What is 3/9 minus 9/21? (Answer: -2/21)

Exact Answer

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Problem: What is 3/9 minus 9/21?
Formula / Expression: 3/9 − 9/21
Final Answer: -2/21
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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 3/9 by 7, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.
Working: 3 × 7/9 × 7 = 21/63 and 9 × 3/21 × 3 = 27/63

Step 3: Subtract the Numerators
Now subtract the numerators (21 − 27 = -6) and keep the common denominator 63 unchanged.
Working: 21 − 27/63 = -6/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: -6 ÷ 3/63 ÷ 3 = -2/21

Step 5: Decimal & Percentage Representation
Dividing the numerator -2 by denominator 21 produces a repeating decimal (approximately -0.095238, or -9.5238%).
Working: -2 ÷ 21 = -0.095238 (-9.5238%)

Key Values:
- Simplified Fraction: -2/21
- Mixed Number Form: -2/21
- Decimal Value: -0.095238
- Percentage: -9.5238%

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Solved with FractionsCalc:
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3/9 − 9/21 = -2/21

Simplified Fraction

-2/21

Mixed Number

Proper (-2/21)

Decimal Value

-0.095238

Percentage

-9.5238%

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Step-by-Step Solution: 3/9 − 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 3/9 by 7, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.

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

Step 3

Subtract the Numerators

Now subtract the numerators (21 − 27 = -6) and keep the common denominator 63 unchanged.

21 − 27/63 = -6/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 6 and 63, which is 3. Divide both the numerator and denominator by 3.

-6 ÷ 3/63 ÷ 3 = -2/21

Step 5

Decimal & Percentage Representation

Dividing the numerator -2 by denominator 21 produces a repeating decimal (approximately -0.095238, or -9.5238%).

-2 ÷ 21 = -0.095238 (-9.5238%)

Visual Representation

The diagram below illustrates 3/9 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-2/21`
Mixed Number Form	`-2/21`
Decimal Form	`-0.095238`
Percentage	`-9.5238%`

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Frequently Asked Questions

What is 3/9 minus 9/21 as a fraction?

3/9 − 9/21 in simplest fraction form is -2/21.

What is 3/9 minus 9/21 as a decimal?

3/9 − 9/21 converted to a decimal is -0.095238.

What is 3/9 minus 9/21 as a percentage?

3/9 − 9/21 expressed as a percentage is -9.5238%.

Does 3/9 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.095238...) because the denominator contains prime factors other than 2 and 5.