What is 2/16 plus 3/10? (Answer: 17/40)

Exact Answer

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Problem: What is 2/16 plus 3/10?
Formula / Expression: 2/16 + 3/10
Final Answer: 17/40
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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 2/16 by 5, and multiply the numerator and denominator of 3/10 by 8 so both fractions share the common base 80.
Working: 2 × 5/16 × 5 = 10/80 and 3 × 8/10 × 8 = 24/80

Step 3: Add the Numerators
Now add the numerators (10 + 24 = 34) and keep the common denominator 80 unchanged.
Working: 10 + 24/80 = 34/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 80, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/80 ÷ 2 = 17/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 40 yields an exact terminating decimal of 0.425 (or 42.5%).
Working: 17 ÷ 40 = 0.425 (42.5%)

Key Values:
- Simplified Fraction: 17/40
- Mixed Number Form: 17/40
- Decimal Value: 0.425
- Percentage: 42.5%

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Solved with FractionsCalc:
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2/16 + 3/10 = 17/40

Simplified Fraction

17/40

Mixed Number

Proper (17/40)

Decimal Value

0.425

Percentage

42.5%

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

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 2/16 by 5, and multiply the numerator and denominator of 3/10 by 8 so both fractions share the common base 80.

2 × 5/16 × 5 = 10/80 and 3 × 8/10 × 8 = 24/80

Step 3

Add the Numerators

Now add the numerators (10 + 24 = 34) and keep the common denominator 80 unchanged.

10 + 24/80 = 34/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 80, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/80 ÷ 2 = 17/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 40 yields an exact terminating decimal of 0.425 (or 42.5%).

17 ÷ 40 = 0.425 (42.5%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/40`
Mixed Number Form	`17/40`
Decimal Form	`0.425`
Percentage	`42.5%`

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Frequently Asked Questions

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

2/16 + 3/10 in simplest fraction form is 17/40.

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

2/16 + 3/10 converted to a decimal is 0.425.

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

2/16 + 3/10 expressed as a percentage is 42.5%.

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

It results in an exact terminating decimal (0.425) because the denominator in simplest terms contains only prime factors 2 and/or 5.