How to do 120 divided by 3: A Simple Guide for Everyone
Have you ever found yourself staring at numbers and wondering, "What's 120 divided by 3?" You're not alone! Math can sometimes feel like a puzzle, but breaking down problems into smaller steps makes them much easier to solve. This article will walk you through exactly how to divide 120 by 3, using methods that are straightforward and easy for any American to understand.
Understanding Division
Before we dive into the specific problem, let's quickly refresh our understanding of division. Division is essentially the process of splitting a larger number into equal groups. When we ask "How to do 120 divided by 3?", we're asking how many groups of 3 we can make from a total of 120, or what number results from splitting 120 into 3 equal parts.
Method 1: The Standard Division Algorithm (Long Division)
This is the most common and reliable method taught in schools across America. Here’s how to apply it to 120 divided by 3:
- Set up the problem: Write the dividend (120) inside the division symbol (like a house), and the divisor (3) outside to the left.
____
3 | 120 - Divide the first digit of the dividend: Look at the first digit of 120, which is 1. Can 3 go into 1? No, 3 is larger than 1. So, we move to the next digit.
- Divide the first two digits: Now, consider the first two digits of 120, which are 12. How many times does 3 go into 12? We can think of our multiplication facts: 3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12. So, 3 goes into 12 exactly 4 times.
- Write the quotient above: Write the '4' directly above the '2' in 120, aligning it with the digits you just used.
4___
3 | 120 - Multiply: Multiply the digit you just placed in the quotient (4) by the divisor (3). 4 x 3 = 12.
- Subtract: Write the result (12) directly below the first two digits of the dividend (12) and subtract. 12 - 12 = 0.
4___
3 | 120
--12
0 - Bring down the next digit: Bring down the next digit from the dividend (which is 0) next to the result of the subtraction.
4___
3 | 120
--12
00 - Repeat the process: Now, we have 0. How many times does 3 go into 0? It goes in 0 times. Write '0' next to the '4' in the quotient.
40
3 | 120
--12
00 - Multiply and Subtract again: Multiply 0 (from the quotient) by 3 (the divisor). 0 x 3 = 0. Write 0 below the 0 and subtract. 0 - 0 = 0.
40
3 | 120
--12
00
--0
0
Since there are no more digits to bring down and our remainder is 0, the division is complete. The answer, or quotient, is 40.
Method 2: Breaking Down the Number
Sometimes, we can make division easier by breaking the dividend into parts that are easier to divide by the divisor. This is especially helpful for numbers that are multiples of 10 or have easily divisible parts.
For 120 divided by 3, we can see that 120 is made up of 12 tens.
- We know that 12 divided by 3 is 4.
- Since 120 is 12 tens, and 12 divided by 3 is 4, then 120 divided by 3 will be 4 tens.
- 4 tens is equal to 40.
So, 120 ÷ 3 = 40.
Method 3: Using a Calculator
In today's world, a calculator is a handy tool for quick calculations.
- Turn on your calculator.
- Enter the number 120.
- Press the division button (usually represented by '/').
- Enter the number 3.
- Press the equals button (usually represented by '=').
The calculator will display the answer: 40.
Verification: Why 40 is the Correct Answer
To make sure our answer is correct, we can use multiplication. Division and multiplication are inverse operations, meaning they undo each other.
If 120 divided by 3 equals 40, then 40 multiplied by 3 should equal 120.
Let's check:
40 x 3 = ?
We can do this as:
(4 tens) x 3 = 12 tens
And 12 tens is indeed 120.
So, 40 x 3 = 120. This confirms that our answer of 40 for 120 divided by 3 is correct.
Frequently Asked Questions (FAQ)
How do I know which number is the dividend and which is the divisor?
In a division problem like "120 divided by 3," the dividend is the number being divided (120), and the divisor is the number you are dividing by (3). The result of the division is called the quotient.
Why is division important?
Division is a fundamental mathematical operation used in everyday life for many tasks. It helps us to share items equally, calculate proportions, understand rates, manage budgets, and solve a wide variety of problems that involve splitting quantities into equal parts.
What if there's a remainder in division?
If there's a remainder, it means that the dividend cannot be perfectly divided by the divisor into whole numbers. For example, 7 divided by 3 is 2 with a remainder of 1, because you can make two groups of 3 from 7, and you'll have 1 left over. In the case of 120 divided by 3, there is no remainder, meaning it divides evenly.
Are there other ways to visualize 120 divided by 3?
Yes! You can imagine having 120 candies and wanting to give an equal number to 3 friends. You would give each friend 40 candies. Or, you could think of 120 inches of fabric being cut into 3 equal pieces, with each piece being 40 inches long.
