Math Problems with Solutions for Grade 4

Practice Grade 4 math with word problems on fractions, addition, subtraction, multiplication, division, shapes, and number patterns. Includes step-by-step solutions and strategies like using tables; great for students, parents, and teachers.

Question 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.
Answer the following questions:
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 \[ 17,098,242 - 9,598,094 = 7,500,148 \; \text{kilometers squared} \] d) The total area of the countries listed above is given by \( 9,629,091 + 17,098,242 + 9,598,094 + 9,984,670 \) \[ + 242,400 + 3,287,263 = 49,839,760 \; \text{kilometers squared} \] 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

Question 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 \[ 1200 - 768 = 432 \; \text{miles} \]

Question 3

Sofia and Max each made a special fruit drink. Sofia used 2/6 of a bottle of orange juice. Max used 1/3 of a bottle of orange juice.

a) Who used more orange juice?

b) How much more orange juice did that person use?

Solution:

We are comparing Sofia: \(\frac{2}{6}\) of a bottle and Max: \(\frac{1}{3}\) of a bottle. Make the denominators the same to compare

Max's fraction is \(\frac{1}{3}\), but we can write \(\frac{1}{3}\) as an equivalent fraction with a denominator of 6 by multiplying numerator and denominator by 2: \[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \] a) Now both fractions are \(\frac{2}{6}\), so: They used the same amount of orange juice.

b) Since they used the same amount: \[ \frac{2}{6} - \frac{2}{6} = 0 \] No one used more. The difference is 0.

Question 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 \[ 123 × 25 = 3075 \; \text{sweets} \]

Question 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 \[ 365 \times 100 = 36,500 \; \text{days} \]

Question 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:
p> Pages read in the first book in one week which is 7 days with 25 pages everyday. \[ 25 \times 7 = 175 \; \text{pages} \] Pages read in the second book in 12 days with 23 pages everyday. \[ 23 \times 12 = 276 \; \text{pages} \] Total number of pages read \[ 175 + 276 = 451 \; \text{pages} \]

Question 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. \[ 123 \div 8 = 15 \; \text{with remainder} \; = 3 \] 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.

Question 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 \[ 5 \times 4 = \$ 20 \] Money spent on sandwiches \[ 8 \times 6 = \$48 \] Total money spent \[ 20 + 48 = \$68 \] Money left after shopping \[ 100 - 68 = \$32 \]

Question 9

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). \[ 175 \div 4 = 43 \; \text{with remainder} = 3 \] Each one should take 43 cards and 3 are left.

Question 10

Examine this pattern: 2, 6, 12, 20, 30, ... What is the 7th number in the pattern?

Solution:

Find differences between successive numbers: \[ 6 - 2 = 4 {\displaystyle \implies } 6 = 2 + 4 \] \[12 - 6 = 6 {\displaystyle \implies } 12 = 6 + 6 \] \[ 20 - 12 = 8 {\displaystyle \implies } 20 = 12 + 8 \] \[ 30 - 20 = 10 {\displaystyle \implies } 30 = 20 + 10 \] The Pattern is: Add 4, then 6, then 8, then 10, ...

Next differences: 12 and 14 \[ 30 + 12 = 42 \] \[42 + 14 = 56 \] The 7th number is 56.

Question 11

Liam ordered a large pizza cut into 8 equal slices. He ate 3 slices for lunch. Later, his sister Ava ate 2 slices.

a) What fraction of the pizza did Liam eat?

b) What fraction did Ava eat?

c) What fraction of the pizza is left?

d) If they want to split the remaining pizza equally between them, how many slices will each get?

Solution:

a) The whole pizza has 8 equal slices. Liam ate **3 slices** out of 8. So, the fraction he ate is: \[ \dfrac{3}{8} \] b) Ava ate 2 slices out of 8. So, the fraction she ate is: \[ \dfrac{2}{8} \] c) Total eaten = Liam's \(\dfrac{3}{8}\) + Ava's \(\dfrac{2}{8}\) \[ \dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8} \] So, the fraction left is: \[ 1 - \dfrac{5}{8} = \dfrac{3}{8} \] d) There are 3 slices left. If Liam and Ava share them equally, they each get: \[ \dfrac{3}{2} = 1 \dfrac{1}{2} \text{ slices} \]

Question 12

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?

perimeter, question 3.

