# Word Problems Involving Addition and Subtraction

Word problems involving addition and subtraction are discussed here step by step.

There are no magic rules to make problem solving easy, but a systematic approach can help to the problems easily.

Word problems based on addition are broadly of two types:

(a) When objects of two or more collections are put together.

For example:

Amy has 20 lemon sweets and 14 orange sweets. What is the total number of sweets Amy has?

(b) When an increase in number takes place.

For example:

Victor has 14 stamps. His friend gave him 23 stamps. How many stamps does Victor have in all?

The key words used in problems involving addition are:

sum; total; in all; all together.

Word problems based on subtraction are of several types:

(a) Partitioning : Take away, remove, given away.

(b) Reducing : Find out how much has been given away or how much remains.

(c) Comparison : More than / less than.

(d) Inverse of addition : How much more to be added. The key words to look out for in a problem sum involving subtraction are:
take away; how many more ; how many less ; how many left ; greater ; smaller.

1. The girls had 3 weeks to sell tickets for their play. In the first week, they sold 75 tickets. In the second week they sold 108 tickets and in the third week they sold 210 tickets. How may tickets did they sell in all?

Tickets sold in the first week = 75

Tickets sold in the second week = 108

Tickets sold in the third week = 210

Total number of tickets sold = 75 + 108 + 210 = 393

Answer: 393 tickets were sold in all.

2. Mr. Bose spent $450 for petrol on Wednesday. He spent$125 more than that on Thursday. How much did he spend on petrol on those two days.

This problem has to be solved in two steps.

Step 1: Money spent for petrol on Thursday

450 + 125 = $575 Step 2: Money spent for petrol on both days 450 + 575 =$1025

Examples on word problems on addition and subtraction:

1. What is the sum of 4373, 4191 and 3127?

Solution:

The numbers are arranged in columns and added.

 (i) Ones are added: 3 + 1 + 7 = 11 = 1 Ten + 1 one (ii) Tens are added: 1 + 7 + 9 + 2 = 19 tens = 1 hundred + 9 ten (iii) Hundreds are added: 1 + 3 + 1 + 1 = 6 Hundred (iv) Thousands are added: 4 + 4 + 3 = 11 Thousand

Therefore, sum =11,691

2. What is the difference of 3867 and 1298?

Solution:

The numbers are arranged in columns and subtracted:

 (i) Ones are subtracted: 7 < 8 1 is borrowed from 6 ten. So, 1 T or 10 + 7 = 17, 17 - 8 = 9 (ii) Tens are subtracted; 5 T < 9 T, So, 1 H or 10 T is borrowed from 8 H, 1 H = 10 T + 5 T = 15T 15T - 9T = 6 (iii) Hundreds are subtracted 7 H – 2 H = 5 H (iv) Thousands are subtracted 3 Th – 1 Th = 2 Th

Therefore, difference = 2569

3. Subtract 4358 from the sum of 5632 and 1324.

Solution:

Sum of 5632 and 1324

Difference of 6956 and 4358

 (i) 6 < 8, 1 T or 10 ones are borrowed 1 T or 10+ 6 =16, 16 - 8 = 8 (ii) 4 T < 5 T, 1 H or 10 T is borrowed 10 T + 4 T = 14 T, 14 T – 5 T = 9 T (iii) 8 H – 3 H = 5 H (iv) 6 Th – 4 Th = 2 Th

Therefore, 2598 is the answer.

4. Find the number, which is

(i) 1240 greater than 3267.

(ii) 1353 smaller than 5292.

Solution:

(i) The number is 1240 more than 3267

Therefore, the number = 3267 + 1240 or = 4507

(ii) The number is 1353 less than 5292

Therefore, the number

= 5292 – 1353 or

= 3939

5. The population of a town is 16732. If there are 9569 males then find the number of females in the town.

Solution:

 Population of the town Number of males Therefore, number of females =   1 6 7 3 2 =   - 9 5 6 9 =     7 1 6 3

6. In a factory there are 35,675 workers. 10,750 workers come in the first shift, 12,650 workers in the second shift and the rest come in the third shift. How many workers come in the third shift?

Solution:

Number of workers coming in the first and second shift

= 10750 + 12650 = 23400

Therefore, number of workers coming in the third shift = 35675 - 23400 = 12275

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