What is 6/14 plus 11/21? (Answer: 20/21)

Exact Answer

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Problem: What is 6/14 plus 11/21?
Formula / Expression: 6/14 + 11/21
Final Answer: 20/21
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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 6/14 by 3, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.
Working: 6 × 3/14 × 3 = 18/42 and 11 × 2/21 × 2 = 22/42

Step 3: Add the Numerators
Now add the numerators (18 + 22 = 40) and keep the common denominator 42 unchanged.
Working: 18 + 22/42 = 40/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 40 ÷ 2/42 ÷ 2 = 20/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).
Working: 20 ÷ 21 = 0.952381 (95.2381%)

Key Values:
- Simplified Fraction: 20/21
- Mixed Number Form: 20/21
- Decimal Value: 0.952381
- Percentage: 95.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-14-plus-11-21/
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6/14 + 11/21 = 20/21

Simplified Fraction

20/21

Mixed Number

Proper (20/21)

Decimal Value

0.952381

Percentage

95.2381%

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Step-by-Step Solution: 6/14 + 11/21

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 6/14 by 3, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.

6 × 3/14 × 3 = 18/42 and 11 × 2/21 × 2 = 22/42

Step 3

Add the Numerators

Now add the numerators (18 + 22 = 40) and keep the common denominator 42 unchanged.

18 + 22/42 = 40/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 40 and 42, which is 2. Divide both the numerator and denominator by 2.

40 ÷ 2/42 ÷ 2 = 20/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 21 produces a repeating decimal (approximately 0.952381, or 95.2381%).

20 ÷ 21 = 0.952381 (95.2381%)

Visual Representation

The diagram below illustrates 6/14 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/21`
Mixed Number Form	`20/21`
Decimal Form	`0.952381`
Percentage	`95.2381%`

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Frequently Asked Questions

What is 6/14 plus 11/21 as a fraction?

6/14 + 11/21 in simplest fraction form is 20/21.

What is 6/14 plus 11/21 as a decimal?

6/14 + 11/21 converted to a decimal is 0.952381.

What is 6/14 plus 11/21 as a percentage?

6/14 + 11/21 expressed as a percentage is 95.2381%.

Does 6/14 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.952381...) because the denominator contains prime factors other than 2 and 5.