Dividing 2 by 2/3 may seem like a simple mathematical operation, but it’s worth exploring in detail to understand the concept fully. In this blog post, we will break down the process, discuss fractional division, and provide real-world examples to illustrate the concept. By the end of this article, you should have a clear understanding of how to divide a whole number by a fraction, as well as why this operation is essential in various practical scenarios.

## What is 2 Divided by 2/3?

*When you divide 2 by 2/3, it’s equivalent to multiplying 2 by the reciprocal of 2/3, which is 3/2. So, 2 ÷ 2/3 = 2 × 3/2 = 3. Therefore, 2 divided by 2/3 equals 3.*

**Introduction**

Division is one of the fundamental arithmetic operations, and it is used in everyday life for various purposes. When we divide one number by another, we are essentially asking, “How many times does the divisor fit into the dividend?” In this blog post, we will focus on dividing a whole number by a fraction, specifically, dividing 2 by 2/3.

**Understanding Fractions**

Before we dive into dividing 2 by 2/3, let’s briefly review what fractions are and how they work.

A fraction consists of two parts: the numerator and the denominator. The numerator represents the number of equal parts we have, while the denominator represents the total number of equal parts that make up a whole.

For example, in the fraction 2/3:

- The numerator (2) represents that we have 2 equal parts.
- The denominator (3) represents that the whole is divided into 3 equal parts.

**Dividing by a Fraction**

Now that we have a basic understanding of fractions, let’s discuss how to divide a whole number by a fraction. To do this, we can use the concept of reciprocal fractions.

The reciprocal (or multiplicative inverse) of a fraction is obtained by swapping the numerator and the denominator. In other words, if we have a fraction a/b, its reciprocal is b/a.

For example, the reciprocal of 2/3 is 3/2.

**Division as Multiplication**

Dividing a whole number by a fraction is equivalent to multiplying that whole number by the reciprocal of the fraction. So, when we divide 2 by 2/3, we can rewrite it as:

2 ÷ (2/3) = 2 × (3/2)

**Solving the Expression**

Now, let’s solve the expression step by step:

2 × (3/2)

First, we multiply the whole number (2) by the numerator of the fraction (3):

2 × 3 = 6

Then, we multiply the result by the reciprocal’s denominator (2):

6 × 2 = 12

So, 2 divided by 2/3 equals 12.

**Real-World Examples**

To make this concept more tangible, let’s explore some real-world examples where dividing by a fraction is useful.

**1. Recipes**

Imagine you’re following a recipe that calls for 2/3 cup of sugar, but you want to make a smaller batch. You only have 2/3 of the amount of sugar required. How much sugar should you use? To find out, you would divide the original amount by the fraction:

Original amount = 2/3 cup Desired amount = ?

Desired amount = 2/3 ÷ (2/3) Desired amount = 2/3 × (3/2) (Using the reciprocal) Desired amount = 1 cup

So, you should use 1 cup of sugar to make your scaled-down recipe.

**2. Time and Speed**

Suppose you are on a road trip, and you need to calculate how long it will take to travel a certain distance. You know that you are driving at an average speed of 60 miles per hour (mph), and you need to cover a distance of 120 miles. To find out how long the journey will take, you can use the formula:

Time = Distance ÷ Speed

Time = 120 miles ÷ 60 mph = 2 hours

Now, let’s say you encounter traffic, and your speed reduces to 2/3 of the original speed (40 mph). How long will it take to cover the same 120-mile distance at this reduced speed? To find out, you can divide the distance by the fraction representing your reduced speed:

Time = 120 miles ÷ (2/3) (Using the reciprocal of 2/3) Time = 120 miles × (3/2) Time = 180 minutes

So, it will take 3 hours (or 180 minutes) to cover the same distance at a speed of 40 mph.

**3. Cooking and Scaling Recipes**

When you’re in the kitchen, scaling recipes up or down is a common task. Let’s say you have a recipe that serves 4 people, but you need to adjust it to serve 6 people. You can use division to calculate the scaling factor:

Scaling factor = Desired servings ÷ Original servings

Scaling factor = 6 ÷ 4 = 1.5

Now, you can use this scaling factor to adjust the quantities of ingredients. For example, if the recipe originally calls for 2 cups of flour, you can find the new amount for 6 servings:

New amount of flour = 2 cups × 1.5 = 3 cups

So, you would need 3 cups of flour to serve 6 people.

**4. Price Comparison**

Suppose you’re shopping for a product, and you want to compare the prices of two different packages. Package A costs $5 for 2/3 of a pound, and Package B costs $8 for 1 pound. To determine which package offers a better deal, you can calculate the price per pound for each package:

Price per pound for Package A = $5 ÷ (2/3) (Using the reciprocal of 2/3) Price per pound for Package A = $5 × (3/2) = $7.50 per pound

Price per pound for Package B = $8 ÷ 1 = $8 per pound

In this case, Package A is the better deal, as it costs $7.50 per pound compared to Package B’s $8 per pound.

**Conclusion**

Dividing a whole number by a fraction is a fundamental mathematical operation that has practical applications in various aspects of daily life, from cooking and recipes to calculations involving time, distance, and pricing. Understanding how to divide by a fraction involves using the reciprocal of the fraction and applying it as a multiplication operation. By mastering this concept, you can make informed decisions and solve a wide range of real-world problems efficiently. Whether you’re adjusting recipes, calculating travel times, or comparing prices, the ability to divide by a fraction is a valuable mathematical skill.

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