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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
Notice that 10 is an exact multiple of 5 (5 × 2 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.
Working: LCD(10, 5) = 10

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

Step 3: Add the Numerators
Now add the numerators (1 + 4 = 5) and keep the common denominator 10 unchanged.
Working: 1 + 4/10 = 5/10

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 5 and 10, which is 5. Divide both the numerator and denominator by 5.
Working: 5 ÷ 5/10 ÷ 5 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 1/10 + 2/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 10 is an exact multiple of 5 (5 × 2 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.

LCD(10, 5) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

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

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

Step 3

Add the Numerators

Now add the numerators (1 + 4 = 5) and keep the common denominator 10 unchanged.

1 + 4/10 = 5/10

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 5 and 10, which is 5. Divide both the numerator and denominator by 5.

5 ÷ 5/10 ÷ 5 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 1/10 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 1/10 plus 2/5 as a fraction?

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

What is 1/10 plus 2/5 as a decimal?

1/10 + 2/5 converted to a decimal is 0.5.

What is 1/10 plus 2/5 as a percentage?

1/10 + 2/5 expressed as a percentage is 50%.

Does 1/10 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.