Solution:

The perimeter P of the rectangle is equal to: \[ P_1 = 15 + 25 + 15 + 25 = 80 \] 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 and its perimeter \( P_2\) is given by: \[ P_2 = 4 \times \text{length of one side} \] \[ 80 = 4 \times 20 \] then the length of a side is equal to 20 umits

Question 13

There are 123 boxes of sweets in a store. Each box contains 25 sweets.

The store owner wants to make special gift packs using some of the sweets from the boxes. She decides to use 1 out of every 5 sweets for the gift packs. The rest of the sweets stay in the boxes.

a) How many sweets are used to make gift packs?

b) How many sweets remain in the boxes?

c) About how many boxes of sweets are needed to make the gift packs?

Solution:

a) Total number of sweets is: \[ 123 \times 25 = 3075 \; \text{sweets} \] The number of sweets used for gift packs (1 out of every 5) is: \[ \dfrac{1}{5} \times 3075 = 3075 \div 5 = 615 \; \text{sweets} \] b) Number of sweets remaining in the boxes: \[ 3075 - 615 = 2460 \; \text{sweets} \] c) Number of boxes used for gift packs:

Each box has 25 sweets, So, \[ 615 \div 25 = 24.6 \; \text{boxes} \] Since we cannot use a part of a box without opening it, we round 24.6 up to 25 and say: About 25 boxes of sweets are used to make the gift packs.

Question 14

There are 365 days in one year, and 100 years in one century. Ingnoring leap years, how many weeks are in one century?

Solution:

Total number of days in one century (ignoring leap years) is: \[ 100 \times 365 = 36,500 \text{ days} \] There are 7 days in one week, so the number of weeks in one century is: \[ 36,500 \div 7 = 5,214 \text{ weeks and } 2 \text{ days} \] There are 5,214 full weeks and 2 extra days in one century (if we ignore leap years).

Question 15

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:

One week is 7 days. Billy read the first book in one week with 25 pages everyday. The total pages of the first book: \[ 25 \times 7 = 175 \text{ pages} \] Billy read the second book in 12 days with 23 pages everyday, The total pages of the second book: \[ 23 \times 12 = 276 \text{ pages} \] Total number of pages read: \[ 175 + 276 = 451 \text{ pages} \]

Question 16

Emma is using sugar from one bag. In the morning, she used \(\frac{1}{8}\) of the bag. In the afternoon, she used half of what was left.

a) What fraction of the sugar bag did Emma use in the afternoon?

b) How much sugar did she use in total?

c) What fraction of the bag is still left?

Solution:

a) Emma used \( \frac{1}{8} \) in the morning, so the amount left after the morning is: \[ 1 - \frac{1}{8} = \frac{8}{8} - \frac{1}{8} = \frac{7}{8} \] Emma used half of what was left, and what was left was \(\frac{7}{8}\): \[ \frac{1}{2} \times \frac{7}{8} = \dfrac{1 \times 7}{2 \times 8} = \frac{7}{16} \] So in the afternoon, she used \(\frac{7}{16}\) of the bag.

a) Ema used \(\frac{1}{8}\) in the morning and \(\frac{7}{16}\) in the afternoon:

Total \( T \) used: \[ T = \frac{1}{8} + \frac{7}{16} \] We convert \( \frac{1}{8} \) to a fraction with denominator 16: \[ \frac{1}{8} = \frac{1 \times 2}{8 \times 2} = \frac{2}{16} \] Substitute and add: \[ T = \frac{2}{16} + \frac{7}{16} = \frac{9}{16} \] A total of \(\frac{9}{16}\) of the bag used used,

c) The fraction of the bag left is: \[ 1 - \frac{9}{16} = \frac{16}{16} - \frac{9}{16} = \frac{16 - 9}{16} = \frac{7}{16} \] \(\frac{7}{16}\) of the sugar bag is left.

Question 17

John had \$100 to buy drinks and sandwiches for his birthday party. He bought 5 small boxes of drinks at \$4 per box and 8 boxes of sandwiches at \$6 per box. How much money was left after the shopping?

Solution:

Money spent on drinks: \[ 5 \times 4 = \$20 \] Money spent on sandwiches: \[ 8 \times 6 = \$48 \] Total money spent: \[ 20 + 48 = \$68 \] Money left after shopping: \[ 100 - 68 = \$32 \] John had \$32 left after the shopping.

