What is 3/30 plus 2/8? (Answer: 7/20)

Exact Answer

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Problem: What is 3/30 plus 2/8?
Formula / Expression: 3/30 + 2/8
Final Answer: 7/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 30 × 8 = 240, keeping the calculation simpler).
Working: LCD(30, 8) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 3/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.
Working: 3 × 4/30 × 4 = 12/120 and 2 × 15/8 × 15 = 30/120

Step 3: Add the Numerators
Now add the numerators (12 + 30 = 42) and keep the common denominator 120 unchanged.
Working: 12 + 30/120 = 42/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 120, which is 6. Divide both the numerator and denominator by 6.
Working: 42 ÷ 6/120 ÷ 6 = 7/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 20 yields an exact terminating decimal of 0.35 (or 35%).
Working: 7 ÷ 20 = 0.35 (35%)

Key Values:
- Simplified Fraction: 7/20
- Mixed Number Form: 7/20
- Decimal Value: 0.35
- Percentage: 35%

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Solved with FractionsCalc:
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3/30 + 2/8 = 7/20

Simplified Fraction

7/20

Mixed Number

Proper (7/20)

Decimal Value

0.35

Percentage

35%

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Step-by-Step Solution: 3/30 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 30 × 8 = 240, keeping the calculation simpler).

LCD(30, 8) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 3/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.

3 × 4/30 × 4 = 12/120 and 2 × 15/8 × 15 = 30/120

Step 3

Add the Numerators

Now add the numerators (12 + 30 = 42) and keep the common denominator 120 unchanged.

12 + 30/120 = 42/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 120, which is 6. Divide both the numerator and denominator by 6.

42 ÷ 6/120 ÷ 6 = 7/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 20 yields an exact terminating decimal of 0.35 (or 35%).

7 ÷ 20 = 0.35 (35%)

Visual Representation

The diagram below illustrates 3/30 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/20`
Mixed Number Form	`7/20`
Decimal Form	`0.35`
Percentage	`35%`

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Frequently Asked Questions

What is 3/30 plus 2/8 as a fraction?

3/30 + 2/8 in simplest fraction form is 7/20.

What is 3/30 plus 2/8 as a decimal?

3/30 + 2/8 converted to a decimal is 0.35.

What is 3/30 plus 2/8 as a percentage?

3/30 + 2/8 expressed as a percentage is 35%.

Does 3/30 plus 2/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.35) because the denominator in simplest terms contains only prime factors 2 and/or 5.