2.1 Dividing Fractions

​Dividing Fractions
Tutorial

​Objective
In this lesson, you will interpret and find quotients of fractions in real-world situations.

​How to Divide Fractions
Division can be thought of as repeated subtraction. When you divide one quantity by another, you're finding the number of times you can subtract the second quantity from the first. Let's look at an example. Suppose you need to divide a 10-meter ribbon into 5 equal pieces. As you can see in the picture, each piece would be 2 meters long, because 10 ÷ 5 = 2. The formula relating the quantities in division is dividend = divisor × quotient. In this division problem, 10 is the dividend, 5 is the divisor, and 2 is the quotient. When you divide one fraction by another, you are finding the number of times that you can subtract the divisor from the dividend. In the rest of the lesson, we'll look at how to divide fractions.

Cách chia hai phân số cho nhau 

Chúng ta có thể coi phép chia là phép trừ lặp đi lặp lại.  Khi chia một đại lượng cho một đại lượng khác, bạn đang tìm số lần mà bạn lấy đại lượng đầu trừ đi đại lượng thứ hai. 

Hãy xem một ví dụ.  Giả sử bạn cần chia một dải ruy băng dài 10 mét thành 5 mảnh bằng nhau. Như bạn có thể thấy trong hình trên, mỗi mảnh sẽ dài 2 mét, vì 10 ÷ 5 = 2. 

Công thức liên quan đến các đại lượng của phép chia là số bị chia = số chia × thương.  Trong bài toán về phép chia này, 10 là số bị chia, 5 là số chia và 2 là thương. 

Khi bạn chia một phân số cho một phân số khác, bạn đang tìm số lần mà bạn có thể lấy số bị chia trừ đi số chia. Trong phần còn lại của bài này, chúng ta sẽ tìm hiểu về cách chia hai phân số cho nhau.

​So if Ron divides his -pound brownie into -pound pieces, he ends up with 4 pieces. You can use visual models to divide fractions in other problems, just as we did here. 

Multiple Choice

Sean has 4 cookies. He wants to divide the cookies among his friends so that each friend gets $$\frac{2}{3}$$ of a cookie. How many friends can he give $$\frac{2}{3}$$ of a cookie? 

• 12

• 8

• 6

• 4

Raul and his friends, each of whom weighs 120 of a ton, are standing on a truck scale. The total weight shown by the scale is  34 of a ton. The same truck scale is also used to weigh various other objects and animals. Raul can use his understanding of division with fractions to find the weights and numbers of items on the scale.

This table shows the weights of various groups of people, animals, and objects. In some cases, the number of items on the scale is missing and in others, the weight of each item in the group is missing. Throughout this activity, you will use the information in the table to calculate the missing values.

​

Activity

Open Ended

How can you find the total number of people on the scale when Raul and his friends are weighed?

Multiple Choice

Weight of one person in tons  $$=\frac{1}{20}$$ .
Total weight in tons $$=\frac{3}{4}$$ . How many people were weighed on the scale?

• 15 people

• 1 person
• 10 people
• 5 people

Multiple Choice

Weight of baby elephants in tons  $$=\frac{3}{4}$$ .
Weight of one baby elephant in tons $$=\frac{3}{8}$$ . How many people were weighed on the scale?

• 3 people
• 4 people
• 1 person
• 2 people

Open Ended

Which group weighed the most per item on the scale? How much did it weigh?

Drag and Drop

Which group weighed the least per item on the scale? How much did it weigh?

Answer: The lightest items weighed were the ​

Placeholder

, each of which weighed ​

Placeholder

Drag these tiles and drop them in the correct blank above

1/32

1/24

desks

goats

cars

7/8

Labelling

Part F: Now that you’ve calculated all the missing values, complete the table.

Drag labels to their correct position on the image

1/32

5

15

8

1/8

2

4

12

3/2

7/16

Open Ended

Self-Evaluation

How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Match

Match each fraction division problem to its result. Drag the items on the left to the correct location on the right.

42

20

• $$\frac{9}{40}$$

• 42

• $$1\frac{13}{20}$$

• 20

​Congratulations!
You have completed the tutorial Dividing Fractions.