What is 3/7 divided by 7/21? (Answer: 9/7)

Exact Answer

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Problem: What is 3/7 divided by 7/21?
Formula / Expression: 3/7 ÷ 7/21
Final Answer: 1 2/7 (9/7)
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Step-by-Step Solution:

Step 1: Find the Reciprocal of the Second Fraction
Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 7/21 to get 21/7.
Working: 3/7 ÷ 7/21 = 3/7 × 21/7

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (3 × 21 = 63) and denominators (7 × 7 = 49).
Working: 3 × 21/7 × 7 = 63/49

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 49, which is 7. Divide both the numerator and denominator by 7.
Working: 63 ÷ 7/49 ÷ 7 = 9/7

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (9) is greater than the denominator (7), divide 9 by 7: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/7.
Working: 9/7 = 1 2/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 7 produces a repeating decimal (approximately 1.285714, or 128.5714%).
Working: 9 ÷ 7 = 1.285714 (128.5714%)

Key Values:
- Simplified Fraction: 9/7
- Mixed Number Form: 1 2/7
- Decimal Value: 1.285714
- Percentage: 128.5714%

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Solved with FractionsCalc:
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3/7 ÷ 7/21 = 9/7

Simplified Fraction

9/7

Mixed Number

1 2/7

Decimal Value

1.285714

Percentage

128.5714%

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Step-by-Step Solution: 3/7 ÷ 7/21

Step 1

Find the Reciprocal of the Second Fraction

Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 7/21 to get 21/7.

3/7 ÷ 7/21 = 3/7 × 21/7

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (3 × 21 = 63) and denominators (7 × 7 = 49).

3 × 21/7 × 7 = 63/49

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 49, which is 7. Divide both the numerator and denominator by 7.

63 ÷ 7/49 ÷ 7 = 9/7

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (9) is greater than the denominator (7), divide 9 by 7: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/7.

9/7 = 12/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 7 produces a repeating decimal (approximately 1.285714, or 128.5714%).

9 ÷ 7 = 1.285714 (128.5714%)

Visual Representation

The diagram below illustrates 3/7 divided by 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/7`
Mixed Number Form	`1 2/7`
Decimal Form	`1.285714`
Percentage	`128.5714%`

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Frequently Asked Questions

What is 3/7 divided by 7/21 as a fraction?

3/7 ÷ 7/21 in simplest fraction form is 9/7 (or 1 2/7 as a mixed number).

What is 3/7 divided by 7/21 as a decimal?

3/7 ÷ 7/21 converted to a decimal is 1.285714.

What is 3/7 divided by 7/21 as a percentage?

3/7 ÷ 7/21 expressed as a percentage is 128.5714%.

How do you write 3/7 divided by 7/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 9/7 can be written as the mixed number 1 2/7.

Does 3/7 divided by 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.285714...) because the denominator contains prime factors other than 2 and 5.