What is 12/21 plus 14/24? (Answer: 97/84)

Exact Answer

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Problem: What is 12/21 plus 14/24?
Formula / Expression: 12/21 + 14/24
Final Answer: 1 13/84 (97/84)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 12/21 by 8, and multiply the numerator and denominator of 14/24 by 7 so both fractions share the common base 168.
Working: 12 × 8/21 × 8 = 96/168 and 14 × 7/24 × 7 = 98/168

Step 3: Add the Numerators
Now add the numerators (96 + 98 = 194) and keep the common denominator 168 unchanged.
Working: 96 + 98/168 = 194/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 194 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 194 ÷ 2/168 ÷ 2 = 97/84

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (97) is greater than the denominator (84), divide 97 by 84: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/84.
Working: 97/84 = 1 13/84

Step 6: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 84 produces a repeating decimal (approximately 1.154762, or 115.4762%).
Working: 97 ÷ 84 = 1.154762 (115.4762%)

Key Values:
- Simplified Fraction: 97/84
- Mixed Number Form: 1 13/84
- Decimal Value: 1.154762
- Percentage: 115.4762%

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Solved with FractionsCalc:
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12/21 + 14/24 = 97/84

Simplified Fraction

97/84

Mixed Number

1 13/84

Decimal Value

1.154762

Percentage

115.4762%

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Step-by-Step Solution: 12/21 + 14/24

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 24) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 12/21 by 8, and multiply the numerator and denominator of 14/24 by 7 so both fractions share the common base 168.

12 × 8/21 × 8 = 96/168 and 14 × 7/24 × 7 = 98/168

Step 3

Add the Numerators

Now add the numerators (96 + 98 = 194) and keep the common denominator 168 unchanged.

96 + 98/168 = 194/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 194 and 168, which is 2. Divide both the numerator and denominator by 2.

194 ÷ 2/168 ÷ 2 = 97/84

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (97) is greater than the denominator (84), divide 97 by 84: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/84.

97/84 = 113/84

Step 6

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 84 produces a repeating decimal (approximately 1.154762, or 115.4762%).

97 ÷ 84 = 1.154762 (115.4762%)

Visual Representation

The diagram below illustrates 12/21 plus 14/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/84`
Mixed Number Form	`1 13/84`
Decimal Form	`1.154762`
Percentage	`115.4762%`

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Frequently Asked Questions

What is 12/21 plus 14/24 as a fraction?

12/21 + 14/24 in simplest fraction form is 97/84 (or 1 13/84 as a mixed number).

What is 12/21 plus 14/24 as a decimal?

12/21 + 14/24 converted to a decimal is 1.154762.

What is 12/21 plus 14/24 as a percentage?

12/21 + 14/24 expressed as a percentage is 115.4762%.

How do you write 12/21 plus 14/24 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 97/84 can be written as the mixed number 1 13/84.

Does 12/21 plus 14/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.154762...) because the denominator contains prime factors other than 2 and 5.