# Solutions and Explanations to Maths Problems - Grade 4 Math

Solutions and detailed explanations to Grade 4 math problems are presented.

## Problems and their Solutions

1. The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 17,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
a) Which of these countries has the smallest area?
b) Which of these countries has the largest area?
c) What is the difference between the areas of Russia and China?
d) Find the total area of all countries listed above?
e) Order these countries from the largest to the smallest areas?
Solution
a) The smallest area is 242,400 kilometers squared and it is that of the UK.
b) The largest area is 17,098,242 kilometers squared and corresponds to Russia.
c) The difference between the areas of Russia and China is given by
17,098,242 - 9,598,094 = 7,500,148 kilometers squared
d) The total area of the countries listed above is given by
9,629,091 + 17,098,242 + 9,598,094 + 9,984,670 + 242,400 + 3,287,263 = 49,839,760 kilometers squared
e) We first order the areas from the largest to the smallest.
17,098,242 | 9,984,670 | 9,629,091 | 9,598,094 | 3,287,263 | 242,400
Which correspond to the following countries
Russia, Canada, USA, China, India, UK

2. Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
Solution
The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles

3. The rectangle on the left and the square on the right have the same perimeter. What is the length of one side of the square?

.

Solution
The perimeter P of the rectangle is equal to
P = 15 + 25 + 15 + 25 = 80
The perimeter of the square is equal to the perimeter of the rectangle and is then equal to 80. The square has 4 sides of equal lengths. Since
80 = 20 + 20 + 20 + 20
then the length of a side is equal to 20

4. There are 123 boxes of sweets in a store. There are 25 sweets in each box. How many sweets are in the store?
Solution
To find how many sweets, we multiply 123 by 25
123 × 25 = 3075 sweets

5. There are 365 days in one year, and 100 years in one century. How many days are in one century?
Solution
In 100 years, which is one century, there
365 × 100 = 36,500 days

6. Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
Solution
Pages read in the first book in one week which is 7 days with 25 pages everyday.
25 × 7 = 175 pages
Pages read in the second book in 12 days with 23 pages everyday.
23 × 12 = 276 pages
175 + 276 = 451 pages

7. 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
Solution
To find the number of vans, we divide 123 by 8.
123 ÷ 8 = 15 and remainder = 3
So 15 vans are needed to transport 15 × 8 = 120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.

8. John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at$4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping? Solution Money spent on drinks 5 × 4 =$20
Money spent on sandwiches
8 × 6 = $48 Total money spent 20 + 48 =$68
Money left after shopping
100 - 68 = $32 9. A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? Solution To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4. 5500 ÷ 4 = 1375 toys 10. Tom, Julia, Mike and Fran have 175 cards to use in a certain game. They decided to share them equally. How many cards should each one take and how many cards are left? Solution To know how many cards each should take, divide 175 by 4 (Tom, Julia, Mike and Fran). 175 ÷ 4 = 43 with remainder = 3 Each one should take 43 cards and 3 are left. 11. The shaded shape is made of 5 congruent squares. The side of one square is 4 cm. Find the total area of the shaded shape. Solution The area of one square is equal to 4 × 4 = 16 centimeters squared The whole shape has 5 squares. The total area is 16 + 16 + 16 + 16 + 16 = 80 centimeters squared or 16 × 5 = 80 centimeters squared 12. Sam, Carla and Sarah spent on afternoon collecting sea shells. Sam collected 11. If we add the number of sea shells collected by Sam and Carla, the total would be 24. If we add the number of sea shells collected by Carla and Sarah, the total would be 25 shells. How many shells did each one collect? 13. Mr Joshua runs 6 kilometers everyday from Monday to Friday. He also runs 12 kilometers a day on Saturday and Sunday. How many kilometers does Joshua run in a week? 14. Tom and Bob are brothers and they each had the same amount of money which they put together to buy a toy. The cost of the toy was$22. If the cashier gave them a change of 6$, how much money did each have? 15. John has 5 boxes of sweets. One group of boxes has 5 sweets in each box. The second group of boxes has 4 sweets in each box. John has a total of 22 sweets. How many boxes of each type John has?(Hint: use table) 16. There is a total of 16 chickens and rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 50. How many chickens and how many rabbits are there?(Hint:use a table) 17. There are 4 more chickens than rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 44. How many chickens and how many rabbits are there?(Hint:use a table) ## Answers to the Above Problems 1. UK 2. Russia 3. 7,500,148 4. 49,839,760 5. Russia, Canada, USA, China, India, Uk. 1. 432 miles 2. 20 3. 3075 sweets 4. 36,500 days in one century 5. 451 pages 6. 16 vans 7.$32
8. 1375 toys per day
9. 43 each and 3 left
10. 80 cm squared
11. Sam: 11, Carla: 13 and Sarah: 12
12. 54 kilometers
13. \$14
14. 2 boxes with 5 seets each and 3 boxes with 4 seets each
15. 7 chickens and 9 rabbits
16. 10 chickens and 6 rabbits