What is 2/14 plus 2/12? (Answer: 13/42)

Exact Answer

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Problem: What is 2/14 plus 2/12?
Formula / Expression: 2/14 + 2/12
Final Answer: 13/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 12 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 14 × 12 = 168, keeping the calculation simpler).
Working: LCD(14, 12) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/14 by 6, and multiply the numerator and denominator of 2/12 by 7 so both fractions share the common base 84.
Working: 2 × 6/14 × 6 = 12/84 and 2 × 7/12 × 7 = 14/84

Step 3: Add the Numerators
Now add the numerators (12 + 14 = 26) and keep the common denominator 84 unchanged.
Working: 12 + 14/84 = 26/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/84 ÷ 2 = 13/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).
Working: 13 ÷ 42 = 0.309524 (30.9524%)

Key Values:
- Simplified Fraction: 13/42
- Mixed Number Form: 13/42
- Decimal Value: 0.309524
- Percentage: 30.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-14-plus-2-12/
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2/14 + 2/12 = 13/42

Simplified Fraction

13/42

Mixed Number

Proper (13/42)

Decimal Value

0.309524

Percentage

30.9524%

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Step-by-Step Solution: 2/14 + 2/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 12 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 14 × 12 = 168, keeping the calculation simpler).

LCD(14, 12) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/14 by 6, and multiply the numerator and denominator of 2/12 by 7 so both fractions share the common base 84.

2 × 6/14 × 6 = 12/84 and 2 × 7/12 × 7 = 14/84

Step 3

Add the Numerators

Now add the numerators (12 + 14 = 26) and keep the common denominator 84 unchanged.

12 + 14/84 = 26/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 84, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/84 ÷ 2 = 13/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).

13 ÷ 42 = 0.309524 (30.9524%)

Visual Representation

The diagram below illustrates 2/14 plus 2/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/42`
Mixed Number Form	`13/42`
Decimal Form	`0.309524`
Percentage	`30.9524%`

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Frequently Asked Questions

What is 2/14 plus 2/12 as a fraction?

2/14 + 2/12 in simplest fraction form is 13/42.

What is 2/14 plus 2/12 as a decimal?

2/14 + 2/12 converted to a decimal is 0.309524.

What is 2/14 plus 2/12 as a percentage?

2/14 + 2/12 expressed as a percentage is 30.9524%.

Does 2/14 plus 2/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.309524...) because the denominator contains prime factors other than 2 and 5.