What is 2/10 plus 5/16? (Answer: 41/80)

Exact Answer

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Problem: What is 2/10 plus 5/16?
Formula / Expression: 2/10 + 5/16
Final Answer: 41/80
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 10 × 16 = 160, keeping the calculation simpler).
Working: LCD(10, 16) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/10 by 8, and multiply the numerator and denominator of 5/16 by 5 so both fractions share the common base 80.
Working: 2 × 8/10 × 8 = 16/80 and 5 × 5/16 × 5 = 25/80

Step 3: Add the Numerators
Now add the numerators (16 + 25 = 41) and keep the common denominator 80 unchanged.
Working: 16 + 25/80 = 41/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 80 is 1, confirming that 41/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 80 yields an exact terminating decimal of 0.5125 (or 51.25%).
Working: 41 ÷ 80 = 0.5125 (51.25%)

Key Values:
- Simplified Fraction: 41/80
- Mixed Number Form: 41/80
- Decimal Value: 0.5125
- Percentage: 51.25%

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Solved with FractionsCalc:
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2/10 + 5/16 = 41/80

Simplified Fraction

41/80

Mixed Number

Proper (41/80)

Decimal Value

0.5125

Percentage

51.25%

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Step-by-Step Solution: 2/10 + 5/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 10 × 16 = 160, keeping the calculation simpler).

LCD(10, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 2/10 by 8, and multiply the numerator and denominator of 5/16 by 5 so both fractions share the common base 80.

2 × 8/10 × 8 = 16/80 and 5 × 5/16 × 5 = 25/80

Step 3

Add the Numerators

Now add the numerators (16 + 25 = 41) and keep the common denominator 80 unchanged.

16 + 25/80 = 41/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 80 is 1, confirming that 41/80 cannot be reduced further—it is already in its simplest irreducible form.

41/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 80 yields an exact terminating decimal of 0.5125 (or 51.25%).

41 ÷ 80 = 0.5125 (51.25%)

Visual Representation

The diagram below illustrates 2/10 plus 5/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/80`
Mixed Number Form	`41/80`
Decimal Form	`0.5125`
Percentage	`51.25%`

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Frequently Asked Questions

What is 2/10 plus 5/16 as a fraction?

2/10 + 5/16 in simplest fraction form is 41/80.

What is 2/10 plus 5/16 as a decimal?

2/10 + 5/16 converted to a decimal is 0.5125.

What is 2/10 plus 5/16 as a percentage?

2/10 + 5/16 expressed as a percentage is 51.25%.

Does 2/10 plus 5/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5125) because the denominator in simplest terms contains only prime factors 2 and/or 5.