What is 2/12 minus 9/21? (Answer: -11/42)

Exact Answer

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Problem: What is 2/12 minus 9/21?
Formula / Expression: 2/12 − 9/21
Final Answer: -11/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).
Working: LCD(12, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 2/12 by 7, and multiply the numerator and denominator of 9/21 by 4 so both fractions share the common base 84.
Working: 2 × 7/12 × 7 = 14/84 and 9 × 4/21 × 4 = 36/84

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 36 = -22) and keep the common denominator 84 unchanged.
Working: 14 − 36/84 = -22/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: -22 ÷ 2/84 ÷ 2 = -11/42

Step 5: Decimal & Percentage Representation
Dividing the numerator -11 by denominator 42 produces a repeating decimal (approximately -0.261905, or -26.1905%).
Working: -11 ÷ 42 = -0.261905 (-26.1905%)

Key Values:
- Simplified Fraction: -11/42
- Mixed Number Form: -11/42
- Decimal Value: -0.261905
- Percentage: -26.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-12-minus-9-21/
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2/12 − 9/21 = -11/42

Simplified Fraction

-11/42

Mixed Number

Proper (-11/42)

Decimal Value

-0.261905

Percentage

-26.1905%

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Step-by-Step Solution: 2/12 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).

LCD(12, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 2/12 by 7, and multiply the numerator and denominator of 9/21 by 4 so both fractions share the common base 84.

2 × 7/12 × 7 = 14/84 and 9 × 4/21 × 4 = 36/84

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 36 = -22) and keep the common denominator 84 unchanged.

14 − 36/84 = -22/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 84, which is 2. Divide both the numerator and denominator by 2.

-22 ÷ 2/84 ÷ 2 = -11/42

Step 5

Decimal & Percentage Representation

Dividing the numerator -11 by denominator 42 produces a repeating decimal (approximately -0.261905, or -26.1905%).

-11 ÷ 42 = -0.261905 (-26.1905%)

Visual Representation

The diagram below illustrates 2/12 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-11/42`
Mixed Number Form	`-11/42`
Decimal Form	`-0.261905`
Percentage	`-26.1905%`

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Frequently Asked Questions

What is 2/12 minus 9/21 as a fraction?

2/12 − 9/21 in simplest fraction form is -11/42.

What is 2/12 minus 9/21 as a decimal?

2/12 − 9/21 converted to a decimal is -0.261905.

What is 2/12 minus 9/21 as a percentage?

2/12 − 9/21 expressed as a percentage is -26.1905%.

Does 2/12 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.261905...) because the denominator contains prime factors other than 2 and 5.