What is 11/24 plus 10/21? (Answer: 157/168)

Exact Answer

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Problem: What is 11/24 plus 10/21?
Formula / Expression: 11/24 + 10/21
Final Answer: 157/168
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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 11/24 by 7, and multiply the numerator and denominator of 10/21 by 8 so both fractions share the common base 168.
Working: 11 × 7/24 × 7 = 77/168 and 10 × 8/21 × 8 = 80/168

Step 3: Add the Numerators
Now add the numerators (77 + 80 = 157) and keep the common denominator 168 unchanged.
Working: 77 + 80/168 = 157/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 157 and 168 is 1, confirming that 157/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 157/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 157 by denominator 168 produces a repeating decimal (approximately 0.934524, or 93.4524%).
Working: 157 ÷ 168 = 0.934524 (93.4524%)

Key Values:
- Simplified Fraction: 157/168
- Mixed Number Form: 157/168
- Decimal Value: 0.934524
- Percentage: 93.4524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-24-plus-10-21/
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11/24 + 10/21 = 157/168

Simplified Fraction

157/168

Mixed Number

Proper (157/168)

Decimal Value

0.934524

Percentage

93.4524%

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Step-by-Step Solution: 11/24 + 10/21

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 11/24 by 7, and multiply the numerator and denominator of 10/21 by 8 so both fractions share the common base 168.

11 × 7/24 × 7 = 77/168 and 10 × 8/21 × 8 = 80/168

Step 3

Add the Numerators

Now add the numerators (77 + 80 = 157) and keep the common denominator 168 unchanged.

77 + 80/168 = 157/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 157 and 168 is 1, confirming that 157/168 cannot be reduced further—it is already in its simplest irreducible form.

157/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 157 by denominator 168 produces a repeating decimal (approximately 0.934524, or 93.4524%).

157 ÷ 168 = 0.934524 (93.4524%)

Visual Representation

The diagram below illustrates 11/24 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`157/168`
Mixed Number Form	`157/168`
Decimal Form	`0.934524`
Percentage	`93.4524%`

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Frequently Asked Questions

What is 11/24 plus 10/21 as a fraction?

11/24 + 10/21 in simplest fraction form is 157/168.

What is 11/24 plus 10/21 as a decimal?

11/24 + 10/21 converted to a decimal is 0.934524.

What is 11/24 plus 10/21 as a percentage?

11/24 + 10/21 expressed as a percentage is 93.4524%.

Does 11/24 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.934524...) because the denominator contains prime factors other than 2 and 5.