How Many Times Does 12 Go Into 144? Best 173 Answer

We never share your email address and you can unsubscribe at any time.

Subscribe to our FREE newsletter and start improving your life in just 5 minutes a day.

Division ‘÷’ | Basics of Arithmetic See also: Fractions

This page covers the basics of division (÷).

See our other arithmetic pages for discussions and examples of: addition (+), subtraction (-), and multiplication (×).

division

The usual notation for division is (÷). In spreadsheets and other computer applications, the symbol “/” (slash) is used.

Division is the opposite of multiplication in mathematics.

Division is often considered the most difficult of the four main arithmetic functions. This page explains how division calculations are performed. Once we have a good understanding of the method and the rules, we can use a calculator for more tricky calculations without making mistakes.

Division allows us to divide, or “divide,” numbers to find an answer. For example, consider how we would find the answer to 10 ÷ 2 (ten divided by two). This is the same as “sharing” 10 candies between 2 children. Both children must end up with the same number of sweets. In this example, the answer is 5.

Some quick rules about division: When you divide 0 by any other number, the answer is always 0. For example: 0 ÷ 2 = 0. That’s 0 candy divided equally between 2 children – each child gets 0 candy .

When you divide a number by 0, you don’t divide at all (that’s quite a problem in math). 2 ÷ 0 is not possible. You have 2 candies but no children to divide them among. You cannot divide by 0.

If you divide by 1, the result is the same as the number you divided. 2 ÷ 1 = 2. Two candies shared by one child.

When you divide by 2, you halve the number. 2 ÷ 2 = 1.

Each number divided by the same number is 1. 20 ÷ 20 = 1. Twenty candies divided by twenty children – each child gets one candy.

Numbers must be divided in the correct order. 10 ÷ 2 = 5, while 2 ÷ 10 = 0.2. Ten candies divided by two children is very different than 2 candies divided by 10 children.

All fractions like ½, ¼ and ¾ are sums of divisions. ½ is 1 ÷ 2. A candy shared by two children. See our Fractions page for more information.

Multiple Subtractions

Just as multiplication is a quick way to do multiple additions, division is a quick way to do multiple subtractions.

For example:

If John has 10 gallons of fuel in his car and uses 2 gallons a day, how many days before he runs out?

We can solve this problem by performing a series of subtractions or counting backwards by twos.

On Day 1, John starts with 10 gallons and ends with 8 gallons. 10 – 2 = 8

John starts with gallons and ends with gallons. On Day 2, John starts with 8 gallons and ends with 6 gallons. 8 – 2 = 6

John starts with gallons and ends with gallons. On Day 3, John starts with 6 gallons and ends with 4 gallons. 6 – 2 = 4

John starts with gallons and ends with gallons. On Day 4, John starts with 4 gallons and ends with 2 gallons. 4 – 2 = 2

John starts with gallons and ends with gallons. On day 5, John starts with 2 gallons and ends with 0 gallons. 2 – 2 = 0

John runs out of fuel on day 5.

A faster way to do this calculation would be to divide 10 by 2. That is, how many times does 2 go in 10, or how many lots of two gallons are in ten gallons? 10 ÷ 2 = 5.

The multiplication table (see Multiplication) can be used to find the answer to simple division calculations.

In the example above, we needed to calculate 10 ÷ 2. To do this, use the multiplication table to find the column for 2 (the red-shaded heading). Work down the column until you find the number you are looking for, 10. Move left across the row to see the answer (the red shaded heading) 5.

Multiplication tables × 1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 6 6 8 4 20 3.4 368 4 7 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100

We can do other simple division calculations using the same method. 56 ÷ 8 = 7 for example. Find 7 in the top row, look down the column until you find 56, and then find the corresponding row number, 8.

If possible, try to memorize the multiplication table above, as it makes solving simple multiplication and division much faster.

