Multiplication And Division

Multiplication is a mathematical operation that combines groups of numbers to find a total. It's like repeated addition.

For example: \(3\times4\)

\(3\times4\) means adding \(3\) four times: \(3+3+3+3=12\).

Division, on the other hand, is the opposite of multiplication. It's splitting a total into equal parts.

For example: \(12 \div 3\)

\(12 \div 3\) means dividing \(12\) into \(3\) equal groups: \(12 \div 3=4\).

Word Problems

Word problems involving multiplication often relate to situations where items are combined or repeated, like buying multiple items at a store or calculating the total number of objects in several groups.

Division word problems typically involve scenarios where a total quantity is shared equally among a certain number of groups or people, such as distributing candies equally among friends or dividing a total amount of money between siblings.

In both cases, understanding the context of the problem and translating it into mathematical operations is crucial for finding the solution.

In this article, the lesson objectives are: 

1. Word problems involving multiplication and/or division
2. Word problems involving multiplication and/or division with remainder 

1. Word Problems Involving Multiplication and/or Division

Question 1: 

A shop owner bought 16 boxes of markers. In each box, there were 144 markers. She repacked the markers equally into 6 containers. How many markers were there in each container?

Solution: 

Total number of markers Mrs Lee bought

\(\begin{align}​​ &= 16 \times 144\\ &= 2304 \end{align}\)

Number of markers in each container

\(\begin{align}​​ &= 2304 \div 6\\ &= 384 \end{align}\)

There were 384 markers in each container. 

Answer:

384 markers

Question 2: 

Jonathan sold 7 laptops in a week for 4 weeks. Given that each laptop was sold for $988, find the total amount of money Jonathan received from the sale of all the laptops over the 4 weeks.

Solution: 

Total number of laptops sold in 4 weeks

\(\begin{align}​​ &= 4 \times 7\\ &= 28 \end{align}\)

Total amount of money received 

\(\begin{align}​​ &= 28 \times $988\\ &= $27\;664 \end{align}\)

The total amount Jonathan received was $27 664. 

Answer:

$27 664

Question 3: 

Mr Lee sold 15 television sets each month from January to May. Each television set was sold for $375. How much money did he receive from selling all the television sets from January to May?

Solution: 

Total number of television sets sold from January to May

\(\begin{align}​​ &= 5 \times 15\\ &= 75 \end{align}\)

Total amount of money received

\(\begin{align}​​ &= 75 \times $375\\ &= $28\;125 \end{align}\)

He received $28 125 from selling all the television sets from January to May. 

Answer:

$28 125

Question 4: 

7856 people visited a food fair over the weekend. Half of the people visited the food fair on Saturday. Given that there were thrice as many adults as children at the food fair on Sunday, how many children were there on Sunday?

Solution: 

Number of people who visited the food fair on Sunday

\(\begin{align}​​ &= 7856 \div 2\\ &= 3928 \end{align}\)

\(​\begin{align} 4 \text{ units} &= 3928\\ 1 \text{ unit} &= 3928 \div 4\\ &= 982 \end{align}\)

982 children visited the food fair on Sunday. 

Answer:

982 children 

Question 5: 

In a shopping centre, there are 6312 people. Half of them are females and half of the males are boys. How many boys are there?

Solution: 

Since half of the people are females, the remaining half of the people are males. 

Number of males

\(\begin{align}​​ &= 6312 \div 2\\ &= 3156 \end{align}\)

Number of boys

\(\begin{align}​​ &= 3156 \div 2\\ &= 1578 \end{align}\)

There are 1578 boys. 

Answer:

1578 boys

Question 6: 

Sam has 5 times as much money as Roy. They have $1500 altogether. How much more money does Sam have than Roy? 

Solution:

\(​\begin{align} 6 \text{ units} &= $1500\\ 1 \text{ unit} &= $1500 \div 6\\ &= $250 \end{align}\)

Difference between the amount of money Sam and Roy have

\(​​\begin{align} &= 5 \text{ units} - 1 \text{ unit}\\ &= 4 \text{ units}\\ &= 4 \times $250\\ &= $1000 \end{align}\)

Sam has $1000 more than Roy. 

Answer:

$1000

2. Word Problems Involving Multiplication and/or Division With Remainder

Question 1: 

Oranges are packed and sold in boxes of 12 only. Each box of oranges costs $8. Ahmad has $150. What is the greatest number of oranges he can buy?

Solution: 

Number of boxes he can buy

\(\begin{align}​​ &= $150 \div $8\\ &= 18 \text{ R } $6 \end{align}\)

Ahmad can buy 18 boxes of 12 oranges and he will have $6 left. 

Greatest number of oranges he can buy

\(\begin{align}​​ &= 18 \times 12\\ &= 216 \end{align}\)

The greatest number of oranges he can buy is 216.

Answer:

216 oranges

Question 2: 

Farmer Tan harvested 3867 oranges and packed them into bags of 8. Given that he sold each bag for $5, how much will he receive from the sale of all the bags of oranges?

Solution: 

Number of bags

\(\begin{align}​​ &= 3867 \div 8\\ &= 483 \text{ R } 3 \text{ oranges} \end{align}\)

Farmer Tan packed 483 bags of oranges and had 3 oranges left. 

Total amount he received

\(\begin{align}​​ &= 483 \times $5\\ &= $2415 \end{align}\)

He received $2415 from the sale of all the bags of oranges. 

Answer:

$2415

Question 3: 

Jason collected 2895 baseball cards. He wants to pack them into small plastic holders. Given that each plastic holder can hold a maximum of 8 cards, what is the minimum number of plastic holders he needs to pack all his cards? 

Solution: 

Number of groups of 8 cards

\(\begin{align}​​ &= 2895 \div 8\\ &= 361 \text{ R } 7 \text{ cards} \end{align}\)

There are 361 groups of 8 cards and 7 remaining cards. 

Since each plastic holder can hold a maximum of 8 cards, Jason needs 361 plastic holders to hold the 361 groups of 8 cards. 

Jason will also need another plastic holder to hold the 7 remaining cards. 

Minimum number of plastic holders Jason needs to pack all his cards

\(\begin{align}​​ &= 361 +1\\ &= 362 \end{align}\)

The minimum number of plastic holders Jason needs is 362. 

Answer:

362 plastic holders

Question 4: 

There were 1192 passengers who boarded the cable car to Sentosa. Each cabin could carry at most 6 passengers. What was the least number of cabins needed to carry all the passengers?

Solution: 

Number of groups of 6 passengers

\(= 1192 \div 6\\ = 198 \small \text{ R 4 passengers} \)

There were 198 groups of 6 passengers and another 4 passengers remaining.

Since each cabin could carry at most 6 passengers, we will need 198 cabins to carry the  198 groups of 6 passengers. 

Another cabin will be needed to carry the 4 remaining passengers.

Least number of cabins needed to carry all the passengers
\(= 198 +1\\ = 199\)

The least number of cabins needed to carry all the passengers is 199. 

Answer:

199 cabins