What is 1/5 plus 1/2? (Answer: 7/10)

Exact Answer

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Problem: What is 1/5 plus 1/2?
Formula / Expression: 1/5 + 1/2
Final Answer: 7/10
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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 1/5 by 2, and multiply the numerator and denominator of 1/2 by 5 so both fractions share the common base 10.
Working: 1 × 2/5 × 2 = 2/10 and 1 × 5/2 × 5 = 5/10

Step 3: Add the Numerators
Now add the numerators (2 + 5 = 7) and keep the common denominator 10 unchanged.
Working: 2 + 5/10 = 7/10

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 10 is 1, confirming that 7/10 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).
Working: 7 ÷ 10 = 0.7 (70%)

Key Values:
- Simplified Fraction: 7/10
- Mixed Number Form: 7/10
- Decimal Value: 0.7
- Percentage: 70%

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Solved with FractionsCalc:
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1/5 + 1/2 = 7/10

Simplified Fraction

7/10

Mixed Number

Proper (7/10)

Decimal Value

0.7

Percentage

70%

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Step-by-Step Solution: 1/5 + 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 1/5 by 2, and multiply the numerator and denominator of 1/2 by 5 so both fractions share the common base 10.

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

Step 3

Add the Numerators

Now add the numerators (2 + 5 = 7) and keep the common denominator 10 unchanged.

2 + 5/10 = 7/10

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 10 is 1, confirming that 7/10 cannot be reduced further—it is already in its simplest irreducible form.

7/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).

7 ÷ 10 = 0.7 (70%)

Visual Representation

The diagram below illustrates 1/5 plus 1/2 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/10`
Mixed Number Form	`7/10`
Decimal Form	`0.7`
Percentage	`70%`

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Frequently Asked Questions

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

1/5 + 1/2 in simplest fraction form is 7/10.

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

1/5 + 1/2 converted to a decimal is 0.7.

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

1/5 + 1/2 expressed as a percentage is 70%.

Does 1/5 plus 1/2 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.7) because the denominator in simplest terms contains only prime factors 2 and/or 5.