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Kids Math

Division Basics

What is division?

Division is breaking a number up into an equal number of parts.

Example:

20 divided by 4 = ?

If you take 20 things and put them into four equal sized groups, there will be 5 things in each group. The answer is 5.



20 divided by 4 = 5.

Signs for Division

There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction.

Example signs for "a divided by b":

a ÷ b
a/b
a
b

Dividend, Divisor, and Quotient

Each part of a division equation has a name. The three main names are the dividend, the divisor, and the quotient. Dividend ÷ Divisor = Quotient

Example:

In the problem 20 ÷ 4 = 5

Dividend = 20
Divisor = 4
Quotient = 5

Special Cases

There are three special cases to consider when dividing.

1) Dividing by 1: When dividing something by 1, the answer is the original number. In other words, if the divisor is 1 then the quotient equals the dividend.

Examples:

20 ÷ 1 = 20
14.7 ÷ 1 = 14.7

2) Dividing by 0: You cannot divide a number by 0. The answer to this question is undefined.

3) Dividend equals Divisor: If the dividend and the divisor are the same number (and not 0), then the answer is always 1.

Examples:

20 ÷ 20 = 1
14.7 ÷ 14.7 = 1

Remainder

If the answer to a division problem is not a whole number, the "leftovers" are called the remainder.

For example, if you were to try and divide 20 by 3 you would discover that 3 does not divide evenly into 20. The closest numbers to 20 that 3 can divide into are 18 and 21. You pick the closest number that 3 divides into that is smaller than 20. That is 18.

18 divided by 3 = 6, but there are still some leftovers. 20 -18 = 2. There are 2 remaining.

We write the remainder after an "r" in the answer.

20 ÷ 3 = 6 r 2

Examples:

12 ÷ 5 = 2 r 2
23 ÷ 4 = 5 r 3
18 ÷ 7 = 2 r 4

Division is the Opposite of Multiplication

Another way to think of division is as the opposite of multiplication. Taking the first example on this page:

20 ÷ 4 = 5

You can do the reverse, replacing the = with a x sign and the ÷ with an equal sign:

5 x 4 = 20

Examples:

12 ÷ 4 = 3
3 x 4 = 12

21 ÷ 3 = 7
7 x 3 = 21

Using multiplication is a great way to check your division work and get better scores on your math tests!

Advanced Kids Math Subjects

Multiplication
Intro to Multiplication
Long Multiplication
Multiplication Tips and Tricks

Division
Intro to Division
Long Division
Division Tips and Tricks

Fractions
Intro to Fractions
Equivalent Fractions
Simplifying and Reducing Fractions
Adding and Subtracting Fractions
Multiplying and Dividing Fractions

Decimals
Decimals Place Value
Adding and Subtracting Decimals
Multiplying and Dividing Decimals
Statistics
Mean, Median, Mode, and Range
Picture Graphs

Algebra
Order of Operations
Exponents
Ratios
Ratios, Fractions, and Percentages

Geometry
Polygons
Quadrilaterals
Triangles
Pythagorean Theorem
Circle
Perimeter
Surface Area

Misc
Basic Laws of Math
Prime Numbers
Roman Numerals
Binary Numbers


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