What is 2/12 plus 6/21? (Answer: 19/42)

Exact Answer

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Problem: What is 2/12 plus 6/21?
Formula / Expression: 2/12 + 6/21
Final Answer: 19/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).
Working: LCD(12, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/12 by 7, and multiply the numerator and denominator of 6/21 by 4 so both fractions share the common base 84.
Working: 2 × 7/12 × 7 = 14/84 and 6 × 4/21 × 4 = 24/84

Step 3: Add the Numerators
Now add the numerators (14 + 24 = 38) and keep the common denominator 84 unchanged.
Working: 14 + 24/84 = 38/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 38 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: 38 ÷ 2/84 ÷ 2 = 19/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).
Working: 19 ÷ 42 = 0.452381 (45.2381%)

Key Values:
- Simplified Fraction: 19/42
- Mixed Number Form: 19/42
- Decimal Value: 0.452381
- Percentage: 45.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-12-plus-6-21/
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2/12 + 6/21 = 19/42

Simplified Fraction

19/42

Mixed Number

Proper (19/42)

Decimal Value

0.452381

Percentage

45.2381%

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Step-by-Step Solution: 2/12 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).

LCD(12, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/12 by 7, and multiply the numerator and denominator of 6/21 by 4 so both fractions share the common base 84.

2 × 7/12 × 7 = 14/84 and 6 × 4/21 × 4 = 24/84

Step 3

Add the Numerators

Now add the numerators (14 + 24 = 38) and keep the common denominator 84 unchanged.

14 + 24/84 = 38/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 38 and 84, which is 2. Divide both the numerator and denominator by 2.

38 ÷ 2/84 ÷ 2 = 19/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).

19 ÷ 42 = 0.452381 (45.2381%)

Visual Representation

The diagram below illustrates 2/12 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/42`
Mixed Number Form	`19/42`
Decimal Form	`0.452381`
Percentage	`45.2381%`

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Frequently Asked Questions

What is 2/12 plus 6/21 as a fraction?

2/12 + 6/21 in simplest fraction form is 19/42.

What is 2/12 plus 6/21 as a decimal?

2/12 + 6/21 converted to a decimal is 0.452381.

What is 2/12 plus 6/21 as a percentage?

2/12 + 6/21 expressed as a percentage is 45.2381%.

Does 2/12 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452381...) because the denominator contains prime factors other than 2 and 5.