What is 3/24 plus 11/21? (Answer: 109/168)

Exact Answer

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Problem: What is 3/24 plus 11/21?
Formula / Expression: 3/24 + 11/21
Final Answer: 109/168
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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 3/24 by 7, and multiply the numerator and denominator of 11/21 by 8 so both fractions share the common base 168.
Working: 3 × 7/24 × 7 = 21/168 and 11 × 8/21 × 8 = 88/168

Step 3: Add the Numerators
Now add the numerators (21 + 88 = 109) and keep the common denominator 168 unchanged.
Working: 21 + 88/168 = 109/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 168 is 1, confirming that 109/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 168 produces a repeating decimal (approximately 0.64881, or 64.881%).
Working: 109 ÷ 168 = 0.64881 (64.881%)

Key Values:
- Simplified Fraction: 109/168
- Mixed Number Form: 109/168
- Decimal Value: 0.64881
- Percentage: 64.881%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-24-plus-11-21/
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3/24 + 11/21 = 109/168

Simplified Fraction

109/168

Mixed Number

Proper (109/168)

Decimal Value

0.64881

Percentage

64.881%

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Step-by-Step Solution: 3/24 + 11/21

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 3/24 by 7, and multiply the numerator and denominator of 11/21 by 8 so both fractions share the common base 168.

3 × 7/24 × 7 = 21/168 and 11 × 8/21 × 8 = 88/168

Step 3

Add the Numerators

Now add the numerators (21 + 88 = 109) and keep the common denominator 168 unchanged.

21 + 88/168 = 109/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 168 is 1, confirming that 109/168 cannot be reduced further—it is already in its simplest irreducible form.

109/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 168 produces a repeating decimal (approximately 0.64881, or 64.881%).

109 ÷ 168 = 0.64881 (64.881%)

Visual Representation

The diagram below illustrates 3/24 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/168`
Mixed Number Form	`109/168`
Decimal Form	`0.64881`
Percentage	`64.881%`

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Frequently Asked Questions

What is 3/24 plus 11/21 as a fraction?

3/24 + 11/21 in simplest fraction form is 109/168.

What is 3/24 plus 11/21 as a decimal?

3/24 + 11/21 converted to a decimal is 0.64881.

What is 3/24 plus 11/21 as a percentage?

3/24 + 11/21 expressed as a percentage is 64.881%.

Does 3/24 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.64881...) because the denominator contains prime factors other than 2 and 5.