Question 18

55 workes at a factory produce 5500 toys per week. If the workers at this factory work 4 days a week, and they produce the same number of toys each day, how many toys are produced each day by each worker?

Solution:

To find the number of toys produced each day, divide the total number of toys produced in one week by the number of working days 4: \[ \dfrac{5500}{4} = 1375 \text{ toys} \] 1375 toys are produced each day by 55 workers, hence each worker produces: \[ 1375 \div 55 = 25 \] Each worker produces 25 toys per day.

Question 19

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 find how many cards each person should take, divide 175 by 4 (since there are 4 people): \[ 175 \div 4 = 43 \text{ Remainder } 3 \] Each person should take: \[ 43 \text{ cards} \] There will be: \[ 3 \text{ cards left over} \] Each one should take 43 cards, and 3 cards are left.

Question 20

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.

shaded area, question 11

Solution:

The area of one square is equal to: \[ 4 × 4 = 16 \; \text{centimeters squared} \] The whole shape has 5 squares. The total area is: \[ 16 + 16 + 16 + 16 + 16 = 80 \; \text{centimeters squared} \] or \[ 16 × 5 = 80 \; \text{centimeters squared} \]

Question 21

Sam, Carla and Sarah spent an 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?

Solution:

Sam = 11 shells

Sam + Carla = 24 shells

So to find how many Carla collected: \[ \text{Carla} = 24 - \text{Sam} = 24 - 11 = 13 \] Carla + Sarah = 25 shells

We just found that Carla collected 13, so: \[ \text{Sarah} = 25 - \text{Carla} = 25 - 13 = 12 \] Sam collected: 11 shells , Carla collected: 13 shells and Sarah collected: 12 shells.

Question 22

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?

Solution:

From Monday to Friday, there are 5 days. He runs 6 kilometers each day: \[ 6 \times 5 = 30 \text{ kilometers} \] On Saturday and Sunday, there are 2 days. He runs 12 kilometers each day: \[ 12 \times 2 = 24 \text{ kilometers} \] Total kilometers run in a week: \[ 30 + 24 = 54 \text{ kilometers} \] Mr. Joshua runs 54 kilometers in a week.

Question 23

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?

Solution:

First, find the total amount of money they had together. They bought a toy for \$22 and got \$6 back: \[ 22 + 6 = 28 \] So, together they had \$28. Since they had the same amount, divide 28 by 2: \[ 28 \div 2 = 14 \] Each of them had \$14.

Question 24

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?

Solution:

Two methods are presented to solve this problem. If you have not done any algebra, the table method is good for you. If you know algebra and equation solving, then both methods are good for you.

Table method

We can create a table to try different numbers of boxes with 5 sweets and see how many boxes with 4 sweets are needed to reach a total of 22 sweets.

Note the the total number of boxes is 5, hence once "Number of boxes with 5 sweets" is selected in the first column on the left, the "Number of boxes with 4 sweets" is equal to 5 - "Number of boxes with 5 sweets".

Number of boxes with 5 sweets Number of boxes with 4 sweets Total sweets
0 5 - 0 = 5 \( 0 \times 5 + 5 \times 4 = 20 \)
1 5 - 1 = 4 \(1 \times 5 + 4 \times 4 = 21 \)
2 5 - 2 = 3 \( \color{red}{2 \times 5 + 3 \times 4 = 22} \)
3 5 - 3 = 2 \(3 \times 5 + 2 \times 4 = 23 \)
4 5 - 4 = 1 \(4 \times 5 + 1 \times 4 = 24 \)
5 5 - 5 = 0 \(5 \times 5 + 0 \times 4 = 25\)
From the table, we can see that when John has 2 boxes with 5 sweets and 3 boxes with 4 sweets , the total number of sweets is exactly 22.

John has 2 boxes with 5 sweets and 3 boxes with 4 sweets.

