What is 2/35 divided by 9/21? (Answer: 2/15)

Exact Answer

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Problem: What is 2/35 divided by 9/21?
Formula / Expression: 2/35 ÷ 9/21
Final Answer: 2/15
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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: 2/35 ÷ 9/21 = 2/35 × 21/9

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (35 × 9 = 315).
Working: 2 × 21/35 × 9 = 42/315

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 315, which is 21. Divide both the numerator and denominator by 21.
Working: 42 ÷ 21/315 ÷ 21 = 2/15

Step 4: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 15 produces a repeating decimal (approximately 0.133333, or 13.3333%).
Working: 2 ÷ 15 = 0.133333 (13.3333%)

Key Values:
- Simplified Fraction: 2/15
- Mixed Number Form: 2/15
- Decimal Value: 0.133333
- Percentage: 13.3333%

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Solved with FractionsCalc:
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2/35 ÷ 9/21 = 2/15

Simplified Fraction

2/15

Mixed Number

Proper (2/15)

Decimal Value

0.133333

Percentage

13.3333%

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Step-by-Step Solution: 2/35 ÷ 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.

2/35 ÷ 9/21 = 2/35 × 21/9

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (35 × 9 = 315).

2 × 21/35 × 9 = 42/315

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 315, which is 21. Divide both the numerator and denominator by 21.

42 ÷ 21/315 ÷ 21 = 2/15

Step 4

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 15 produces a repeating decimal (approximately 0.133333, or 13.3333%).

2 ÷ 15 = 0.133333 (13.3333%)

Visual Representation

The diagram below illustrates 2/35 divided by 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/15`
Mixed Number Form	`2/15`
Decimal Form	`0.133333`
Percentage	`13.3333%`

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Frequently Asked Questions

What is 2/35 divided by 9/21 as a fraction?

2/35 ÷ 9/21 in simplest fraction form is 2/15.

What is 2/35 divided by 9/21 as a decimal?

2/35 ÷ 9/21 converted to a decimal is 0.133333.

What is 2/35 divided by 9/21 as a percentage?

2/35 ÷ 9/21 expressed as a percentage is 13.3333%.

Does 2/35 divided by 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.133333...) because the denominator contains prime factors other than 2 and 5.