What is 3/6 minus 9/21? (Answer: 1/14)

Exact Answer

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Problem: What is 3/6 minus 9/21?
Formula / Expression: 3/6 − 9/21
Final Answer: 1/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 6 × 21 = 126, keeping the calculation simpler).
Working: LCD(6, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.
Working: 3 × 7/6 × 7 = 21/42 and 9 × 2/21 × 2 = 18/42

Step 3: Subtract the Numerators
Now subtract the numerators (21 − 18 = 3) and keep the common denominator 42 unchanged.
Working: 21 − 18/42 = 3/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 3 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 3 ÷ 3/42 ÷ 3 = 1/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 14 produces a repeating decimal (approximately 0.071429, or 7.1429%).
Working: 1 ÷ 14 = 0.071429 (7.1429%)

Key Values:
- Simplified Fraction: 1/14
- Mixed Number Form: 1/14
- Decimal Value: 0.071429
- Percentage: 7.1429%

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Solved with FractionsCalc:
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3/6 − 9/21 = 1/14

Simplified Fraction

1/14

Mixed Number

Proper (1/14)

Decimal Value

0.071429

Percentage

7.1429%

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Step-by-Step Solution: 3/6 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 6 × 21 = 126, keeping the calculation simpler).

LCD(6, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 3/6 by 7, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.

3 × 7/6 × 7 = 21/42 and 9 × 2/21 × 2 = 18/42

Step 3

Subtract the Numerators

Now subtract the numerators (21 − 18 = 3) and keep the common denominator 42 unchanged.

21 − 18/42 = 3/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 3 and 42, which is 3. Divide both the numerator and denominator by 3.

3 ÷ 3/42 ÷ 3 = 1/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 14 produces a repeating decimal (approximately 0.071429, or 7.1429%).

1 ÷ 14 = 0.071429 (7.1429%)

Visual Representation

The diagram below illustrates 3/6 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/14`
Mixed Number Form	`1/14`
Decimal Form	`0.071429`
Percentage	`7.1429%`

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Frequently Asked Questions

What is 3/6 minus 9/21 as a fraction?

3/6 − 9/21 in simplest fraction form is 1/14.

What is 3/6 minus 9/21 as a decimal?

3/6 − 9/21 converted to a decimal is 0.071429.

What is 3/6 minus 9/21 as a percentage?

3/6 − 9/21 expressed as a percentage is 7.1429%.

Does 3/6 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.071429...) because the denominator contains prime factors other than 2 and 5.