What is 2/5 divided by 10/21? (Answer: 21/25)

Exact Answer

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Problem: What is 2/5 divided by 10/21?
Formula / Expression: 2/5 ÷ 10/21
Final Answer: 21/25
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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 10/21 to get 21/10.
Working: 2/5 ÷ 10/21 = 2/5 × 21/10

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (5 × 10 = 50).
Working: 2 × 21/5 × 10 = 42/50

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 50, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/50 ÷ 2 = 21/25

Step 4: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 25 yields an exact terminating decimal of 0.84 (or 84%).
Working: 21 ÷ 25 = 0.84 (84%)

Key Values:
- Simplified Fraction: 21/25
- Mixed Number Form: 21/25
- Decimal Value: 0.84
- Percentage: 84%

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Solved with FractionsCalc:
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2/5 ÷ 10/21 = 21/25

Simplified Fraction

21/25

Mixed Number

Proper (21/25)

Decimal Value

0.84

Percentage

84%

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Step-by-Step Solution: 2/5 ÷ 10/21

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 10/21 to get 21/10.

2/5 ÷ 10/21 = 2/5 × 21/10

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (5 × 10 = 50).

2 × 21/5 × 10 = 42/50

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 50, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/50 ÷ 2 = 21/25

Step 4

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 25 yields an exact terminating decimal of 0.84 (or 84%).

21 ÷ 25 = 0.84 (84%)

Visual Representation

The diagram below illustrates 2/5 divided by 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/25`
Mixed Number Form	`21/25`
Decimal Form	`0.84`
Percentage	`84%`

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Frequently Asked Questions

What is 2/5 divided by 10/21 as a fraction?

2/5 ÷ 10/21 in simplest fraction form is 21/25.

What is 2/5 divided by 10/21 as a decimal?

2/5 ÷ 10/21 converted to a decimal is 0.84.

What is 2/5 divided by 10/21 as a percentage?

2/5 ÷ 10/21 expressed as a percentage is 84%.

Does 2/5 divided by 10/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.84) because the denominator in simplest terms contains only prime factors 2 and/or 5.