What is 3/7 minus 7/21? (Answer: 2/21)

Exact Answer

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Problem: What is 3/7 minus 7/21?
Formula / Expression: 3/7 − 7/21
Final Answer: 2/21
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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 3/7 by 3, and multiply the numerator and denominator of 7/21 by 1 so both fractions share the common base 21.
Working: 3 × 3/7 × 3 = 9/21 and 7 × 1/21 × 1 = 7/21

Step 3: Subtract the Numerators
Now subtract the numerators (9 − 7 = 2) and keep the common denominator 21 unchanged.
Working: 9 − 7/21 = 2/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 2 and 21 is 1, confirming that 2/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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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3/7 − 7/21 = 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: 3/7 − 7/21

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

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

Step 3

Subtract the Numerators

Now subtract the numerators (9 − 7 = 2) and keep the common denominator 21 unchanged.

9 − 7/21 = 2/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 2 and 21 is 1, confirming that 2/21 cannot be reduced further—it is already in its simplest irreducible form.

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 3/7 minus 7/21 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 3/7 minus 7/21 as a fraction?

3/7 − 7/21 in simplest fraction form is 2/21.

What is 3/7 minus 7/21 as a decimal?

3/7 − 7/21 converted to a decimal is 0.095238.

What is 3/7 minus 7/21 as a percentage?

3/7 − 7/21 expressed as a percentage is 9.5238%.

Does 3/7 minus 7/21 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.