On the web page "Operations with negative numbers", we are going to discuss how to handle negative numbers while we are simplifying two or more numbers with negative sign.
Symbol of first and second number |
What we have to do |
-- |
Add both numbers and put "big number" sign for the answer. |
+ - (or) - + |
Subtract small number from big number and put "big number" sign for the answer. |
The above rule is applicable for simplifying any two or more integers,fractions and decimals.
This flowchart will explain you how to handle two numbers with different symbol.
Question 1 :
Simplify -5 + 3
Solution :
What we have to check?
Consider the symbol of two numbers. The symbol of first number is negative and the symbol of second number is positive.
Do we have to add or subtract?
Since the symbols of both numbers are different we have to subtract small number from large number.Here small number is 3 and large number is 5. By subtraction we will get 2.
What symbol we have to put for answer?
We have to put symbol of big number. Here the big number is 5 and we have negative symbol for this.
-5 + 3 = -2 is the answer.
We have explained this concept in the below flowchart.
Let us see the next problem on "operations with negative numbers"
Question 2 :
Simplify -15 + 13 - 27 - 43 + 77
Solution :
First we have to write the numbers which are having same symbol.Here the numbers 15,27 and 43 are having same symbol
= - 15 - 27 - 43 + 13 + 77
Let us see the next problem on "operations with negative numbers"
- x - = + + x - = - - x + = - |
Negative x Negative = Positive Positive x Negative = Negative Negative x Positive = Negative |
- / - = + + / - = - - / + = - |
Negative / Negative = Positive Positive / Negative = Negative Negative / Positive = Negative |
Let us see the next problem on "operations with negative numbers"
Question 3 :
Multiply -15 x (-13) x 2
Solution :
Whenever we want to multiply two or more numbers with different signs, first we have to multiply the signs and then we have to multiply the numbers.
(negative x negative = positive)
(positive x positive = positive)
So, the sign for the final answer is positive.
= 390
Whenever we have a negative number as exponent and we need to make it as positive,we have to flip the base that is write the reciprocal of the base and we can change the negative exponent as positive exponent.
Let us see the next problem on "operations with negative numbers"
Question 4 :
Simplify 2^(-3)
Solution :
Question 5 :
Simplify (2/7)^(-3)
Solution :
Question 6 :
Evaluate (-3) ⁵
Solution :
= (-3) x (-3) x (-3) x (-3) x (-3)
= -343
The same problem can be done in the simple way also.
Whenever we have negative number in the base and positive integer in the power, then we have to check the power whether it is odd or even. If the power is odd the answer will have negative sign. If the power is even the answer will have positive sign.
Let us see the next problem on "operations with negative numbers"
Question 7 :
Simplify -xy⁻¹/9z⁻²
Solution :
= -xy⁻¹/9z⁻²
We have negative power for y and z.So we have to write the reciprocal of y and z and we can change the negative power as positive.
= -(x/9) (1/y)¹ (1/z)²
= -x / 9 and z²
Let us see the next problem on "operations with negative numbers"
Question 8 :
Simplify (5x/3yz)⁻³
Solution :
= (5x / 3yz) ⁻ ³
We have negative power for the whole fraction.To make it as positive exponent we have to flip the fraction.
= ( 3yz / 5x) ³
= 3³y³z³/5³x³
= 27y³z³/125x³
Let us see the next problem on "operations with negative numbers"
Question 9 :
Simplify (52 x⁶/13x⁻⁷)
Solution :
= (X 52 is ⁶ / 13X ⁻ ⁷)
We have negative power for the x term which is in the denominator.To make it as positive we are going to write it in numerator.
= (52 x⁶x⁷/13)
= 4 x⁽⁶⁺⁷⁾
= 4 x¹³
After having gone through the stuff given above, we hope that the students would have understood "Operations with negative numbers".
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