What is 5/16 plus 2/5? (Answer: 57/80)

Exact Answer

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Problem: What is 5/16 plus 2/5?
Formula / Expression: 5/16 + 2/5
Final Answer: 57/80
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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 5/16 by 5, and multiply the numerator and denominator of 2/5 by 16 so both fractions share the common base 80.
Working: 5 × 5/16 × 5 = 25/80 and 2 × 16/5 × 16 = 32/80

Step 3: Add the Numerators
Now add the numerators (25 + 32 = 57) and keep the common denominator 80 unchanged.
Working: 25 + 32/80 = 57/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 57 and 80 is 1, confirming that 57/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 57/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 80 yields an exact terminating decimal of 0.7125 (or 71.25%).
Working: 57 ÷ 80 = 0.7125 (71.25%)

Key Values:
- Simplified Fraction: 57/80
- Mixed Number Form: 57/80
- Decimal Value: 0.7125
- Percentage: 71.25%

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Solved with FractionsCalc:
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5/16 + 2/5 = 57/80

Simplified Fraction

57/80

Mixed Number

Proper (57/80)

Decimal Value

0.7125

Percentage

71.25%

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Step-by-Step Solution: 5/16 + 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 5/16 by 5, and multiply the numerator and denominator of 2/5 by 16 so both fractions share the common base 80.

5 × 5/16 × 5 = 25/80 and 2 × 16/5 × 16 = 32/80

Step 3

Add the Numerators

Now add the numerators (25 + 32 = 57) and keep the common denominator 80 unchanged.

25 + 32/80 = 57/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 57 and 80 is 1, confirming that 57/80 cannot be reduced further—it is already in its simplest irreducible form.

57/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 80 yields an exact terminating decimal of 0.7125 (or 71.25%).

57 ÷ 80 = 0.7125 (71.25%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/80`
Mixed Number Form	`57/80`
Decimal Form	`0.7125`
Percentage	`71.25%`

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Frequently Asked Questions

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

5/16 + 2/5 in simplest fraction form is 57/80.

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

5/16 + 2/5 converted to a decimal is 0.7125.

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

5/16 + 2/5 expressed as a percentage is 71.25%.

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

It results in an exact terminating decimal (0.7125) because the denominator in simplest terms contains only prime factors 2 and/or 5.