What is 2/5 plus 4/10? (Answer: 4/5)

Exact Answer

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Problem: What is 2/5 plus 4/10?
Formula / Expression: 2/5 + 4/10
Final Answer: 4/5
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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(5, 10) = 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 4/10 by 1 so both fractions share the common base 10.
Working: 2 × 2/5 × 2 = 4/10 and 4 × 1/10 × 1 = 4/10

Step 3: Add the Numerators
Now add the numerators (4 + 4 = 8) and keep the common denominator 10 unchanged.
Working: 4 + 4/10 = 8/10

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 8 and 10, which is 2. Divide both the numerator and denominator by 2.
Working: 8 ÷ 2/10 ÷ 2 = 4/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).
Working: 4 ÷ 5 = 0.8 (80%)

Key Values:
- Simplified Fraction: 4/5
- Mixed Number Form: 4/5
- Decimal Value: 0.8
- Percentage: 80%

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Solved with FractionsCalc:
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2/5 + 4/10 = 4/5

Simplified Fraction

4/5

Mixed Number

Proper (4/5)

Decimal Value

0.8

Percentage

80%

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Step-by-Step Solution: 2/5 + 4/10

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(5, 10) = 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 4/10 by 1 so both fractions share the common base 10.

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

Step 3

Add the Numerators

Now add the numerators (4 + 4 = 8) and keep the common denominator 10 unchanged.

4 + 4/10 = 8/10

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 8 and 10, which is 2. Divide both the numerator and denominator by 2.

8 ÷ 2/10 ÷ 2 = 4/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).

4 ÷ 5 = 0.8 (80%)

Visual Representation

The diagram below illustrates 2/5 plus 4/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/5`
Mixed Number Form	`4/5`
Decimal Form	`0.8`
Percentage	`80%`

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Frequently Asked Questions

What is 2/5 plus 4/10 as a fraction?

2/5 + 4/10 in simplest fraction form is 4/5.

What is 2/5 plus 4/10 as a decimal?

2/5 + 4/10 converted to a decimal is 0.8.

What is 2/5 plus 4/10 as a percentage?

2/5 + 4/10 expressed as a percentage is 80%.

Does 2/5 plus 4/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.8) because the denominator in simplest terms contains only prime factors 2 and/or 5.