What is 2/15 plus 2/12? (Answer: 3/10)

Exact Answer

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Problem: What is 2/15 plus 2/12?
Formula / Expression: 2/15 + 2/12
Final Answer: 3/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 15 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 15 × 12 = 180, keeping the calculation simpler).
Working: LCD(15, 12) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 2/15 by 4, and multiply the numerator and denominator of 2/12 by 5 so both fractions share the common base 60.
Working: 2 × 4/15 × 4 = 8/60 and 2 × 5/12 × 5 = 10/60

Step 3: Add the Numerators
Now add the numerators (8 + 10 = 18) and keep the common denominator 60 unchanged.
Working: 8 + 10/60 = 18/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 18 and 60, which is 6. Divide both the numerator and denominator by 6.
Working: 18 ÷ 6/60 ÷ 6 = 3/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 10 yields an exact terminating decimal of 0.3 (or 30%).
Working: 3 ÷ 10 = 0.3 (30%)

Key Values:
- Simplified Fraction: 3/10
- Mixed Number Form: 3/10
- Decimal Value: 0.3
- Percentage: 30%

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Solved with FractionsCalc:
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2/15 + 2/12 = 3/10

Simplified Fraction

3/10

Mixed Number

Proper (3/10)

Decimal Value

0.3

Percentage

30%

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Step-by-Step Solution: 2/15 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 15 × 12 = 180, keeping the calculation simpler).

LCD(15, 12) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 2/15 by 4, and multiply the numerator and denominator of 2/12 by 5 so both fractions share the common base 60.

2 × 4/15 × 4 = 8/60 and 2 × 5/12 × 5 = 10/60

Step 3

Add the Numerators

Now add the numerators (8 + 10 = 18) and keep the common denominator 60 unchanged.

8 + 10/60 = 18/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 18 and 60, which is 6. Divide both the numerator and denominator by 6.

18 ÷ 6/60 ÷ 6 = 3/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 10 yields an exact terminating decimal of 0.3 (or 30%).

3 ÷ 10 = 0.3 (30%)

Visual Representation

The diagram below illustrates 2/15 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/10`
Mixed Number Form	`3/10`
Decimal Form	`0.3`
Percentage	`30%`

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Frequently Asked Questions

What is 2/15 plus 2/12 as a fraction?

2/15 + 2/12 in simplest fraction form is 3/10.

What is 2/15 plus 2/12 as a decimal?

2/15 + 2/12 converted to a decimal is 0.3.

What is 2/15 plus 2/12 as a percentage?

2/15 + 2/12 expressed as a percentage is 30%.

Does 2/15 plus 2/12 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.3) because the denominator in simplest terms contains only prime factors 2 and/or 5.