What is 1/24 plus 2/21? (Answer: 23/168)

Exact Answer

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Problem: What is 1/24 plus 2/21?
Formula / Expression: 1/24 + 2/21
Final Answer: 23/168
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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 1/24 by 7, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.
Working: 1 × 7/24 × 7 = 7/168 and 2 × 8/21 × 8 = 16/168

Step 3: Add the Numerators
Now add the numerators (7 + 16 = 23) and keep the common denominator 168 unchanged.
Working: 7 + 16/168 = 23/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 168 is 1, confirming that 23/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 168 produces a repeating decimal (approximately 0.136905, or 13.6905%).
Working: 23 ÷ 168 = 0.136905 (13.6905%)

Key Values:
- Simplified Fraction: 23/168
- Mixed Number Form: 23/168
- Decimal Value: 0.136905
- Percentage: 13.6905%

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Solved with FractionsCalc:
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1/24 + 2/21 = 23/168

Simplified Fraction

23/168

Mixed Number

Proper (23/168)

Decimal Value

0.136905

Percentage

13.6905%

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Step-by-Step Solution: 1/24 + 2/21

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 1/24 by 7, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.

1 × 7/24 × 7 = 7/168 and 2 × 8/21 × 8 = 16/168

Step 3

Add the Numerators

Now add the numerators (7 + 16 = 23) and keep the common denominator 168 unchanged.

7 + 16/168 = 23/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 168 is 1, confirming that 23/168 cannot be reduced further—it is already in its simplest irreducible form.

23/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 168 produces a repeating decimal (approximately 0.136905, or 13.6905%).

23 ÷ 168 = 0.136905 (13.6905%)

Visual Representation

The diagram below illustrates 1/24 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/168`
Mixed Number Form	`23/168`
Decimal Form	`0.136905`
Percentage	`13.6905%`

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Frequently Asked Questions

What is 1/24 plus 2/21 as a fraction?

1/24 + 2/21 in simplest fraction form is 23/168.

What is 1/24 plus 2/21 as a decimal?

1/24 + 2/21 converted to a decimal is 0.136905.

What is 1/24 plus 2/21 as a percentage?

1/24 + 2/21 expressed as a percentage is 13.6905%.

Does 1/24 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.136905...) because the denominator contains prime factors other than 2 and 5.