What is 2/24 minus 2/21? (Answer: -1/84)

Exact Answer

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Problem: What is 2/24 minus 2/21?
Formula / Expression: 2/24 − 2/21
Final Answer: -1/84
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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 2/24 by 7, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.
Working: 2 × 7/24 × 7 = 14/168 and 2 × 8/21 × 8 = 16/168

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 16 = -2) and keep the common denominator 168 unchanged.
Working: 14 − 16/168 = -2/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 2 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: -2 ÷ 2/168 ÷ 2 = -1/84

Step 5: Decimal & Percentage Representation
Dividing the numerator -1 by denominator 84 produces a repeating decimal (approximately -0.011905, or -1.1905%).
Working: -1 ÷ 84 = -0.011905 (-1.1905%)

Key Values:
- Simplified Fraction: -1/84
- Mixed Number Form: -1/84
- Decimal Value: -0.011905
- Percentage: -1.1905%

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Solved with FractionsCalc:
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2/24 − 2/21 = -1/84

Simplified Fraction

-1/84

Mixed Number

Proper (-1/84)

Decimal Value

-0.011905

Percentage

-1.1905%

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Step-by-Step Solution: 2/24 − 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 2/24 by 7, and multiply the numerator and denominator of 2/21 by 8 so both fractions share the common base 168.

2 × 7/24 × 7 = 14/168 and 2 × 8/21 × 8 = 16/168

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 16 = -2) and keep the common denominator 168 unchanged.

14 − 16/168 = -2/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 2 and 168, which is 2. Divide both the numerator and denominator by 2.

-2 ÷ 2/168 ÷ 2 = -1/84

Step 5

Decimal & Percentage Representation

Dividing the numerator -1 by denominator 84 produces a repeating decimal (approximately -0.011905, or -1.1905%).

-1 ÷ 84 = -0.011905 (-1.1905%)

Visual Representation

The diagram below illustrates 2/24 minus 2/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-1/84`
Mixed Number Form	`-1/84`
Decimal Form	`-0.011905`
Percentage	`-1.1905%`

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Frequently Asked Questions

What is 2/24 minus 2/21 as a fraction?

2/24 − 2/21 in simplest fraction form is -1/84.

What is 2/24 minus 2/21 as a decimal?

2/24 − 2/21 converted to a decimal is -0.011905.

What is 2/24 minus 2/21 as a percentage?

2/24 − 2/21 expressed as a percentage is -1.1905%.

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

It results in a repeating decimal (approximately -0.011905...) because the denominator contains prime factors other than 2 and 5.