Informative line

Application Of Whole Numbers In Real Life

Mathematical Modeling on Addition

  • We all frequently perform calculations in our daily life.
  • For example, we calculate our daily expenditure, find the increase or decrease in temperature, calculate distance traveled by us etc.
  • So, in order to solve real life problems, we need to identify what kind of operations are to be performed and where.
  • Using some keywords we can figure out that addition has to be performed in the given word problem.
  • Few of them are given below.

If a problem asks for any of the following:

(i) Total

(ii) In all

(iii) How many

and some specific words are used to show an increase in the quantity, like

Extra

More

Added

Then there is a chance for addition in that problem.

For example:

  1. Arthus has 9 candies. He gets 6 more from Clark. How many candies does Arthus have in all?

In the given example, 'more' word represents an increase in the number of candies and 'in all' helps to identify that addition is to be done.

       2.There are 3 marbles. 7 more marbles are being added. How many are there in total?

In the given example, 'more' word represents an increase in the number of marbles and how many in total helps to identify that addition has to be done.

Illustration Questions

Brian has 112 peanuts. James gives Brian 78 more. How many peanuts does Brian have in all?  

A 190

B 112

C 78

D 34

×

Number of peanuts Brian has = 112

Number of peanuts given by James = 78

In order to calculate 'in all' or total peanuts that Brian has, we need to add them.

Thus, total peanuts that Brian has = 112 + 78 = 190 peanuts 

Hence, option (A) is correct.

Brian has 112 peanuts. James gives Brian 78 more. How many peanuts does Brian have in all?  

A

190

.

B

112

C

78

D

34

Option A is Correct

Mathematical Modeling on Subtraction

  • To figure out that subtraction is to be done in the given word problem, some identifying keywords can be used. 
  • Few of them are given below.

If a problem asks for any of the following:

(i) How many are left

(ii) How many does he/she end with

(iii) How many more

and some specific words are used to show a decrease in the quantity like

Takes 

Removes 

Gives

Shares

Then there is a chance for subtraction in that problem.

For example:

  1. There are 97 bananas in a box. Karen takes 43 bananas. How many are left?

In the given example, 'takes' word represents a decrease in the number of bananas and 'How many are left' helps to identify that the given problem is of subtraction.

       2. Kelly has 57 tickets. She gives 15 to Nicole. How many tickets does Kelly end with?

In the given example, 'gives' word represents decrease in the number of tickets and 'How many does Kelly end with' helps to identify that the given problem is of subtraction.

  • If a problem asks for comparison between two values, then there is a chance for subtraction in that problem. 

For example:

  • Brenda weighs 88 pounds. Doris weighs 63 pounds. By how much does Brenda weigh more than Doris?

In the given example, 'than' word represents comparison between two values, so there is a chance for subtraction in this problem.

Illustration Questions

Maria removes 52 cookies from a box. There were originally 150 cookies in the box. How many cookies are left in the box?

A 202

B 150

C 98

D 52

×

Total cookies in a box = 150

Number of cookies removed by Maria from the box = 52

In order to calculate the number of cookies left, we have to subtract number of cookies removed by Maria from total number of cookies in the box.

Cookies left = 150 - 52 = 98

\(\therefore\) 98 cookies are left in the box.

Hence, option (C) is correct.

Maria removes 52 cookies from a box. There were originally 150 cookies in the box. How many cookies are left in the box?

A

202

.

B

150

C

98

D

52

Option C is Correct

Mathematical Modeling on Multiplication

  • To figure out that multiplication is to be done in a given word problem, a simple logic can be used. 

"If value of single unit is given and problem asks for the value of more than one unit, then multiplication is used"

For example

  • Ellen went to a garage sale to buy chairs. Cost of each chair was 15 dollars and she bought 12. How much money did Ellen spend?
  • In the given example, cost of one chair is given and we have been asked to calculate the cost of 12 chairs. 
  • To calculate the cost of 12 chairs, we will multiply the cost of one chair by 12.

Illustration Questions

Book covers cost $2 each. Cody bought 35 of them. What is the total amount of money that he spent on the book covers? 

A $37

B $33

C $35

D $70

×

Cost of one cover = $2

Number of book covers Cody bought = 35

Total money spent = 2 × 35 = 70

\(\therefore\) Cody spent $70 on the book covers.

Hence, option (D) is correct.

Book covers cost $2 each. Cody bought 35 of them. What is the total amount of money that he spent on the book covers? 

A

$37

.

B

$33

C

$35

D

$70

Option D is Correct

Mathematical Modeling on Division

  • To figure out that division is to be done in a given word problem, a simple logic can be used.

"If value of more than one unit is given and the problem asks for value of a single (each) unit, then division is to be done."

For example:

  • 88 cookies are being shared equally among 4 people. How many does each person get ?
  • In the given example, total number of cookies is given and we have to calculate each person's share.
  • To calculate number of cookies shared by each person we will divide the total number of cookies by 4. 

Illustration Questions

There are 12 students in the class. If 84 peanuts are to be divided equally among the students, how many does each student get? 

A 12

B 7

C 84

D 96

×

Total students in the class = 12

Total peanuts = 84

Number of peanuts ach student gets = 84 \(\div\) 12

= 7 peanuts

 

Hence, option (B) is correct.

There are 12 students in the class. If 84 peanuts are to be divided equally among the students, how many does each student get? 

A

12

.

B

7

C

84

D

96

Option B is Correct

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