What is 2/45 divided by 2/21? (Answer: 7/15)

Exact Answer

==================================================
Problem: What is 2/45 divided by 2/21?
Formula / Expression: 2/45 ÷ 2/21
Final Answer: 7/15
==================================================

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: 2/45 ÷ 2/21 = 2/45 × 21/2

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 21 = 42) and denominators (45 × 2 = 90).
Working: 2 × 21/45 × 2 = 42/90

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 90, which is 6. Divide both the numerator and denominator by 6.
Working: 42 ÷ 6/90 ÷ 6 = 7/15

Step 4: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).
Working: 7 ÷ 15 = 0.466667 (46.6667%)

Key Values:
- Simplified Fraction: 7/15
- Mixed Number Form: 7/15
- Decimal Value: 0.466667
- Percentage: 46.6667%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-45-divided-by-2-21/
==================================================

2/45 ÷ 2/21 = 7/15

Simplified Fraction

7/15

Mixed Number

Proper (7/15)

Decimal Value

0.466667

Percentage

46.6667%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 2/45 ÷ 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.

2/45 ÷ 2/21 = 2/45 × 21/2

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 21 = 42) and denominators (45 × 2 = 90).

2 × 21/45 × 2 = 42/90

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 90, which is 6. Divide both the numerator and denominator by 6.

42 ÷ 6/90 ÷ 6 = 7/15

Step 4

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).

7 ÷ 15 = 0.466667 (46.6667%)

Visual Representation

The diagram below illustrates 2/45 divided by 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/15`
Mixed Number Form	`7/15`
Decimal Form	`0.466667`
Percentage	`46.6667%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/45 divided by 2/21 as a fraction?

2/45 ÷ 2/21 in simplest fraction form is 7/15.

What is 2/45 divided by 2/21 as a decimal?

2/45 ÷ 2/21 converted to a decimal is 0.466667.

What is 2/45 divided by 2/21 as a percentage?

2/45 ÷ 2/21 expressed as a percentage is 46.6667%.

Does 2/45 divided by 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.466667...) because the denominator contains prime factors other than 2 and 5.