What is 2/30 divided by 2/21? (Answer: 7/10)

Exact Answer

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Problem: What is 2/30 divided by 2/21?
Formula / Expression: 2/30 ÷ 2/21
Final Answer: 7/10
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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: 2/30 ÷ 2/21 = 2/30 × 21/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (30 × 2 = 60).
Working: 2 × 21/30 × 2 = 42/60

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 60, which is 6. Divide both the numerator and denominator by 6.
Working: 42 ÷ 6/60 ÷ 6 = 7/10

Step 4: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).
Working: 7 ÷ 10 = 0.7 (70%)

Key Values:
- Simplified Fraction: 7/10
- Mixed Number Form: 7/10
- Decimal Value: 0.7
- Percentage: 70%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-30-divided-by-2-21/
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2/30 ÷ 2/21 = 7/10

Simplified Fraction

7/10

Mixed Number

Proper (7/10)

Decimal Value

0.7

Percentage

70%

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Step-by-Step Solution: 2/30 ÷ 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.

2/30 ÷ 2/21 = 2/30 × 21/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (30 × 2 = 60).

2 × 21/30 × 2 = 42/60

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 60, which is 6. Divide both the numerator and denominator by 6.

42 ÷ 6/60 ÷ 6 = 7/10

Step 4

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).

7 ÷ 10 = 0.7 (70%)

Visual Representation

The diagram below illustrates 2/30 divided by 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/10`
Mixed Number Form	`7/10`
Decimal Form	`0.7`
Percentage	`70%`

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Frequently Asked Questions

What is 2/30 divided by 2/21 as a fraction?

2/30 ÷ 2/21 in simplest fraction form is 7/10.

What is 2/30 divided by 2/21 as a decimal?

2/30 ÷ 2/21 converted to a decimal is 0.7.

What is 2/30 divided by 2/21 as a percentage?

2/30 ÷ 2/21 expressed as a percentage is 70%.

Does 2/30 divided by 2/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.7) because the denominator in simplest terms contains only prime factors 2 and/or 5.