Dividing 152 By 7 A Step-by-Step Guide

Aug 4, 2025 by ADMIN 39 views

How to Master Division: A Step-by-Step Guide to Dividing 152 by 7

Hey guys! Ever get tripped up by long division? Don't worry, you're not alone! Division can seem tricky, but breaking it down into simple steps makes it super manageable. In this guide, we're going to tackle dividing 152 by 7. We'll go through each step nice and slow so you can follow along and really nail this skill. Trust me, once you get the hang of it, you'll be dividing numbers like a pro!

Understanding the Basics of Division

Before we jump into the nitty-gritty of dividing 152 by 7, let's quickly recap what division actually means. At its core, division is all about splitting a number (the dividend) into equal groups based on another number (the divisor). The result we get is called the quotient, and sometimes we have a little bit left over, which we call the remainder.

Think of it like this: Imagine you have 152 cookies (yum!) and you want to share them equally among 7 friends. Division helps you figure out how many cookies each friend gets (the quotient) and if you have any cookies left over for yourself (the remainder). So, in our case, 152 is the dividend (the total number of cookies), 7 is the divisor (the number of friends), and we're trying to find the quotient (cookies per friend) and the remainder (leftover cookies).

Now, let's dive into the actual process of long division. We'll use a step-by-step method that's super clear and easy to follow. Get your pencils and paper ready, and let's get started!

Step 1: Setting Up the Problem

Okay, the first thing we need to do is set up our division problem properly. This helps keep everything organized and prevents confusion later on. We're dividing 152 by 7, so we write it out like this:

      ______
7  | 152

See that little “house” shape? That's the division symbol! The number we're dividing (152, the dividend) goes inside the house, and the number we're dividing by (7, the divisor) goes outside on the left. The blank space above the house is where we'll write our answer, the quotient.

Setting it up this way might seem like a small thing, but it's super important for keeping your work neat and tidy. Trust me, when you're dealing with bigger numbers, a clear setup will save you from making silly mistakes. So, make sure you've got your problem set up just like this before we move on to the next step. You're doing great so far!

Step 2: Dividing the First Digit

Alright, now for the fun part – the actual dividing! We're going to start by looking at the first digit of the dividend, which is 1 in 152. We need to ask ourselves: How many times does 7 go into 1? Well, 7 is bigger than 1, so it doesn't go in at all. That means we write a 0 above the 1 in our quotient space:

      0_____
7  | 152

This might seem a bit obvious, but it's an important step in the process. We're essentially saying that 7 goes into 1 zero times. Now, since 7 doesn't go into 1, we need to consider the next digit as well. This is where things get a little more interesting!

Step 3: Dividing the First Two Digits

Since 7 doesn't go into 1, we're going to look at the first two digits of our dividend together, which is 15. Now, we ask ourselves: How many times does 7 go into 15? Think about your 7 times tables. 7 times 1 is 7, 7 times 2 is 14, and 7 times 3 is 21. 21 is too big, so 7 goes into 15 two times.

We write the 2 above the 5 in our quotient space:

      02____
7  | 152

This 2 represents that 7 goes into 15 two whole times. Now, we need to figure out how much of the 15 we've actually used up. This leads us to the next step, which is multiplication.

Step 4: Multiplying and Subtracting

Okay, we know that 7 goes into 15 two times. Now we need to multiply the divisor (7) by the number we just wrote in the quotient (2). So, 7 times 2 is 14. We write this 14 directly below the 15 in our dividend:

      02____
7  | 152
     14

Next, we subtract 14 from 15. 15 minus 14 is 1. We write the 1 below the 14:

This 1 is what's left over after we've divided 7 into 15 two times. Now, we need to bring down the next digit from our dividend to see what we do with this remainder. This is where the process starts to repeat itself, which is what makes long division so systematic.

Step 5: Bringing Down the Next Digit

We've divided 7 into 15, multiplied, subtracted, and now it's time to bring down the next digit from our dividend. The next digit in 152 is 2, so we bring it down next to the 1 that we had left over:

Now we have the number 12. This is the new number we're going to divide by 7. We essentially start the whole process over again, but this time with 12 instead of 15. Are you keeping up? Great! Let's move on to the next step.

Step 6: Dividing Again

Alright, we've brought down the 2, and now we have 12. So, we ask ourselves again: How many times does 7 go into 12? Think about your 7 times tables again. 7 times 1 is 7, and 7 times 2 is 14. 14 is too big, so 7 goes into 12 only one time.

We write the 1 next to the 2 in our quotient space:

This 1 represents that 7 goes into 12 one whole time. Just like before, we now need to figure out how much of the 12 we've used up. So, we multiply again!

Step 7: Multiplying and Subtracting Again

We know that 7 goes into 12 one time, so we multiply the divisor (7) by the number we just wrote in the quotient (1). 7 times 1 is 7. We write this 7 directly below the 12:

Now, we subtract 7 from 12. 12 minus 7 is 5. We write the 5 below the 7:

This 5 is what's left over after we've divided 7 into 12 one time. Now, we need to check if there are any more digits to bring down from our dividend. In this case, we've used up all the digits in 152. That means this 5 is our remainder!

Step 8: Identifying the Quotient and Remainder

We've reached the end of our long division journey! Let's take a look at what we've got. In the quotient space above the division “house,” we have the number 21. This is our quotient, meaning that 152 divided by 7 is 21 with a remainder.

The remainder is the number we have left over at the bottom, which is 5. So, 152 divided by 7 is 21 with a remainder of 5.

We can write this out like this:

152 ÷ 7 = 21 R 5

This means that if you were to divide 152 cookies among 7 friends, each friend would get 21 cookies, and you'd have 5 cookies left over for yourself (or to share, if you're feeling generous!).

Step 9: Checking Your Work

It's always a good idea to double-check your work, especially with long division. Luckily, there's a simple way to do this! We can use the following formula:

(Quotient × Divisor) + Remainder = Dividend

In our case, the quotient is 21, the divisor is 7, the remainder is 5, and the dividend is 152. Let's plug those numbers in:

(21 × 7) + 5 = 152

First, we multiply 21 by 7: 21 × 7 = 147

Then, we add the remainder: 147 + 5 = 152

And there you have it! 152 equals 152, so our answer is correct! Checking your work like this is a great habit to get into, as it helps you catch any mistakes and build confidence in your division skills.

Conclusion: You've Mastered Dividing 152 by 7!

Awesome job, you guys! You've successfully divided 152 by 7 using long division. We broke it down into clear, easy-to-follow steps, and you tackled each one like a champ. Remember, the key to mastering long division is practice, so don't be afraid to try more problems. The more you practice, the more comfortable and confident you'll become.

Now you know that 152 divided by 7 is 21 with a remainder of 5. You also learned how to check your work to make sure your answer is correct. These are valuable skills that will help you in all sorts of math situations.

So, keep practicing, keep learning, and keep conquering those division problems! You've got this!