Learn how to divide 90 by 6 and gain a clear understanding of the concept of division. *Explore real-life examples and word problems involving 90 divided by 6.*

## Understanding Division

### What is Division?

Division is a mathematical operation that helps us distribute or allocate a given quantity into equal parts. It is the process of dividing a number into smaller groups or sections. In simpler terms, division allows us to share or *distribute things fairly among* a certain number of people or groups.

When we divide a number, we are essentially asking how many times a particular number (called the divisor) can be subtracted from another number (called the dividend) without resulting in a negative value. The answer to this question is called the quotient.

### How Does Division Work?

To understand how works, let’s consider a simple example. Let’s say we have 10 cookies and we want to distribute them equally among 2 friends. We can use division to determine how many cookies each friend will receive.

In this case, the number of cookies (10) is the dividend, and the number of friends (2) is the divisor. We divide 10 by 2, and the quotient is 5. This means that each friend will receive 5 cookies.

Division involves several key terms:

**Dividend**: The number being divided.**Divisor**: The number by which the dividend is divided.**Quotient**: The result or answer obtained from the division.**Remainder**: The number left over after division, which is less than the divisor.

When dividing numbers, it is important to note that not all divisions result in a whole number quotient. Sometimes, there is a remainder, which represents the amount left over after dividing as much as possible.

For example, if we divide 10 by 3, the quotient is 3 with a remainder of 1. This means that 3 is the largest whole number that can be divided evenly into 10, and there is 1 left over.

Understanding division is essential in various real-life situations, such as splitting resources, calculating averages, and **solving problems involving ratios** or proportions. By mastering division, we can make fair distributions, solve everyday challenges, and make sense of numerical relationships.

## Dividing 90 by 6

### Dividing 90 by 6: Step-by-Step

To divide 90 by 6, we follow a step-by-step process that allows us to find the quotient and remainder. Let’s break it down:

- Start by writing down the dividend (90) and the divisor (6).
**Ask yourself**: How many times does 6 go into 9? The answer is 1. Write this above the line.- Multiply the quotient (1) by the divisor (6) and subtract the result from the dividend. In this case, 1 multiplied by 6 is 6, and subtracting this from 9 leaves us with 3.
- Bring down the next digit of the dividend. In this case, we bring down the 0.
- Repeat the previous steps. How many times does 6 go into 30? The answer is 5. Write this above the line.
- Multiply the new quotient (5) by the divisor (6) and subtract the result from the remaining part of the dividend. In this case, 5 multiplied by 6 is 30, and subtracting this from 30 leaves us with 0.

After completing these steps, we find that the quotient is 15 and the remainder is 0. Therefore, when we 90 by 6, the result is 15 without any remainder.

### Quotient and Remainder

When we divide two numbers, we obtain both a quotient and a remainder. The quotient represents the number of times the divisor can be evenly divided into the dividend, while the remainder is the amount left over after dividing as much as possible.

In the case of dividing 90 by 6, the quotient is 15, which means that 6 can go into 90 exactly 15 times. The remainder is 0 since there is no amount left over. This tells us that 90 is divisible by 6 without any remainder.

### Divisibility Rules for 6

**Divisibility rules help us determine if a number is divisible by another number without actually performing the division.** In the case of 6, there is a simple rule we can use:

A number is divisible by 6 if it is divisible by both 2 and 3.

This means that if a number is even (divisible by 2) and the sum of its digits is divisible by 3, then it is also divisible by 6. For example, let’s consider the number 90. It is even since the last digit is 0, which means it is divisible by 2. Additionally, the sum of its digits (9 + 0) is 9, which is divisible by 3. Therefore, we can conclude that 90 is divisible by 6 according to the divisibility rule.

By understanding these steps, the concept of quotient and remainder, and the divisibility rule for 6, we can confidently divide 90 by 6 and solve related problems.

## Applications of 90 divided by 6

### Real-Life Examples

When it comes to real-life applications, can be incredibly useful. Let’s explore some scenarios where dividing 90 by 6 can come in handy:

**Sharing Equally**: Imagine you have 90 candies and want to distribute them equally among 6 friends. By dividing 90 by 6, you can determine that each friend will receive 15 candies. This ensures fairness and avoids any disputes over the distribution.**Baking Recipes**: Many baking recipes require precise measurements to achieve the desired outcome. If a recipe calls for 90 grams of flour and you want to increase the quantity by 6 times, dividing 90 by 6 gives you the amount of flour needed for each portion. In this case, each portion would require 15 grams of flour.**Budgeting Expenses**: Let’s say you have a budget of $90 for groceries and you want to divide it equally among 6 weeks. By dividing 90 by 6, you can allocate $15 per week for groceries. This helps you stay within your budget and plan your expenses effectively.

### Word Problems Involving 90 divided by 6

Word problems can be an excellent way to apply division concepts to real-world scenarios. Here are a few word problems involving the division of 90 by 6:

**Sharing Supplies**: A teacher has 90 pencils and wants to distribute them equally among 6 students. How many pencils will each student receive? The answer is 15 pencils per student.**Grouping Objects**: A gardener has 90 flowers that need to be arranged in bouquets of 6. How many bouquets can be made? The answer is 15 bouquets can be made.**Party Planning**: A party planner needs to distribute 90 party favors into equal goody bags, with 6 favors in each bag. How many goody bags will be needed? The answer is 15 goody bags will be needed.

By **solving word problems like** these, you can develop a practical understanding of how division can be applied to various situations.

In summary, understanding division and its applications can be incredibly useful in everyday life. *Whether it’s sharing items equally, following baking recipes, budgeting expenses, or solving word problems, the ability to divide numbers allows us to solve real-world challenges efficiently.* So, the next time you encounter a situation that requires division, remember the simple yet powerful concept of dividing 90 by 6.