## Math 6 Chapter 3 Lesson 14: Finding the fractional value of a given number

## 1. Summary of theory Tóm

To find \(\frac{m}{n}\) of a given number b, we calculate \(b.\frac{m}{n}\,\,(m,n\, \in \,\mathbb {N},\,n\, \ne 0)\)

**Example 1: **Class 6C has 30 students, in which \(\frac{1}{3}\) the number of students achieving the title of excellent student, 60% are good students, the rest are average students. Calculate the number of good, good and average students of class 6C.

**Solution guide**

To calculate the number of good students in class 6C, we must find \(\frac{1}{3}\) of 30 students.

To do that, we divide 30 by 3 and then multiply the result by 1, that is, we multiply 30 by \(\frac{1}{3}\)

We have: \(30.\frac{1}{3} = 10\) (student)

Also, to calculate the number of good students, we have to find 60% of 30 students.

Thus, we have to foot 30 with 60% get:

\(30.60\% = 30.\frac{{60}}{{100}} = 18\) (student)

Average number of students is 30 – 10 – 18 = 2 (students)

**Example 2:** Find

a) \(\frac{3}{4}\) of 60

b) \(\frac{2}{7}\) of 28 000 VND

**Solution guide**

a) \(\frac{3}{4}\) of 60 is \(\frac{3}{4}.60=45\)

b) \(\frac{2}{7}\) of 28 000 dong is \(\frac{2}{7}.28 000= 8000\) dong.

## 2. Illustrated exercise

**Question 1: **Class 6B has 45 students. In which, 2/9 students like to play skipping rope, 4/15 students like to play soccer. The rest like other sports. Calculate the number of students in class 6A who like to play table tennis and volleyball.

**Solution guide**

Number of students in class 6B who like to play skipping rope is :

45 . 2/9 = 10 (student)

The number of students in class 6A who like to play soccer is:

45 . 4/15 = 12 (student)

**Verse 2: **Find

a) \(\dfrac{3}{4}\) of \(76cm\)

b) \(62,5\%\) of \(96\) tons

c) \(0.25\) of 1 hour.

**Solution guide**

a) \(\dfrac{3}{4}\) of \(76cm\) is \(\dfrac{3}{4}.76 = 57\,cm\)

b) \(62.5\%\) of \(96\) tons is \(62.5\% .96 = \dfrac{{625}}{{100}}.96 = 60\) tons

c) \(0.25\) of 1 hour is \(0.25.1 = \dfrac{1}{4}\) hours.

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Four fields yield all 1 ton of rice. The number of paddy harvested in the first three fields is equal to \(\frac{1}{4};\,0,4\) and 15% of the total rice harvested in all four plots, respectively. Calculate the volume of paddy harvested in the fourth plot.

**Verse 2:** \(\frac{2}{5}\) of number a is 480. Find 12.5% of number a.

**Question 3:** A three-digit number, the hundreds digit is 4.

### 3.2. Multiple choice exercises Bài

**Question 1: **Find a number whose \(\frac{2}{5}\)% is equal to 1.5

A. 175

B. 275

C. 375

D. 475

**Verse 2: **\(\frac{2}{7}\) of 35 is:

A. 5

B. 10

C. 70

D. 15

**Question 3: **Compare 36% of 50 and 50% of 36

A. 36% of 50 > 50% of 36

B. 36% of 50 < 50% of 36

C. 36% of 50 = 50% of 36

D. Not comparable

**Question 4: **\(\frac{4}{5}\) of 60cm is:

A. 12cm

B. 15cm

C. 48cm

D. 52cm

**Question 5: **Khanh has 45 candies. Khanh gave Linh \(\frac{2}{3}\) that candy. How many candies did Khanh give Linh?

A. 30 candies

B. 36 candies

C. 40 pieces of candy

D. 18 candies

## 4. Conclusion

Through this lesson, you should understand the following main topics:

- Know how to find the fractional value of a given number
- Apply lessons learned to solve related problems.

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