Algebra method

Let's say John has \( x \) boxes with 5 sweets each. Then he must have \( 5 - x \) boxes with 4 sweets each (because he has 5 boxes in total). Now we find how many sweets he has: \[ \text{Sweets from boxes with 5 sweets} = 5x \] \[ \text{Sweets from boxes with 4 sweets} = 4(5 - x) \] Total sweets: \[ 5x + 4(5 - x) = 22 \] Now solve the equation: \[ 5x + 20 - 4x = 22 \] \[ x + 20 = 22 \] \[ x = 2 \] So, John has: \[ x = 2 \quad \text{boxes with 5 sweets each} \] \[ 5 - x = 3 \quad \text{boxes with 4 sweets each} \] John has 2 boxes with 5 sweets and 3 boxes with 4 sweets. ?

Question 25

There is a total of 16 chickens and rabbits on 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)

Solution:

Let the number of chickens be denoted by \( C \) and the number of rabbits by \( R \).

The total number of animals is 16: \[ C + R = 16 \] The chickens have 2 legs each and the rabbits have 4 legs each.

The total number of legs is 50: \[ 2C + 4R = 50 \] Below is the table with different possibilities for \( C \) (chickens) and their corresponding number of legs:

Note that: \( C + R = 16 \) \[ \begin{array}{|c|c|c|} \hline \text{Chickens (C)} & \text{Rabbits (R)} & \text{Total Legs} = 2 C + 4 R\\ \hline 0 & 16 & 2 \times 0 + 4 \times 16 = 64 \\ 1 & 15 & 2 \times 1 + 4 \times 15 = 2 + 60 = 62 \\ 2 & 14 & 2 \times 2 + 4 \times 14 = 4 + 56 = 60 \\ 3 & 13 & 2 \times 3 + 4 \times 13 = 6 + 52 = 58 \\ 4 & 12 & 2 \times 4 + 4 \times 12 = 8 + 48 = 56 \\ 5 & 11 & 2 \times 5 + 4 \times 11 = 10 + 44 = 54 \\ 6 & 10 & 2 \times 6 + 4 \times 10 = 12 + 40 = 52 \\ 7 & 9 & \color{red}{ 2 \times 7 + 4 \times 9 = 14 + 36 = 50 \quad \text{(Correct Answer)}}\\ \hline \end{array} \]

From the table, when there are 7 chickens and 9 rabbits, the total number of legs is exactly 50.

Thus, there are 7 chickens and 9 rabbits in the farm.

Question 26

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?

Solution:

Two methods are presented to solve this problem. If you have not done any algebra, the table method is good for you. If you know algebra and equation solving, then both methods are good for you.

Algebra method

Let the number of rabbits be denoted by \( R \), and the number of chickens be denoted by \( C \).

There are 4 more chickens than rabbits, so: \[ C = R + 4 \]

Chickens have 2 legs each, and rabbits have 4 legs each.

The total number of legs is 44, so: \[ 2C + 4R = 44 \] We can substitute \( C = R + 4 \) into the second equation: \[ 2(R + 4) + 4R = 44 \] Simplifying: \[ 2R + 8 + 4R = 44 \] \[ 6R + 8 = 44 \] \[ 6R = 44 - 8 \] \[ 6R = 36 \] \[ R = 6 \] Now substitute \( R = 6 \) into \( C = R + 4 \): \[ C = 6 + 4 = 10 \] So, there are 10 chickens and 6 rabbits.

Table method

In this table we start by the number of rabbits, calculate the number of chickens and the total number of legs. We stop calculations when the condition of the total number of legs (44) is satisfied. \[ \begin{array}{|c|c|c|} \hline \text{Rabbits (R)} & \text{Chickens (C = R + 4)} & \text{Total Legs} = 2C + 4 R \\ \hline 0 & 4 & 2 \times 4 + 4 \times 0 = 8 \\ 1 & 5 & 2 \times 5 + 4 \times 1 = 10 + 4 = 14 \\ 2 & 6 & 2 \times 6 + 4 \times 2 = 12 + 8 = 20 \\ 3 & 7 & 2 \times 7 + 4 \times 3 = 14 + 12 = 26 \\ 4 & 8 & 2 \times 8 + 4 \times 4 = 16 + 16 = 32 \\ 5 & 9 & 2 \times 9 + 4 \times 5 = 18 + 20 = 38 \\ 6 & 10 & \color{red}{2 \times 10 + 4 \times 6 = 20 + 24 = 44 \quad \text{(Correct Answer)}} \\ \hline \end{array} \] Thus there are 10 chickens and 6 rabbits.