What is 3/16 plus 2/5? (Answer: 47/80)

Exact Answer

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Problem: What is 3/16 plus 2/5?
Formula / Expression: 3/16 + 2/5
Final Answer: 47/80
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 5 = 80.
Working: LCD(16, 5) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 3/16 by 5, and multiply the numerator and denominator of 2/5 by 16 so both fractions share the common base 80.
Working: 3 × 5/16 × 5 = 15/80 and 2 × 16/5 × 16 = 32/80

Step 3: Add the Numerators
Now add the numerators (15 + 32 = 47) and keep the common denominator 80 unchanged.
Working: 15 + 32/80 = 47/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 80 is 1, confirming that 47/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 80 yields an exact terminating decimal of 0.5875 (or 58.75%).
Working: 47 ÷ 80 = 0.5875 (58.75%)

Key Values:
- Simplified Fraction: 47/80
- Mixed Number Form: 47/80
- Decimal Value: 0.5875
- Percentage: 58.75%

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Solved with FractionsCalc:
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3/16 + 2/5 = 47/80

Simplified Fraction

47/80

Mixed Number

Proper (47/80)

Decimal Value

0.5875

Percentage

58.75%

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Step-by-Step Solution: 3/16 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 5 = 80.

LCD(16, 5) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 3/16 by 5, and multiply the numerator and denominator of 2/5 by 16 so both fractions share the common base 80.

3 × 5/16 × 5 = 15/80 and 2 × 16/5 × 16 = 32/80

Step 3

Add the Numerators

Now add the numerators (15 + 32 = 47) and keep the common denominator 80 unchanged.

15 + 32/80 = 47/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 80 is 1, confirming that 47/80 cannot be reduced further—it is already in its simplest irreducible form.

47/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 80 yields an exact terminating decimal of 0.5875 (or 58.75%).

47 ÷ 80 = 0.5875 (58.75%)

Visual Representation

The diagram below illustrates 3/16 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/80`
Mixed Number Form	`47/80`
Decimal Form	`0.5875`
Percentage	`58.75%`

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Frequently Asked Questions

What is 3/16 plus 2/5 as a fraction?

3/16 + 2/5 in simplest fraction form is 47/80.

What is 3/16 plus 2/5 as a decimal?

3/16 + 2/5 converted to a decimal is 0.5875.

What is 3/16 plus 2/5 as a percentage?

3/16 + 2/5 expressed as a percentage is 58.75%.

Does 3/16 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5875) because the denominator in simplest terms contains only prime factors 2 and/or 5.