Division of larger numbers

You can use a calculator to do division calculations, especially when dividing larger numbers that are more difficult to calculate mentally. However, it is important to understand how pitch calculations are performed manually. This is useful if you don’t have a calculator handy, but also important to ensure you are using the calculator correctly and not making any mistakes. Division may look daunting, but in fact, like most arithmetic, it is logical.

As with any math, it’s easiest to understand if we work through an example:

Dave’s car needs new tires. He needs to replace all four tires on the car, plus the spare tire.

Dave received a £480 offer from a local garage which includes the tyres, fitting and disposal of the old tyres. How much does each tire cost?

The problem we need to calculate here is 480 ÷ 5. Is that the same as saying how many times does 5 go into 480?

We usually write this as follows:

5 4 8 0

We work from left to right in a logical system.

We start by dividing 4 by 5 and immediately run into a problem. 4 cannot be divided by 5 to get an integer because 5 is greater than 4.

The language we use in math can be confusing. Another way of looking at it is to say, “How many times does 5 turn into 4?”. We know that 2 fits into 4 twice (4 ÷ 2 = 2) and we know that 1 fits into 4 four times (4 ÷ 1 = 4), but 5 doesn’t fit into 4 because 5 is greater than 4. The number we are dividing by (in this case 5) must be an integer of the number we are dividing by (in this case 4). It doesn’t have to be an exact integer, as you will see.

Since 5 doesn’t fit in 4, we put a 0 in the first (hundreds) column. For help with the hundreds, tens, and ones columns, see our page on numbers.

hundreds tens units 0 5 4 8 0

Next we move to the right to include the tens column. Now we can see how many times 5 goes into 48.

5 goes into 48 because 48 is greater than 5. However, we need to find out how often it goes.

If we refer to our multiplication table, we can see that 9 × 5 = 45 and 10 × 5 = 50.

48, the number you’re looking for, lies between these two values. Remember, we’re interested in how many times 5 goes into 48. Ten times is too much.

We can see that 5 fits an integer (9) times into 48, but not exactly, leaving 3.

9 × 5 = 45

48 – 45 = 3

We can now say that 5 goes into 48 nine times, but with a remainder of 3. The remainder is what’s left when we subtract the number we found from the number we’re dividing by: 48 – 45 = 3

So 5 × 9 = 45 + 3 equals 48.

We can enter 9 in the tens column as the answer for the second part of the calculation and put our remainder before our last number in the ones column. Our last number will be 30.

hundreds tens units 0 9 5 4 8 30

We now divide 30 by 5 (or find out how many times 5 goes into 30). Using our multiplication table, we can see that the answer is exactly 6, with no remainder. 5 × 6 = 30. We write 6 in the units column of our answer.

hundreds tens units 0 9 6 5 4 8 30

Since there are no remainders, we have finished the calculation and get the answer 96.

Dave’s new tires are £96 each. 480 ÷ 5 = 96 and 96 × 5 = 480.

recipe department

Our last splitting example is based on a recipe. When cooking, recipes often tell you how much food they will make, enough to feed 6 people for example.

The following ingredients are needed to make 24 fairy cakes, however we only want to make 8 fairy cakes. For this example we have slightly modified the ingredients (original recipe at: BBC Food).

The first thing we need to determine is how many eights are in 24 – use the multiplication table above or your memory. 3 × 8 = 24 – if we divide 24 by 8 we get 3. Therefore we need to divide each ingredient below by 3 to have the right amount of mixture to make 8 fairy cakes.

ingredients

120 g butter, softened at room temperature

120g powdered sugar

3 free range eggs, lightly beaten

1 tsp vanilla extract

120 g self-raising flour

1-2 tbsp milk

The amount of butter, sugar and flour is the same, 120 g. It is therefore only necessary to calculate 120 ÷ 3 once, since the answer for these three ingredients is the same.

3 1 2 0

As before, we start in the left column (hundreds) and divide 1 by 3. However, 3 ÷ 1 doesn’t work since 3 is greater than 1. Next we look at how many times 3 goes into 12 takes, we can see that 3 goes into 12 exactly 4 times with no remainder.

