What is 3/12 plus 2/5? (Answer: 13/20)

Exact Answer

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Problem: What is 3/12 plus 2/5?
Formula / Expression: 3/12 + 2/5
Final Answer: 13/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 5 = 60.
Working: LCD(12, 5) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 3/12 by 5, and multiply the numerator and denominator of 2/5 by 12 so both fractions share the common base 60.
Working: 3 × 5/12 × 5 = 15/60 and 2 × 12/5 × 12 = 24/60

Step 3: Add the Numerators
Now add the numerators (15 + 24 = 39) and keep the common denominator 60 unchanged.
Working: 15 + 24/60 = 39/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 60, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/60 ÷ 3 = 13/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 20 yields an exact terminating decimal of 0.65 (or 65%).
Working: 13 ÷ 20 = 0.65 (65%)

Key Values:
- Simplified Fraction: 13/20
- Mixed Number Form: 13/20
- Decimal Value: 0.65
- Percentage: 65%

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Solved with FractionsCalc:
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3/12 + 2/5 = 13/20

Simplified Fraction

13/20

Mixed Number

Proper (13/20)

Decimal Value

0.65

Percentage

65%

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Step-by-Step Solution: 3/12 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 12 × 5 = 60.

LCD(12, 5) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 3/12 by 5, and multiply the numerator and denominator of 2/5 by 12 so both fractions share the common base 60.

3 × 5/12 × 5 = 15/60 and 2 × 12/5 × 12 = 24/60

Step 3

Add the Numerators

Now add the numerators (15 + 24 = 39) and keep the common denominator 60 unchanged.

15 + 24/60 = 39/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 60, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/60 ÷ 3 = 13/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 20 yields an exact terminating decimal of 0.65 (or 65%).

13 ÷ 20 = 0.65 (65%)

Visual Representation

The diagram below illustrates 3/12 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/20`
Mixed Number Form	`13/20`
Decimal Form	`0.65`
Percentage	`65%`

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Frequently Asked Questions

What is 3/12 plus 2/5 as a fraction?

3/12 + 2/5 in simplest fraction form is 13/20.

What is 3/12 plus 2/5 as a decimal?

3/12 + 2/5 converted to a decimal is 0.65.

What is 3/12 plus 2/5 as a percentage?

3/12 + 2/5 expressed as a percentage is 65%.

Does 3/12 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.65) because the denominator in simplest terms contains only prime factors 2 and/or 5.