What is 2/9 minus 9/21? (Answer: -13/63)

Exact Answer

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Problem: What is 2/9 minus 9/21?
Formula / Expression: 2/9 − 9/21
Final Answer: -13/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).
Working: LCD(9, 21) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/9 by 7, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 9 × 3/21 × 3 = 27/63

Step 3: Subtract the Numerators
Now subtract the numerators (14 − 27 = -13) and keep the common denominator 63 unchanged.
Working: 14 − 27/63 = -13/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 63 is 1, confirming that -13/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: -13/63

Step 5: Decimal & Percentage Representation
Dividing the numerator -13 by denominator 63 produces a repeating decimal (approximately -0.206349, or -20.6349%).
Working: -13 ÷ 63 = -0.206349 (-20.6349%)

Key Values:
- Simplified Fraction: -13/63
- Mixed Number Form: -13/63
- Decimal Value: -0.206349
- Percentage: -20.6349%

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Solved with FractionsCalc:
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2/9 − 9/21 = -13/63

Simplified Fraction

-13/63

Mixed Number

Proper (-13/63)

Decimal Value

-0.206349

Percentage

-20.6349%

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Step-by-Step Solution: 2/9 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).

LCD(9, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 2/9 by 7, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.

2 × 7/9 × 7 = 14/63 and 9 × 3/21 × 3 = 27/63

Step 3

Subtract the Numerators

Now subtract the numerators (14 − 27 = -13) and keep the common denominator 63 unchanged.

14 − 27/63 = -13/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 63 is 1, confirming that -13/63 cannot be reduced further—it is already in its simplest irreducible form.

-13/63

Step 5

Decimal & Percentage Representation

Dividing the numerator -13 by denominator 63 produces a repeating decimal (approximately -0.206349, or -20.6349%).

-13 ÷ 63 = -0.206349 (-20.6349%)

Visual Representation

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

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-13/63`
Mixed Number Form	`-13/63`
Decimal Form	`-0.206349`
Percentage	`-20.6349%`

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Frequently Asked Questions

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

2/9 − 9/21 in simplest fraction form is -13/63.

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

2/9 − 9/21 converted to a decimal is -0.206349.

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

2/9 − 9/21 expressed as a percentage is -20.6349%.

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

It results in a repeating decimal (approximately -0.206349...) because the denominator contains prime factors other than 2 and 5.