0 4 0 3 1 2 0

So 120g ÷ 3 is 40g. We now know that we need 40g of butter, sugar and flour.

The original recipe calls for 3 eggs and again we divide by 3. So 3 ÷ 3 = 1, so one egg is needed.

Next, the recipe calls for 1 tsp (teaspoon) of vanilla extract. We need to divide a teaspoon by 3. We know that division can be written as a fraction, so 1 ÷ 3 is the same as ⅓ (one third). You will need ⅓ teaspoon of vanilla extract – although in reality it can be difficult to measure ⅓ teaspoon accurately!

Estimating can be useful, and units can be changed! We can also see it differently if we know that a teaspoon corresponds to 5 ml or 5 milliliters. (If you need help with units, see our page on systems of measurement.) If we want to be more specific, we can try dividing 5mL by 3. 3 goes once into 5(3), leaving 2. 2 ÷ 3 is the same as ⅔, so 5 ml divided by 3 is 1⅔ ml, which in decimal is 1.666 ml. We can use our guessing skills and say that one teaspoon divided by three is just over a ml and a half. If you have a few of those tiny measuring spoons in your kitchen, you can be super accurate! We can guess the answer to check if we are right. Three batches of 1.5ml make 4.5ml. So three batches of “just over 1.5ml” make about 5ml. Recipes are rarely an exact science, so a little guessing can be fun and good practice for be our mental arithmetic.

Next, the recipe calls for 1-2 tablespoons of milk. That’s between 1 and 2 tablespoons of milk. We don’t have a definitive amount and how much milk you add will depend on your mix consistency.

We already know that 1 ÷ 3 ⅓ and 2 ÷ 3 ⅔. So we need ⅓–⅔ of a tablespoon of milk to make eight fairy cakes. Let’s take a different look. A tablespoon equals 15 ml. 15 ÷ 3 = 5, so ⅓–⅔ of a tablespoon equals 5–10 ml, which equals 1–2 teaspoons!

How many times can you subtract 6 from 60?

Once

10 times

infinity

out

“How many times can you subtract 6 from 60?” is a tricky question. We think there are three different answers to this question. Once upon a time, because once you subtract 6 from 60, you’re left with 54. So you can’t subtract 6 from 60 times 10 again, because 60 divided by 6 is 10. After you’ve subtracted 6, 10 times from 60, there is there is nothing left to subtract. There’s nothing that says you can’t subtract 6 from 60 indefinitely. Just because you end up with negative numbers doesn’t mean you have to stop subtracting! Enter a similar problem here: Based on our answer to “How many times can you subtract 6 from 60?” You probably know the answer to the next problem on our list. Find out if you were right here!

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e. H. with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 is exact and 12 ÷ 6 = 2 is exact. The other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression that has only two factors (i.e., itself and 1), is called a prime number; A positive integer or algebraic expression that has more than two factors is said to be composite. The prime factors of a number or algebraic expression are those factors that are prime. With the exception of the order in which the prime factors are written, by the fundamental theorem of arithmetic, any integer greater than 1 can be expressed uniquely as the product of its prime factors; For example, 60 can be written as the product 2*2*3*5.

Techniques for factoring large integers are of great importance in public-key cryptography, and relies on the security (or lack thereof) of data transmitted over the Internet. Factoring is also a particularly important step in solving many algebraic problems. For example, the polynomial equation x2 − x − 2 = 0 can be factored as (x − 2)(x + 1) = 0. Since in an integral domain a b = 0 implies that either a = 0 or b = 0, the simpler equations x − 2 = 0 and x + 1 = 0 can be solved to find the two solutions x = 2 and x = −1 of the original equation.

Informally, when you multiply an integer (a “whole” number, positive, negative, or zero) by itself, the resulting product is called a square number, or a perfect square, or simply “a square.” So 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 etc. are all square numbers.

