How Many Times Does 6 Go Into 56? The 135 Top Answers

Problem:

You have $15.36 and you need to split the money between five friends.

Steps to solve:

Total money ÷ number of people = money for each person

15.36 ÷ 6 = ?

• Since the divisor (6) has no decimal places, you do not need to move your decimal place in the dividend.

• Does 6 fit in 15? Yes twice. Write 2 and a decimal point in your quotient.

• Multiply and subtract to get a difference of 3.

• Lower the 3 to make 33.

• Does 6 fit in 33? yes, five times Write 5 in your quotient.

• Multiply and subtract to get a difference of 3.

• Lower the 6 to make 36.

• Does 6 fit in 36? yes, six times Write 6 in your quotient.

• Multiply and subtract to get a difference of 0. (No remainder and no further numbers in the dividend.)

Answers:

$15.36 ÷ 6 = $2.56 for each person.

Problem:

A business wants to make $150 after selling a container of stuffed animals. There are 40 toys in each container. How much does each stuffed animal cost?

Steps to solve:

Total amount they want to craft ÷ number of toys = price of each toy.

150 ÷ ​​40 = ?

• You don’t have to worry about moving decimal points.

• Fits 4 to 150? yes, three times Put 3 in your quotient.

• Multiply and subtract to get a difference of 30.

• You’re out of values ​​in your dividend, so add a decimal point and two zeros.

• Lower the 0 to make 300.

• Does 40 fit into 300? Yes, seven times. Write 7 in your quotient after the decimal point.

• Multiply and subtract to get a difference of 20.

• Reduce the 0 to make 200.

• Does 40 fit in 200? yes, five times Write 5 in your quotient.

• Multiply and subtract to get a difference of 0. (No remainder and no further numbers in the dividend.)

Answers:

$150.00 ÷ 40 = $3.75 for each stuffed animal.

related activities

Counting and numerical value of half dollars

– game activity

“Do you have enough money?” – Values ​​under a dollar

– game activity

We know that many of you will go out and become pirates. You will be out there dividing treasure chests full of money. Maybe you are out with your friends and come across buried treasure. Going into politics may force you to work with budgets and split money between different departments. We just want you to know that even if you are a pirate, there are a few you need to know. There is no escape. We’ll look at the idea of ​​in the sections on addition and subtraction. In the United States we have dollars and cents, and each cent is equal to $0.01. If you’ve made it through the decimal page, sharing money will be like a review for you. That’s really all it has to do with these types of problems. One more example and we’re done. Check your work… • 40 40 stuffed animals * $3.75 for each toy = $150 made by store. • 40 * 3.75 = 150

Multiples of 56 can be defined as any number that is the result of multiplying 56 by an integer. Another way of saying this could be “the numbers you get when you have multiple 56s”.

56 (fifty-six) is the natural number after 55 and before 57.

mathematics [edit]

Regular 56-gon, associated with Typhon by the Pythagoreans

56 is:

Plutarch[7] states that the Pythagoreans assigned Typhon a polygon with 56 sides and that they associated certain polygons with fewer sides with other figures of Greek mythology. While it is impossible to construct a perfect regular 56-sided polygon using a compass and ruler, an accurate approximation which it is claimed[8] may have been used at Stonehenge has recently been discovered and is constructible, if an angle is used, three sectors are allowed since 56 = 23 × 7.[9]

Science, technology and biology[ edit ]

astronomy [edit]

music [edit]

TV and film[edit]

Nasser 56, a documentary

sports [edit]

Organizations [ edit ]

The symbol of the 1956 Hungarian Revolution.

Brazilian politician Enéas Carneiro has a strange way of repeating his party’s number, “Fifty-Six” (cinquenta e seis, in Portuguese), making it a widely used jargon in his country.

56 Stuff, an international arts community and record label.

Department 56 Designers of collectibles, gift items and seasonal decorations such as miniature village houses.

people [edit]

Shirley Temple wore 56 locks as a child. Curls were set by her mother to make sure of the exact number.

Isoroku Yamamoto, nicknamed “Isoroku” because his father was 56 when he was born, and “Isoroku” is an old Japanese term meaning 56.

Geography[ edit ]

The name of the city of Fifty-Six, Arkansas.

The number of counties in the state of Montana.

In the Los Angeles Postal District, zone 56 (now the 90056 ZIP code area) is one of the few not within the Los Angeles city limits (90020 and 90044 are others).

56 is the number of the French department of Morbihan.

There are 56 Longhurst codes.

+56 is the country code for international direct dial calls to Chile.

Archeology[ edit ]

The number of Aubrey Holes (where wooden posts are said to have been) in the first phase of Stonehenge.[12]

Cosmogony[ edit ]

According to Aristotle, 56 is the number of layers in the universe – earth plus 55 crystalline spheres above it.[13]

history [edit]

The number of men who signed the United States Declaration of Independence in 1776.

The number of the men of Netophah in counting the men of Israel after returning from exile (Ezra 2:22).

Occultism[edit]

The minor arcana of a tarot deck should contain 56 cards.

See also[edit]

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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!

Factors of 63 are the integers that divide the original number evenly. There are a total of six factors out of 63, viz. H. 1, 3, 7, 9, 21, and 63. Therefore, the smallest factor is 1, and the largest factor of 63 is 63 itself. Pair factors of 63 are the numbers that, when multiplied in pairs, give the original number. The factors in pairs are (1, 63), (3, 21), and (7, 9). If we add up all the factors of 63, the sum is equal: 1 + 3 + 7 + 9 + 21 + 63 = 104.

