What is 3/10 plus 2/4? (Answer: 4/5)

Exact Answer

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Problem: What is 3/10 plus 2/4?
Formula / Expression: 3/10 + 2/4
Final Answer: 4/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 10 × 4 = 40, keeping the calculation simpler).
Working: LCD(10, 4) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 3/10 by 2, and multiply the numerator and denominator of 2/4 by 5 so both fractions share the common base 20.
Working: 3 × 2/10 × 2 = 6/20 and 2 × 5/4 × 5 = 10/20

Step 3: Add the Numerators
Now add the numerators (6 + 10 = 16) and keep the common denominator 20 unchanged.
Working: 6 + 10/20 = 16/20

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 16 and 20, which is 4. Divide both the numerator and denominator by 4.
Working: 16 ÷ 4/20 ÷ 4 = 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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3/10 + 2/4 = 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: 3/10 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 10 × 4 = 40, keeping the calculation simpler).

LCD(10, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 3/10 by 2, and multiply the numerator and denominator of 2/4 by 5 so both fractions share the common base 20.

3 × 2/10 × 2 = 6/20 and 2 × 5/4 × 5 = 10/20

Step 3

Add the Numerators

Now add the numerators (6 + 10 = 16) and keep the common denominator 20 unchanged.

6 + 10/20 = 16/20

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 16 and 20, which is 4. Divide both the numerator and denominator by 4.

16 ÷ 4/20 ÷ 4 = 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 3/10 plus 2/4 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 3/10 plus 2/4 as a fraction?

3/10 + 2/4 in simplest fraction form is 4/5.

What is 3/10 plus 2/4 as a decimal?

3/10 + 2/4 converted to a decimal is 0.8.

What is 3/10 plus 2/4 as a percentage?

3/10 + 2/4 expressed as a percentage is 80%.

Does 3/10 plus 2/4 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.