DIVISION FACTS
About "Division facts"
Division facts :
We have four binary operations in math. They are
Addition, Subtraction, Multiplication and Division
When we use each of the above binary operations, the result may be different.
It is because of the work done by the binary operation that we have between the two numbers. Knowing the work done by the binary operation is called the fact of that operation.
Here, we are going to know the work done by the binary operation "Division".
Division facts - Examples
Let us consider the following example to understand the important fact of division.
Example :
A person wants to share the money $240 equally to his four sons. How much money will each son receive ?
To get answer for the above question, we will be dividing $240 by 4.
That is,
240 ÷ 4 or 240/4
To know the result of the above division, we are going to use multiplication.
That is,
The result of the above division is equal to, "How many times of the denominator is equal to the numerator ?"
More clearly, how many times 4 goes into 240 ?
60 times of the denominator 4 is equal the numerator 240.
Then, 240 ÷ 4 = 240/4 = 60
Hence, each son will receive $60.
Other facts of division :
(i) Commutative property (does not hold)
(ii) Associative property (does not hold)
(iii) Division by zero (not defined)
(iv) Some other properties of division
Commutative property
Observe the following examples :
15 ÷ 5 = 15/5 = 3
5 ÷ 15 = 5/15 = 1/3
Therefore, 15 ÷ 5 ≠ 5 ÷ 15
From the above example, we observe that division is not commutative.
Hence, commutative property does not hold for division.
Associative property
Observe the following examples :
12 ÷ (6 ÷ 2) = 12 ÷ 3 = 4
(12 ÷ 6) ÷ 2 = 2 ÷ 2 = 1
Therefore, 12 ÷ (6 ÷ 2) ≠ (12 ÷ 6) ÷ 2
From the above example, we observe that division is not associative.
Hence, associative property does not hold for division.
Division by zero
Division of any number (except 0) by zero is meaningless.
Because division by zero is not defined.
That is,
2/0 = Undefined
8/0 = Undefined
Some other properties of division
We know that division is the inverse operation of multiplication.
Positive number / Positive number = Positive number
Negative number / Negative number = Positive number
Negative number / Positive number = Negative number
Positive number / Negative number = Negative number
For example,
250 / 50 = 5
(-144) / (-12) = 12
(-120) / 20 = -6
100 / (-25) = -4
Related topics
- Generating equivalent numerical expressions
- Use repeated multiplication
- Division facts
- Exponents
- Using exponents
- Finding the value of a power
- Finding the value of each power
- Find the missing exponent
- Find the missing base
- Finding the factors of a number
- Finding the prime factorization of a number
- using ladder diagram for prime factorization
- Order of operations
- Exploring the order of operations
- Evaluating the numerical expression
- Using exponents with parentheses
After having gone through the stuff given above, we hope that the students would have understood "Division facts".
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WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