In this article, we will learn in detail how to find the factors of 63 using the division method and the prime factorization method. Also look at some examples related to factors of 63.

What are the factors of 63?

The factors of 63 are the numbers that divide the number 63 exactly with no remainder. In other words, the pair factors of 63 are the numbers that when multiplied in pairs give the original number 63. Since the number 63 is a composite number, 63 has more than two factors. So the factors of 63 are 1, 3, 7, 9, 21, and 63.

Pair factors of 63

The pair factors of 63 are the numbers that are multiplied in pairs to give the product value as 63. Since the factors of 63 can be positive or negative, the pair factors of 63 can also be positive or negative, but they cannot be in fractional or decimal form. Hence the positive and negative pair factors of 63 are given below.

Positive pair factors of 63:

Positive factors of 63 Positive pair factors of 63 1 × 63 (1, 63) 3 × 21 (3, 21) 7 × 9 (7, 9)

Negative pair factors of 63:

Negative factors of 63 Negative pair factors of 63 -1 × – 63 (-1, -63) -3 × -21 (-3, -21) -7 × -9 (-7, -9)

How do you find factors of 63?

63 is an odd number with six dividers. Because the number of factors is less, it is easy to get these factors with two simple methods. They are:

division method

prime factorization method

Factors of 63 using the division method

Using a simple division method, we can evaluate the factors of 63. Let’s get started.

Divide 63 by the smallest possible divisor, which is 1. So one of the factors of 63 is 1.

Now check with the nearest whole number that can fully divide 63. 63/3 = 21. So 3 is a factor.

Continue dividing by integers until we reach 63/63 = 1. Since we can not take any more whole numbers.

So the factors we got are:

63/1 = 63

63/3 = 21

63/7 = 9

63/9 = 7

63/21 = 3

63/63 = 1

Therefore the required factors of 63 are 1,3,7,9,21 and 63.

use trick

Another trick to find the factors of 63 using the division method is given below:

If we divide 63 by 1, we get 63. (1 and 63 are the factors)

If we divide 63 by 3, we get 21. (3 and 21 are the factors)

Now we know that 21 is also a composite number.

Divide 21 by 3, we get 7 (Again, 7 and 3 are the factors)

Therefore, through the above steps, the numbers 1, 63, 21, 7, and 3 become the factors of 63. Since 3 is repeated twice, 3 x 3 = 9 is also a factor of 63. Therefore, the total factors are 1, 3, 7 , 9, 21 and 63.

Prime factorization of 63

The number 63 is a composite number. Now let’s find the prime factors associated with 63.

The first step is to divide the number 63 by the smallest prime factor, i.e. 2.

63 ÷ 2 = 31.5; Fraction cannot be a factor. So move on to the next prime number

Divide 63 by 3.

63 ÷ 3 = 21

Divide 21 by 3 again and keep dividing the output by 3 until you get 1 or a fraction.

21 ÷ 3 = 7

7 ÷ 3 = 2.33; cannot be a factor. Now go to the next prime number 7.

Dividing 7 by 7 we get,

7 ÷ 7 = 1

We ended up getting 1 and it has no factor. Therefore, we cannot proceed any further with the division method. So the prime factorization of 63 is 3 × 3 × 7, or 32 × 7, where 3 and 7 are the prime numbers.

Video lesson on prime factors

Factor tree of 63

Using prime factorization, we have seen how we can factor the number 63 into prime factors. The factor tree created in this way is shown in the figure below.

Facts of the factors of 63

Factors of 63 – 1, 3, 7, 9, 21 and 63

Prime factorization of 63 – 3 × 3 × 7

Prime factor of 63 – 3 and 7

Pair factors of 63 – (1, 63), (3, 21) and (7, 9)

Sum of factors 63 – 104

Related Articles

Solved examples on factors of 63

Example 1:

Find the common divisors of 63 and 62.

Solution:

The divisors of 63 are 1, 3, 7, 9, 21, and 63

The factors of 62 are 1, 2, 31, 62.

So the common divisor of 63 and 62 is 1.

Example 2:

Find the common divisors of 63 and 64.

Solution:

Factors of 63 = 1, 3, 7, 9, 21 and 63

Factors of 64 = 1, 2, 4, 8, 16, 32 and 64

Therefore, the common divisor of 63 and 64 is 1.

Example 3:

Find the common divisors of 63 and 61.

Solution:

The divisors of 63 are 1, 3, 7, 9, 21, and 63

The factors of 61 are 1 and 61.

Therefore, the common factor of 63 and 61 is only 1 since 61 is a prime number.

Practice questions on factors of 63

What are the common factors of 63 and 65? What is the second highest factor of 63? What is the difference between the highest factor and the smallest factor of 63? What is the greatest common divisor of 63 and 70?

Learn more about factors and prime factors here with us in BYJU’S and also download BYJU’S – the learning app for a better experience and get video content to study and understand the concepts of math topics.

Once

3 times

infinity

out

“How many times can you subtract 7 from 21?” is a tricky question. We think there are three different answers to this question. It’s once, because once you subtract 7 from 21, you’re left with 14. So you can’t subtract 7 from 21.3 times again, because 21 divided by 7 is 3. After you’ve subtracted 7 from 21 three times, there’s nothing left to subtract from. There’s nothing that says you can’t subtract 7 from 21 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 7 from 21?” You probably know the answer to the next problem on our list. Find out if you were right here!

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!

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!

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