What is 4/12 plus 11/21? (Answer: 6/7)

Exact Answer

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Problem: What is 4/12 plus 11/21?
Formula / Expression: 4/12 + 11/21
Final Answer: 6/7
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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 4/12 by 7, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.
Working: 4 × 7/12 × 7 = 28/84 and 11 × 4/21 × 4 = 44/84

Step 3: Add the Numerators
Now add the numerators (28 + 44 = 72) and keep the common denominator 84 unchanged.
Working: 28 + 44/84 = 72/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 72 and 84, which is 12. Divide both the numerator and denominator by 12.
Working: 72 ÷ 12/84 ÷ 12 = 6/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).
Working: 6 ÷ 7 = 0.857143 (85.7143%)

Key Values:
- Simplified Fraction: 6/7
- Mixed Number Form: 6/7
- Decimal Value: 0.857143
- Percentage: 85.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-12-plus-11-21/
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4/12 + 11/21 = 6/7

Simplified Fraction

6/7

Mixed Number

Proper (6/7)

Decimal Value

0.857143

Percentage

85.7143%

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Step-by-Step Solution: 4/12 + 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 4/12 by 7, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.

4 × 7/12 × 7 = 28/84 and 11 × 4/21 × 4 = 44/84

Step 3

Add the Numerators

Now add the numerators (28 + 44 = 72) and keep the common denominator 84 unchanged.

28 + 44/84 = 72/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 72 and 84, which is 12. Divide both the numerator and denominator by 12.

72 ÷ 12/84 ÷ 12 = 6/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 7 produces a repeating decimal (approximately 0.857143, or 85.7143%).

6 ÷ 7 = 0.857143 (85.7143%)

Visual Representation

The diagram below illustrates 4/12 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/7`
Mixed Number Form	`6/7`
Decimal Form	`0.857143`
Percentage	`85.7143%`

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Frequently Asked Questions

What is 4/12 plus 11/21 as a fraction?

4/12 + 11/21 in simplest fraction form is 6/7.

What is 4/12 plus 11/21 as a decimal?

4/12 + 11/21 converted to a decimal is 0.857143.

What is 4/12 plus 11/21 as a percentage?

4/12 + 11/21 expressed as a percentage is 85.7143%.

Does 4/12 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.857143...) because the denominator contains prime factors other than 2 and 5.