What is 4/16 plus 2/5? (Answer: 13/20)

Exact Answer

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Problem: What is 4/16 plus 2/5?
Formula / Expression: 4/16 + 2/5
Final Answer: 13/20
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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 4/16 by 5, and multiply the numerator and denominator of 2/5 by 16 so both fractions share the common base 80.
Working: 4 × 5/16 × 5 = 20/80 and 2 × 16/5 × 16 = 32/80

Step 3: Add the Numerators
Now add the numerators (20 + 32 = 52) and keep the common denominator 80 unchanged.
Working: 20 + 32/80 = 52/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 80, which is 4. Divide both the numerator and denominator by 4.
Working: 52 ÷ 4/80 ÷ 4 = 13/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 20 yields an exact terminating decimal of 0.65 (or 65%).
Working: 13 ÷ 20 = 0.65 (65%)

Key Values:
- Simplified Fraction: 13/20
- Mixed Number Form: 13/20
- Decimal Value: 0.65
- Percentage: 65%

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Solved with FractionsCalc:
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4/16 + 2/5 = 13/20

Simplified Fraction

13/20

Mixed Number

Proper (13/20)

Decimal Value

0.65

Percentage

65%

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Step-by-Step Solution: 4/16 + 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 4/16 by 5, and multiply the numerator and denominator of 2/5 by 16 so both fractions share the common base 80.

4 × 5/16 × 5 = 20/80 and 2 × 16/5 × 16 = 32/80

Step 3

Add the Numerators

Now add the numerators (20 + 32 = 52) and keep the common denominator 80 unchanged.

20 + 32/80 = 52/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 52 and 80, which is 4. Divide both the numerator and denominator by 4.

52 ÷ 4/80 ÷ 4 = 13/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 20 yields an exact terminating decimal of 0.65 (or 65%).

13 ÷ 20 = 0.65 (65%)

Visual Representation

The diagram below illustrates 4/16 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/20`
Mixed Number Form	`13/20`
Decimal Form	`0.65`
Percentage	`65%`

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Frequently Asked Questions

What is 4/16 plus 2/5 as a fraction?

4/16 + 2/5 in simplest fraction form is 13/20.

What is 4/16 plus 2/5 as a decimal?

4/16 + 2/5 converted to a decimal is 0.65.

What is 4/16 plus 2/5 as a percentage?

4/16 + 2/5 expressed as a percentage is 65%.

Does 4/16 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.65) because the denominator in simplest terms contains only prime factors 2 and/or 5.