What is 3/16 plus 2/10? (Answer: 31/80)

Exact Answer

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Problem: What is 3/16 plus 2/10?
Formula / Expression: 3/16 + 2/10
Final Answer: 31/80
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 16 × 10 = 160, keeping the calculation simpler).
Working: LCD(16, 10) = 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 2/10 by 8 so both fractions share the common base 80.
Working: 3 × 5/16 × 5 = 15/80 and 2 × 8/10 × 8 = 16/80

Step 3: Add the Numerators
Now add the numerators (15 + 16 = 31) and keep the common denominator 80 unchanged.
Working: 15 + 16/80 = 31/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 80 is 1, confirming that 31/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 80 yields an exact terminating decimal of 0.3875 (or 38.75%).
Working: 31 ÷ 80 = 0.3875 (38.75%)

Key Values:
- Simplified Fraction: 31/80
- Mixed Number Form: 31/80
- Decimal Value: 0.3875
- Percentage: 38.75%

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Solved with FractionsCalc:
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3/16 + 2/10 = 31/80

Simplified Fraction

31/80

Mixed Number

Proper (31/80)

Decimal Value

0.3875

Percentage

38.75%

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Step-by-Step Solution: 3/16 + 2/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(16, 10) = 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 2/10 by 8 so both fractions share the common base 80.

3 × 5/16 × 5 = 15/80 and 2 × 8/10 × 8 = 16/80

Step 3

Add the Numerators

Now add the numerators (15 + 16 = 31) and keep the common denominator 80 unchanged.

15 + 16/80 = 31/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 80 is 1, confirming that 31/80 cannot be reduced further—it is already in its simplest irreducible form.

31/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 80 yields an exact terminating decimal of 0.3875 (or 38.75%).

31 ÷ 80 = 0.3875 (38.75%)

Visual Representation

The diagram below illustrates 3/16 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/80`
Mixed Number Form	`31/80`
Decimal Form	`0.3875`
Percentage	`38.75%`

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Frequently Asked Questions

What is 3/16 plus 2/10 as a fraction?

3/16 + 2/10 in simplest fraction form is 31/80.

What is 3/16 plus 2/10 as a decimal?

3/16 + 2/10 converted to a decimal is 0.3875.

What is 3/16 plus 2/10 as a percentage?

3/16 + 2/10 expressed as a percentage is 38.75%.

Does 3/16 plus 2/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.3875) because the denominator in simplest terms contains only prime factors 2 and/or 5.