What is 12/24 plus 12/21? (Answer: 15/14)

Exact Answer

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Problem: What is 12/24 plus 12/21?
Formula / Expression: 12/24 + 12/21
Final Answer: 1 1/14 (15/14)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).
Working: LCD(24, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 12/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.
Working: 12 × 7/24 × 7 = 84/168 and 12 × 8/21 × 8 = 96/168

Step 3: Add the Numerators
Now add the numerators (84 + 96 = 180) and keep the common denominator 168 unchanged.
Working: 84 + 96/168 = 180/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 180 and 168, which is 12. Divide both the numerator and denominator by 12.
Working: 180 ÷ 12/168 ÷ 12 = 15/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.
Working: 15/14 = 1 1/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).
Working: 15 ÷ 14 = 1.071429 (107.1429%)

Key Values:
- Simplified Fraction: 15/14
- Mixed Number Form: 1 1/14
- Decimal Value: 1.071429
- Percentage: 107.1429%

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Solved with FractionsCalc:
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12/24 + 12/21 = 15/14

Simplified Fraction

15/14

Mixed Number

1 1/14

Decimal Value

1.071429

Percentage

107.1429%

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Step-by-Step Solution: 12/24 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).

LCD(24, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 12/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.

12 × 7/24 × 7 = 84/168 and 12 × 8/21 × 8 = 96/168

Step 3

Add the Numerators

Now add the numerators (84 + 96 = 180) and keep the common denominator 168 unchanged.

84 + 96/168 = 180/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 180 and 168, which is 12. Divide both the numerator and denominator by 12.

180 ÷ 12/168 ÷ 12 = 15/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.

15/14 = 11/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).

15 ÷ 14 = 1.071429 (107.1429%)

Visual Representation

The diagram below illustrates 12/24 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/14`
Mixed Number Form	`1 1/14`
Decimal Form	`1.071429`
Percentage	`107.1429%`

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Frequently Asked Questions

What is 12/24 plus 12/21 as a fraction?

12/24 + 12/21 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).

What is 12/24 plus 12/21 as a decimal?

12/24 + 12/21 converted to a decimal is 1.071429.

What is 12/24 plus 12/21 as a percentage?

12/24 + 12/21 expressed as a percentage is 107.1429%.

How do you write 12/24 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 15/14 can be written as the mixed number 1 1/14.

Does 12/24 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.071429...) because the denominator contains prime factors other than 2 and 5.