

1/5 + 3/8 converted to a decimal is 0.575.

What is 1/5 plus 3/8 as a percentage?

1/5 + 3/8 expressed as a percentage is 57.5%.

Does 1/5 plus 3/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.575) because the denominator in simplest terms contains only prime factors 2 and/or 5.