What is 2/16 plus 3/5? (Answer: 29/40)

Exact Answer

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Problem: What is 2/16 plus 3/5?
Formula / Expression: 2/16 + 3/5
Final Answer: 29/40
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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 2/16 by 5, and multiply the numerator and denominator of 3/5 by 16 so both fractions share the common base 80.
Working: 2 × 5/16 × 5 = 10/80 and 3 × 16/5 × 16 = 48/80

Step 3: Add the Numerators
Now add the numerators (10 + 48 = 58) and keep the common denominator 80 unchanged.
Working: 10 + 48/80 = 58/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 80, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/80 ÷ 2 = 29/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 40 yields an exact terminating decimal of 0.725 (or 72.5%).
Working: 29 ÷ 40 = 0.725 (72.5%)

Key Values:
- Simplified Fraction: 29/40
- Mixed Number Form: 29/40
- Decimal Value: 0.725
- Percentage: 72.5%

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Solved with FractionsCalc:
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2/16 + 3/5 = 29/40

Simplified Fraction

29/40

Mixed Number

Proper (29/40)

Decimal Value

0.725

Percentage

72.5%

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Step-by-Step Solution: 2/16 + 3/5

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

2 × 5/16 × 5 = 10/80 and 3 × 16/5 × 16 = 48/80

Step 3

Add the Numerators

Now add the numerators (10 + 48 = 58) and keep the common denominator 80 unchanged.

10 + 48/80 = 58/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 80, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/80 ÷ 2 = 29/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 40 yields an exact terminating decimal of 0.725 (or 72.5%).

29 ÷ 40 = 0.725 (72.5%)

Visual Representation

The diagram below illustrates 2/16 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/40`
Mixed Number Form	`29/40`
Decimal Form	`0.725`
Percentage	`72.5%`

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Frequently Asked Questions

What is 2/16 plus 3/5 as a fraction?

2/16 + 3/5 in simplest fraction form is 29/40.

What is 2/16 plus 3/5 as a decimal?

2/16 + 3/5 converted to a decimal is 0.725.

What is 2/16 plus 3/5 as a percentage?

2/16 + 3/5 expressed as a percentage is 72.5%.

Does 2/16 plus 3/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.725) because the denominator in simplest terms contains only prime factors 2 and/or 5.