What is 2/5 plus 1/2? (Answer: 9/10)

Exact Answer

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Problem: What is 2/5 plus 1/2?
Formula / Expression: 2/5 + 1/2
Final Answer: 9/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 2 = 10.
Working: LCD(5, 2) = 10

Step 2: Convert to Equivalent Fractions with Common Denominator 10
Multiply the numerator and denominator of 2/5 by 2, and multiply the numerator and denominator of 1/2 by 5 so both fractions share the common base 10.
Working: 2 × 2/5 × 2 = 4/10 and 1 × 5/2 × 5 = 5/10

Step 3: Add the Numerators
Now add the numerators (4 + 5 = 9) and keep the common denominator 10 unchanged.
Working: 4 + 5/10 = 9/10

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 9 and 10 is 1, confirming that 9/10 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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 + 1/2 = 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 + 1/2

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 2 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 2 = 10.

LCD(5, 2) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

Multiply the numerator and denominator of 2/5 by 2, and multiply the numerator and denominator of 1/2 by 5 so both fractions share the common base 10.

2 × 2/5 × 2 = 4/10 and 1 × 5/2 × 5 = 5/10

Step 3

Add the Numerators

Now add the numerators (4 + 5 = 9) and keep the common denominator 10 unchanged.

4 + 5/10 = 9/10

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 9 and 10 is 1, confirming that 9/10 cannot be reduced further—it is already in its simplest irreducible form.

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 1/2 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 1/2 as a fraction?

2/5 + 1/2 in simplest fraction form is 9/10.

What is 2/5 plus 1/2 as a decimal?

2/5 + 1/2 converted to a decimal is 0.9.

What is 2/5 plus 1/2 as a percentage?

2/5 + 1/2 expressed as a percentage is 90%.

Does 2/5 plus 1/2 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.