What is 11/21 plus 13/24? (Answer: 179/168)

Exact Answer

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Problem: What is 11/21 plus 13/24?
Formula / Expression: 11/21 + 13/24
Final Answer: 1 11/168 (179/168)
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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 11/21 by 8, and multiply the numerator and denominator of 13/24 by 7 so both fractions share the common base 168.
Working: 11 × 8/21 × 8 = 88/168 and 13 × 7/24 × 7 = 91/168

Step 3: Add the Numerators
Now add the numerators (88 + 91 = 179) and keep the common denominator 168 unchanged.
Working: 88 + 91/168 = 179/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 179 and 168 is 1, confirming that 179/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 179/168

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (179) is greater than the denominator (168), divide 179 by 168: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/168.
Working: 179/168 = 1 11/168

Step 6: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 168 produces a repeating decimal (approximately 1.065476, or 106.5476%).
Working: 179 ÷ 168 = 1.065476 (106.5476%)

Key Values:
- Simplified Fraction: 179/168
- Mixed Number Form: 1 11/168
- Decimal Value: 1.065476
- Percentage: 106.5476%

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Solved with FractionsCalc:
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11/21 + 13/24 = 179/168

Simplified Fraction

179/168

Mixed Number

1 11/168

Decimal Value

1.065476

Percentage

106.5476%

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Step-by-Step Solution: 11/21 + 13/24

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 11/21 by 8, and multiply the numerator and denominator of 13/24 by 7 so both fractions share the common base 168.

11 × 8/21 × 8 = 88/168 and 13 × 7/24 × 7 = 91/168

Step 3

Add the Numerators

Now add the numerators (88 + 91 = 179) and keep the common denominator 168 unchanged.

88 + 91/168 = 179/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 179 and 168 is 1, confirming that 179/168 cannot be reduced further—it is already in its simplest irreducible form.

179/168

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (179) is greater than the denominator (168), divide 179 by 168: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/168.

179/168 = 111/168

Step 6

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 168 produces a repeating decimal (approximately 1.065476, or 106.5476%).

179 ÷ 168 = 1.065476 (106.5476%)

Visual Representation

The diagram below illustrates 11/21 plus 13/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/168`
Mixed Number Form	`1 11/168`
Decimal Form	`1.065476`
Percentage	`106.5476%`

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Frequently Asked Questions

What is 11/21 plus 13/24 as a fraction?

11/21 + 13/24 in simplest fraction form is 179/168 (or 1 11/168 as a mixed number).

What is 11/21 plus 13/24 as a decimal?

11/21 + 13/24 converted to a decimal is 1.065476.

What is 11/21 plus 13/24 as a percentage?

11/21 + 13/24 expressed as a percentage is 106.5476%.

How do you write 11/21 plus 13/24 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 179/168 can be written as the mixed number 1 11/168.

Does 11/21 plus 13/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.065476...) because the denominator contains prime factors other than 2 and 5.