What is 3/14 plus 11/21? (Answer: 31/42)

Exact Answer

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Problem: What is 3/14 plus 11/21?
Formula / Expression: 3/14 + 11/21
Final Answer: 31/42
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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 11/21 by 2 so both fractions share the common base 42.
Working: 3 × 3/14 × 3 = 9/42 and 11 × 2/21 × 2 = 22/42

Step 3: Add the Numerators
Now add the numerators (9 + 22 = 31) and keep the common denominator 42 unchanged.
Working: 9 + 22/42 = 31/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 42 is 1, confirming that 31/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).
Working: 31 ÷ 42 = 0.738095 (73.8095%)

Key Values:
- Simplified Fraction: 31/42
- Mixed Number Form: 31/42
- Decimal Value: 0.738095
- Percentage: 73.8095%

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Solved with FractionsCalc:
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3/14 + 11/21 = 31/42

Simplified Fraction

31/42

Mixed Number

Proper (31/42)

Decimal Value

0.738095

Percentage

73.8095%

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Step-by-Step Solution: 3/14 + 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 3/14 by 3, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.

3 × 3/14 × 3 = 9/42 and 11 × 2/21 × 2 = 22/42

Step 3

Add the Numerators

Now add the numerators (9 + 22 = 31) and keep the common denominator 42 unchanged.

9 + 22/42 = 31/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 42 is 1, confirming that 31/42 cannot be reduced further—it is already in its simplest irreducible form.

31/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).

31 ÷ 42 = 0.738095 (73.8095%)

Visual Representation

The diagram below illustrates 3/14 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/42`
Mixed Number Form	`31/42`
Decimal Form	`0.738095`
Percentage	`73.8095%`

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Frequently Asked Questions

What is 3/14 plus 11/21 as a fraction?

3/14 + 11/21 in simplest fraction form is 31/42.

What is 3/14 plus 11/21 as a decimal?

3/14 + 11/21 converted to a decimal is 0.738095.

What is 3/14 plus 11/21 as a percentage?

3/14 + 11/21 expressed as a percentage is 73.8095%.

Does 3/14 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.738095...) because the denominator contains prime factors other than 2 and 5.