What is 5/9 divided by 7/21? (Answer: 5/3)

Exact Answer

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Problem: What is 5/9 divided by 7/21?
Formula / Expression: 5/9 ÷ 7/21
Final Answer: 1 2/3 (5/3)
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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: 5/9 ÷ 7/21 = 5/9 × 21/7

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (5 × 21 = 105) and denominators (9 × 7 = 63).
Working: 5 × 21/9 × 7 = 105/63

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 63, which is 21. Divide both the numerator and denominator by 21.
Working: 105 ÷ 21/63 ÷ 21 = 5/3

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (5) is greater than the denominator (3), divide 5 by 3: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/3.
Working: 5/3 = 1 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 3 produces a repeating decimal (approximately 1.666667, or 166.6667%).
Working: 5 ÷ 3 = 1.666667 (166.6667%)

Key Values:
- Simplified Fraction: 5/3
- Mixed Number Form: 1 2/3
- Decimal Value: 1.666667
- Percentage: 166.6667%

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5/9 ÷ 7/21 = 5/3

Simplified Fraction

5/3

Mixed Number

1 2/3

Decimal Value

1.666667

Percentage

166.6667%

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Step-by-Step Solution: 5/9 ÷ 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.

5/9 ÷ 7/21 = 5/9 × 21/7

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (5 × 21 = 105) and denominators (9 × 7 = 63).

5 × 21/9 × 7 = 105/63

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 105 and 63, which is 21. Divide both the numerator and denominator by 21.

105 ÷ 21/63 ÷ 21 = 5/3

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (5) is greater than the denominator (3), divide 5 by 3: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/3.

5/3 = 12/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 3 produces a repeating decimal (approximately 1.666667, or 166.6667%).

5 ÷ 3 = 1.666667 (166.6667%)

Visual Representation

The diagram below illustrates 5/9 divided by 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/3`
Mixed Number Form	`1 2/3`
Decimal Form	`1.666667`
Percentage	`166.6667%`

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Frequently Asked Questions

What is 5/9 divided by 7/21 as a fraction?

5/9 ÷ 7/21 in simplest fraction form is 5/3 (or 1 2/3 as a mixed number).

What is 5/9 divided by 7/21 as a decimal?

5/9 ÷ 7/21 converted to a decimal is 1.666667.

What is 5/9 divided by 7/21 as a percentage?

5/9 ÷ 7/21 expressed as a percentage is 166.6667%.

How do you write 5/9 divided by 7/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 5/3 can be written as the mixed number 1 2/3.

Does 5/9 divided by 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.666667...) because the denominator contains prime factors other than 2 and 5.