What is 3/6 divided by 9/21? (Answer: 7/6)

Exact Answer

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Problem: What is 3/6 divided by 9/21?
Formula / Expression: 3/6 ÷ 9/21
Final Answer: 1 1/6 (7/6)
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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 9/21 to get 21/9.
Working: 3/6 ÷ 9/21 = 3/6 × 21/9

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (3 × 21 = 63) and denominators (6 × 9 = 54).
Working: 3 × 21/6 × 9 = 63/54

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 54, which is 9. Divide both the numerator and denominator by 9.
Working: 63 ÷ 9/54 ÷ 9 = 7/6

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (7) is greater than the denominator (6), divide 7 by 6: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/6.
Working: 7/6 = 1 1/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 6 produces a repeating decimal (approximately 1.166667, or 116.6667%).
Working: 7 ÷ 6 = 1.166667 (116.6667%)

Key Values:
- Simplified Fraction: 7/6
- Mixed Number Form: 1 1/6
- Decimal Value: 1.166667
- Percentage: 116.6667%

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3/6 ÷ 9/21 = 7/6

Simplified Fraction

7/6

Mixed Number

1 1/6

Decimal Value

1.166667

Percentage

116.6667%

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Step-by-Step Solution: 3/6 ÷ 9/21

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 9/21 to get 21/9.

3/6 ÷ 9/21 = 3/6 × 21/9

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (3 × 21 = 63) and denominators (6 × 9 = 54).

3 × 21/6 × 9 = 63/54

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 54, which is 9. Divide both the numerator and denominator by 9.

63 ÷ 9/54 ÷ 9 = 7/6

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (7) is greater than the denominator (6), divide 7 by 6: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/6.

7/6 = 11/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 6 produces a repeating decimal (approximately 1.166667, or 116.6667%).

7 ÷ 6 = 1.166667 (116.6667%)

Visual Representation

The diagram below illustrates 3/6 divided by 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/6`
Mixed Number Form	`1 1/6`
Decimal Form	`1.166667`
Percentage	`116.6667%`

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Frequently Asked Questions

What is 3/6 divided by 9/21 as a fraction?

3/6 ÷ 9/21 in simplest fraction form is 7/6 (or 1 1/6 as a mixed number).

What is 3/6 divided by 9/21 as a decimal?

3/6 ÷ 9/21 converted to a decimal is 1.166667.

What is 3/6 divided by 9/21 as a percentage?

3/6 ÷ 9/21 expressed as a percentage is 116.6667%.

How do you write 3/6 divided by 9/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 7/6 can be written as the mixed number 1 1/6.

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

It results in a repeating decimal (approximately 1.166667...) because the denominator contains prime factors other than 2 and 5.