What is 13/24 plus 12/21? (Answer: 187/168)

Exact Answer

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Problem: What is 13/24 plus 12/21?
Formula / Expression: 13/24 + 12/21
Final Answer: 1 19/168 (187/168)
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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 13/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.
Working: 13 × 7/24 × 7 = 91/168 and 12 × 8/21 × 8 = 96/168

Step 3: Add the Numerators
Now add the numerators (91 + 96 = 187) and keep the common denominator 168 unchanged.
Working: 91 + 96/168 = 187/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 187 and 168 is 1, confirming that 187/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 187/168

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (187) is greater than the denominator (168), divide 187 by 168: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/168.
Working: 187/168 = 1 19/168

Step 6: Decimal & Percentage Representation
Dividing the numerator 187 by denominator 168 produces a repeating decimal (approximately 1.113095, or 111.3095%).
Working: 187 ÷ 168 = 1.113095 (111.3095%)

Key Values:
- Simplified Fraction: 187/168
- Mixed Number Form: 1 19/168
- Decimal Value: 1.113095
- Percentage: 111.3095%

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Solved with FractionsCalc:
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13/24 + 12/21 = 187/168

Simplified Fraction

187/168

Mixed Number

1 19/168

Decimal Value

1.113095

Percentage

111.3095%

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Step-by-Step Solution: 13/24 + 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 13/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.

13 × 7/24 × 7 = 91/168 and 12 × 8/21 × 8 = 96/168

Step 3

Add the Numerators

Now add the numerators (91 + 96 = 187) and keep the common denominator 168 unchanged.

91 + 96/168 = 187/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 187 and 168 is 1, confirming that 187/168 cannot be reduced further—it is already in its simplest irreducible form.

187/168

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (187) is greater than the denominator (168), divide 187 by 168: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/168.

187/168 = 119/168

Step 6

Decimal & Percentage Representation

Dividing the numerator 187 by denominator 168 produces a repeating decimal (approximately 1.113095, or 111.3095%).

187 ÷ 168 = 1.113095 (111.3095%)

Visual Representation

The diagram below illustrates 13/24 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`187/168`
Mixed Number Form	`1 19/168`
Decimal Form	`1.113095`
Percentage	`111.3095%`

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Frequently Asked Questions

What is 13/24 plus 12/21 as a fraction?

13/24 + 12/21 in simplest fraction form is 187/168 (or 1 19/168 as a mixed number).

What is 13/24 plus 12/21 as a decimal?

13/24 + 12/21 converted to a decimal is 1.113095.

What is 13/24 plus 12/21 as a percentage?

13/24 + 12/21 expressed as a percentage is 111.3095%.

How do you write 13/24 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 187/168 can be written as the mixed number 1 19/168.

Does 13/24 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.113095...) because the denominator contains prime factors other than 2 and 5.