What is 3/12 plus 11/21? (Answer: 65/84)

Exact Answer

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Problem: What is 3/12 plus 11/21?
Formula / Expression: 3/12 + 11/21
Final Answer: 65/84
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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 3/12 by 7, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.
Working: 3 × 7/12 × 7 = 21/84 and 11 × 4/21 × 4 = 44/84

Step 3: Add the Numerators
Now add the numerators (21 + 44 = 65) and keep the common denominator 84 unchanged.
Working: 21 + 44/84 = 65/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 84 is 1, confirming that 65/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 84 produces a repeating decimal (approximately 0.77381, or 77.381%).
Working: 65 ÷ 84 = 0.77381 (77.381%)

Key Values:
- Simplified Fraction: 65/84
- Mixed Number Form: 65/84
- Decimal Value: 0.77381
- Percentage: 77.381%

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Solved with FractionsCalc:
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3/12 + 11/21 = 65/84

Simplified Fraction

65/84

Mixed Number

Proper (65/84)

Decimal Value

0.77381

Percentage

77.381%

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Step-by-Step Solution: 3/12 + 11/21

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 3/12 by 7, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.

3 × 7/12 × 7 = 21/84 and 11 × 4/21 × 4 = 44/84

Step 3

Add the Numerators

Now add the numerators (21 + 44 = 65) and keep the common denominator 84 unchanged.

21 + 44/84 = 65/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 84 is 1, confirming that 65/84 cannot be reduced further—it is already in its simplest irreducible form.

65/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 84 produces a repeating decimal (approximately 0.77381, or 77.381%).

65 ÷ 84 = 0.77381 (77.381%)

Visual Representation

The diagram below illustrates 3/12 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/84`
Mixed Number Form	`65/84`
Decimal Form	`0.77381`
Percentage	`77.381%`

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Frequently Asked Questions

What is 3/12 plus 11/21 as a fraction?

3/12 + 11/21 in simplest fraction form is 65/84.

What is 3/12 plus 11/21 as a decimal?

3/12 + 11/21 converted to a decimal is 0.77381.

What is 3/12 plus 11/21 as a percentage?

3/12 + 11/21 expressed as a percentage is 77.381%.

Does 3/12 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.77381...) because the denominator contains prime factors other than 2 and 5.