What is 1/7 minus 9/21? (Answer: -2/7)

Exact Answer

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Problem: What is 1/7 minus 9/21?
Formula / Expression: 1/7 − 9/21
Final Answer: -2/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(7, 21) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 1/7 by 3, and multiply the numerator and denominator of 9/21 by 1 so both fractions share the common base 21.
Working: 1 × 3/7 × 3 = 3/21 and 9 × 1/21 × 1 = 9/21

Step 3: Subtract the Numerators
Now subtract the numerators (3 − 9 = -6) and keep the common denominator 21 unchanged.
Working: 3 − 9/21 = -6/21

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 6 and 21, which is 3. Divide both the numerator and denominator by 3.
Working: -6 ÷ 3/21 ÷ 3 = -2/7

Step 5: Decimal & Percentage Representation
Dividing the numerator -2 by denominator 7 produces a repeating decimal (approximately -0.285714, or -28.5714%).
Working: -2 ÷ 7 = -0.285714 (-28.5714%)

Key Values:
- Simplified Fraction: -2/7
- Mixed Number Form: -2/7
- Decimal Value: -0.285714
- Percentage: -28.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-minus-9-21/
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1/7 − 9/21 = -2/7

Simplified Fraction

-2/7

Mixed Number

Proper (-2/7)

Decimal Value

-0.285714

Percentage

-28.5714%

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Step-by-Step Solution: 1/7 − 9/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(7, 21) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 1/7 by 3, and multiply the numerator and denominator of 9/21 by 1 so both fractions share the common base 21.

1 × 3/7 × 3 = 3/21 and 9 × 1/21 × 1 = 9/21

Step 3

Subtract the Numerators

Now subtract the numerators (3 − 9 = -6) and keep the common denominator 21 unchanged.

3 − 9/21 = -6/21

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 6 and 21, which is 3. Divide both the numerator and denominator by 3.

-6 ÷ 3/21 ÷ 3 = -2/7

Step 5

Decimal & Percentage Representation

Dividing the numerator -2 by denominator 7 produces a repeating decimal (approximately -0.285714, or -28.5714%).

-2 ÷ 7 = -0.285714 (-28.5714%)

Visual Representation

The diagram below illustrates 1/7 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-2/7`
Mixed Number Form	`-2/7`
Decimal Form	`-0.285714`
Percentage	`-28.5714%`

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Frequently Asked Questions

What is 1/7 minus 9/21 as a fraction?

1/7 − 9/21 in simplest fraction form is -2/7.

What is 1/7 minus 9/21 as a decimal?

1/7 − 9/21 converted to a decimal is -0.285714.

What is 1/7 minus 9/21 as a percentage?

1/7 − 9/21 expressed as a percentage is -28.5714%.

Does 1/7 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.285714...) because the denominator contains prime factors other than 2 and 5.