The use of integers is used to express our daytoday situations in Mathematical terms.
Examples:
(i) If profit are represented by positive integer then losses by negative integers.
(ii) If heights above sea level by positive integers then depths below sea level by negative integers.
(iii) If rise in price is represented by positive integers, then fall in price by negative integers and so on.
Thus, if +256 represent a profit of $ 256; then a loss of $ 256 is represented by 256.
Similarly, if a depth of 37 below sea level is represented by 37; then +37 represents a height of 37 above sea level and so on.
Use of integers as directed
numbers:
When numbers represent direction, then numbers are called directed numbers.
For example:
(i) If moving 10 m towards North is represented by +10;
10 represents moving 10 m towards South, opposite direction of North.
If a positive (+ve) integer indicates a particular direction; then the negative (ve) integer indicates the opposite direction. Conversely, if a negative (ve) integer indicates any particular direction; then the positive (+ve) integer indicates the opposite direction.
For example:
If +5 represents 5 m towards East; then 4 represents 4 m towards its opposite direction i.e., towards West.
Similarly, if +9 represents 9 m due South, 6 represents 6 m due North. Again if 4 represents 4 km due East; +2 represents 2 km due West
(ii) If 12 m above the earth’s surface is represented by +12; then 18 m below the earth’s surface is represented by 18 and so on.
(iii) If +23 represents a profit of $23; then 19 represents a loss of $19.
(iv) If 63 indicate giving of $63; then taking of $91 is denoted by +91.
(v) If the rise in temperature by 63° C is denoted by +63; then 45 indicates the fall in temperature by 45° C
Write the opposite of the following expressions:
(i) An expenditure of $15.
(ii) A profit of $115.
(iii) A loss of $55.
(iv) Descending 15 m.
(v) Increase in weight by 17 kg.
Solution:
(i) Expenditure of $15 = Income of 15 dollars.
(ii) Profit of $115 = Loss of 115 dollars.
(iii) Loss of $55 = Profit of 55 dollars.
(iv) Descending 15 m or 15 m downwards movement = 15 m upward movement.
(v) Increase in weight by 17 kgs. = Decrease in weight by 17 kgs.
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