ARITHMETIC RULES
About "Arithmetic rules"
Arithmetic rules :
Arithmetic rules is the basic topic required for primary level students.
While using arithmetic operations like addition, subtraction, multiplication and division we need to follow these arithmetic rules. Without knowing these rules we cannot evaluate arithmetic expressions correctly.
Rules followed in arithmetic operations
- Addition and subtraction rules
- Multiplication and division rules
Addition and subtraction rules
whenever we have a numerical expression like -5 + 6 -7, we may have a confusion that we need to add those numbers or subtract?
That time we have to remember the rule given below.
|
Sign of first and second number |
What do we have to do? |
|
+ + - - |
Add both numbers and put "big number" sign for the answer. |
|
+ - (or) - + |
Subtract small number from large number and put "large number" sign for the answer. |
Example 1 :
Simplify -15 + 13 - 27 - 43 + 77
Solution :
First we have to write the numbers which are having same sign.Here the numbers 15,27 and 43 are having same sign
= - 15 - 27 - 43 + 13 + 77
Multiplication and division rules
Whenever we want to multiply or divide two numbers, we must follow the rule given below.
|
+ x + = + - x - = + + x - = - - x + = - |
+ ÷ + = + - ÷ - = + + ÷ - = - - ÷ + = - |
Example 2 :
Multiply -15 x 4
Solution :
-15 x 4 = - 60
By multiplying 15 and 4 we get 60. The signs of two numbers are negative and positive.
By multiplying + and - we get negative. That's why we put negative sign for the answer.
Note:
If the numbers or variables do not have any sign in front of them, then we have to consider that there is positive sign. For example let us conside 4,
Here we don't have any sign in front of them, so we have to consider this as + 4
Likewise let us consider 5a, here the number 5 and the variable a are multiplying. Since there we don't have any sign in the middle of 5 and a we have to consider that there is multiplication.
Now let us see mixed problems based on the above concept.
Example 3 :
Simplify -15 - 4
Solution :
Since the given numbers are having same signs, we have to add them and put the greater number sign.
-15 - 4 = -19
Example 4 :
Simplify -5 + 3
Solution :
Since the given numbers are having different signs, we have to subtract them and put the greater number sign.
-5 + 3 = -2
Example 5 :
Simplify -15 ÷ 3
Solution :
-15 ÷ 3 = -5
After having gone through the stuff given above, we hope that the students would have understood "Arithmetic rules".
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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
