What is 2/5 plus 8/16? (Answer: 9/10)

Exact Answer

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Problem: What is 2/5 plus 8/16?
Formula / Expression: 2/5 + 8/16
Final Answer: 9/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 16 = 80.
Working: LCD(5, 16) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/5 by 16, and multiply the numerator and denominator of 8/16 by 5 so both fractions share the common base 80.
Working: 2 × 16/5 × 16 = 32/80 and 8 × 5/16 × 5 = 40/80

Step 3: Add the Numerators
Now add the numerators (32 + 40 = 72) and keep the common denominator 80 unchanged.
Working: 32 + 40/80 = 72/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 72 and 80, which is 8. Divide both the numerator and denominator by 8.
Working: 72 ÷ 8/80 ÷ 8 = 9/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 10 yields an exact terminating decimal of 0.9 (or 90%).
Working: 9 ÷ 10 = 0.9 (90%)

Key Values:
- Simplified Fraction: 9/10
- Mixed Number Form: 9/10
- Decimal Value: 0.9
- Percentage: 90%

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Solved with FractionsCalc:
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2/5 + 8/16 = 9/10

Simplified Fraction

9/10

Mixed Number

Proper (9/10)

Decimal Value

0.9

Percentage

90%

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Step-by-Step Solution: 2/5 + 8/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 16 = 80.

LCD(5, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

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

2 × 16/5 × 16 = 32/80 and 8 × 5/16 × 5 = 40/80

Step 3

Add the Numerators

Now add the numerators (32 + 40 = 72) and keep the common denominator 80 unchanged.

32 + 40/80 = 72/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 72 and 80, which is 8. Divide both the numerator and denominator by 8.

72 ÷ 8/80 ÷ 8 = 9/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 10 yields an exact terminating decimal of 0.9 (or 90%).

9 ÷ 10 = 0.9 (90%)

Visual Representation

The diagram below illustrates 2/5 plus 8/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/10`
Mixed Number Form	`9/10`
Decimal Form	`0.9`
Percentage	`90%`

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Frequently Asked Questions

What is 2/5 plus 8/16 as a fraction?

2/5 + 8/16 in simplest fraction form is 9/10.

What is 2/5 plus 8/16 as a decimal?

2/5 + 8/16 converted to a decimal is 0.9.

What is 2/5 plus 8/16 as a percentage?

2/5 + 8/16 expressed as a percentage is 90%.

Does 2/5 plus 8/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.9) because the denominator in simplest terms contains only prime factors 2 and/or 5.