What is 2/39 divided by 2/21? (Answer: 7/13)

Exact Answer

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Problem: What is 2/39 divided by 2/21?
Formula / Expression: 2/39 ÷ 2/21
Final Answer: 7/13
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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 2/21 to get 21/2.
Working: 2/39 ÷ 2/21 = 2/39 × 21/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (39 × 2 = 78).
Working: 2 × 21/39 × 2 = 42/78

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 78, which is 6. Divide both the numerator and denominator by 6.
Working: 42 ÷ 6/78 ÷ 6 = 7/13

Step 4: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).
Working: 7 ÷ 13 = 0.538462 (53.8462%)

Key Values:
- Simplified Fraction: 7/13
- Mixed Number Form: 7/13
- Decimal Value: 0.538462
- Percentage: 53.8462%

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Solved with FractionsCalc:
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2/39 ÷ 2/21 = 7/13

Simplified Fraction

7/13

Mixed Number

Proper (7/13)

Decimal Value

0.538462

Percentage

53.8462%

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Step-by-Step Solution: 2/39 ÷ 2/21

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 2/21 to get 21/2.

2/39 ÷ 2/21 = 2/39 × 21/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (39 × 2 = 78).

2 × 21/39 × 2 = 42/78

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 78, which is 6. Divide both the numerator and denominator by 6.

42 ÷ 6/78 ÷ 6 = 7/13

Step 4

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 13 produces a repeating decimal (approximately 0.538462, or 53.8462%).

7 ÷ 13 = 0.538462 (53.8462%)

Visual Representation

The diagram below illustrates 2/39 divided by 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/13`
Mixed Number Form	`7/13`
Decimal Form	`0.538462`
Percentage	`53.8462%`

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Frequently Asked Questions

What is 2/39 divided by 2/21 as a fraction?

2/39 ÷ 2/21 in simplest fraction form is 7/13.

What is 2/39 divided by 2/21 as a decimal?

2/39 ÷ 2/21 converted to a decimal is 0.538462.

What is 2/39 divided by 2/21 as a percentage?

2/39 ÷ 2/21 expressed as a percentage is 53.8462%.

Does 2/39 divided by 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.538462...) because the denominator contains prime factors other than 2 and 5.