What is 3/10 plus 4/8? (Answer: 4/5)

Exact Answer

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Problem: What is 3/10 plus 4/8?
Formula / Expression: 3/10 + 4/8
Final Answer: 4/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 10 × 8 = 80, keeping the calculation simpler).
Working: LCD(10, 8) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 3/10 by 4, and multiply the numerator and denominator of 4/8 by 5 so both fractions share the common base 40.
Working: 3 × 4/10 × 4 = 12/40 and 4 × 5/8 × 5 = 20/40

Step 3: Add the Numerators
Now add the numerators (12 + 20 = 32) and keep the common denominator 40 unchanged.
Working: 12 + 20/40 = 32/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 40, which is 8. Divide both the numerator and denominator by 8.
Working: 32 ÷ 8/40 ÷ 8 = 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 + 4/8 = 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 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 40 (which is smaller than their product 10 × 8 = 80, keeping the calculation simpler).

LCD(10, 8) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 3/10 by 4, and multiply the numerator and denominator of 4/8 by 5 so both fractions share the common base 40.

3 × 4/10 × 4 = 12/40 and 4 × 5/8 × 5 = 20/40

Step 3

Add the Numerators

Now add the numerators (12 + 20 = 32) and keep the common denominator 40 unchanged.

12 + 20/40 = 32/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 40, which is 8. Divide both the numerator and denominator by 8.

32 ÷ 8/40 ÷ 8 = 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 4/8 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 4/8 as a fraction?

3/10 + 4/8 in simplest fraction form is 4/5.

What is 3/10 plus 4/8 as a decimal?

3/10 + 4/8 converted to a decimal is 0.8.

What is 3/10 plus 4/8 as a percentage?

3/10 + 4/8 expressed as a percentage is 80%.

Does 3/10 plus 4/8 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.