What is 3/14 plus 12/21? (Answer: 11/14)

Exact Answer

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Problem: What is 3/14 plus 12/21?
Formula / Expression: 3/14 + 12/21
Final Answer: 11/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).
Working: LCD(14, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/14 by 3, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.
Working: 3 × 3/14 × 3 = 9/42 and 12 × 2/21 × 2 = 24/42

Step 3: Add the Numerators
Now add the numerators (9 + 24 = 33) and keep the common denominator 42 unchanged.
Working: 9 + 24/42 = 33/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/42 ÷ 3 = 11/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).
Working: 11 ÷ 14 = 0.785714 (78.5714%)

Key Values:
- Simplified Fraction: 11/14
- Mixed Number Form: 11/14
- Decimal Value: 0.785714
- Percentage: 78.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-14-plus-12-21/
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3/14 + 12/21 = 11/14

Simplified Fraction

11/14

Mixed Number

Proper (11/14)

Decimal Value

0.785714

Percentage

78.5714%

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Step-by-Step Solution: 3/14 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).

LCD(14, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 3/14 by 3, and multiply the numerator and denominator of 12/21 by 2 so both fractions share the common base 42.

3 × 3/14 × 3 = 9/42 and 12 × 2/21 × 2 = 24/42

Step 3

Add the Numerators

Now add the numerators (9 + 24 = 33) and keep the common denominator 42 unchanged.

9 + 24/42 = 33/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 42, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/42 ÷ 3 = 11/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).

11 ÷ 14 = 0.785714 (78.5714%)

Visual Representation

The diagram below illustrates 3/14 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/14`
Mixed Number Form	`11/14`
Decimal Form	`0.785714`
Percentage	`78.5714%`

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Frequently Asked Questions

What is 3/14 plus 12/21 as a fraction?

3/14 + 12/21 in simplest fraction form is 11/14.

What is 3/14 plus 12/21 as a decimal?

3/14 + 12/21 converted to a decimal is 0.785714.

What is 3/14 plus 12/21 as a percentage?

3/14 + 12/21 expressed as a percentage is 78.5714%.

Does 3/14 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.785714...) because the denominator contains prime factors other than 2 and 5.