More formally, a square number is a number of the form n × n or n2, where n is any integer.

Mathematical background

Objects arranged in a square array

The name “square number” comes from the fact that that specific number of objects can be arranged to fill a perfect square.

Kids can experiment with pennies (or square tiles) to see how many of them can be arranged in a perfectly square arrangement.

Four cents can:

Nine cents can:

And sixteen pfennigs can also:

But seven pfennigs or twelve pfennigs cannot be arranged like that. Numbers (of objects) that can be arranged in a square array are called “square numbers”.

Square arrays must be full if we are to count the number as a square number. Here 12 pennies are arranged in a square, but not a complete square array, so 12 is not a square number.

Kids can enjoy exploring how many cents can be arranged in an open square like this one. They’re not called “square numbers,” but they follow an interesting pattern.

It’s also fun to make squares out of square tiles. The number of square tiles that fit in a square array is a “square number”.

Here are two boards, 3 × 3 and 5 × 5. How many red tiles are in each? Black? Yellow?

Are any of these square numbers?

What if you tile a 4×4 or 6×6 game board the same way?

Can you predict the number of tiles on a 7×7 or 10×10 board?

Square numbers in the multiplication table

Connections with triangular numbers

If you count the green triangles in each of these designs, you will see the sequence of numbers: 1, 3, 6, 10, 15, 21,…, a sequence that is (appropriately) called the triangle numbers.

Counting the white triangles that are in the “spaces” between the green ones, the sequence of numbers starts at 0 (because the first design has no gaps) and then continues: 1, 3, 6, 10, 15, …, triangular numbers again!

Remarkably, if you count all of the small triangles in each design – both green and white – the numbers are squares!

In other words, a connection between square and triangular numbers

Build a stair tread arrangement of Cuisenaire bars, say W, R, G. Then build the next stair tread: W, R, G, P.

Each is “triangular” (if we ignore the stepped edge). Put the two consecutive triangles together and they form a square: . This square is the same size as 16 white sticks arranged in a square. The number 16 is a square number, “4 squared”, the square of the length of the longest stick (measured with white sticks).

Here’s another example: . These add up to a square with an area of ​​64, again the square of the length (in white sticks) of the longest stick. (The brown stick is 8 white sticks long and 64 is 8 times 8 or “8 squared”.)

Steps of square numbers

Stairs that go up and then down again, like this one, also contain a square number of tiles. When the tiles are checkerboard like here, an additional sentence describing the number of red tiles (10), the number of black tiles (6), and the total number of tiles (16) again shows the connection between them triangular numbers and square numbers: 10 + 6 = 16.

Asking 2nd (or even 1st) graders to build stair step patterns and write sets of numbers that describe those patterns is a nice way to practice using descriptive sets of numbers and also “become familiar” with square numbers.

Here are two examples. Color is used here so you can see what is being described. Children like colour, but don’t need it, and can often find creative ways to describe stair step patterns that they have built with solid color tiles. Or they color on 1 inch graph paper to record their stair step pattern and show how they translated it into a set of numbers.

A rhombus made of pennies can also be described by the number set 1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25.

From one square number to the next: two pictures with Cuisenaire sticks

(1) Start with W. Add two consecutive staves, W+R; then two more, R+G; then G+P; then….

1; add 1+2; add 2+3; add 3+4; add 4+5; add 5+6; add 6+7

(2) Start with W. For each new square, add two sticks to match the sides of the previous square and a new W to fill in the corner.

Please disable Adblock to continue browsing our website.

Unfortunately, in the last year Adblock has started to prevent almost all images on our website from loading, which has resulted in mathwarehouse becoming unusable for Adlbock users.

Question:

What is 28 divided by 2?

Division of whole numbers

Dividing one number by another means finding out how many times the number can go into another number. For simpler division problems, you can memorize the answers, but longer numbers mean you have to divide using a series of steps called long division.

Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account. Check out this answer