## Math 6 Chapter 3 Lesson 15: Find a number whose value is a fraction

## 1. Summary of theory Tóm

To find a number whose \(\frac{m}{n}\) is equal to a, we calculate \(a\,\,:\,\,\frac{m}{n}\,\,(m) ,n\, \in {\mathbb{N}^*})\).

**For example: **The An family has a flock of ducks. Know\(\frac{3}{5}\) The number of ducks in An’s family is 27. How many ducks are there in the house?

__Solution guide__

If the number of ducks in An’s house is called x, then according to the problem, we must find x such that \(\frac{3}{5}\) of x equals 27.

We have: \(x.\frac{3}{5} = 27\)

So \(x = 27:\frac{3}{5} = 27.\frac{5}{3} = 45\)

Thus, to find a number whose \(\frac{3}{5}\) is 27, we divide 27 by \(\frac{3}{5}\).

**Verse 2:** The number of water in the first tank is equal to \(\frac{3}{5}\) the number of water in the second pedestal. If 14 liters of water are transferred from the second tank to the first tank, the amount of water in the first tank is equal to \(\frac{{25}}{{23}}\) the number of books in the second tank. Calculate the number of liters of water initially in the tank.

__Solution guide__

Initially the number of liters of water in the first tank equals \(\frac{3}{{3 + 5}} = \frac{3}{8}\) total liters of water

Then the number of liters of water in the first tank is equal to \(\frac{{25}}{{25 + 23}} = \frac{{25}}{{48}}\) total number of books

14 liters of water is: \(\frac{{25}}{{48}} – \frac{3}{8} = \frac{7}{{48}}\) total liters of water

So the total number of llits of water in the two tanks is: \(14:\frac{7}{{48}} = 96\) (liters)

At first, the first tank has: \(96.\frac{3}{8} = 36\) (liters)

The second tank has: 96 – 36 = 60 (liters)

## 2. Illustrated exercise

**Question 1: **

a) Find a number whose 2/7 is equal to 14.

b) Find a number whose \( \displaystyle 3{2 \over 5}\) is equal to \( \displaystyle {{ – 2} \over 3}\)

**Solution guide**

a) The number to look up is : \(\displaystyle 14:{2 \over 7} = 14. {7 \over 2} = 49\)

b) The number to find is :

\(\eqalign{& {{ – 2} \over 3}:3{2 \over 5} = {{ – 2} \over 3}:{{3.5 + 2} \over 5} \cr & = {{ – 2} \over 3}:{{17} \over 5} = {{ – 2} \over 3}. {5 \over {17}} = {{ – 10} \over {51}} \cr} \)

**Verse 2:** A tank is full of water, after using up 350 liters of water, there is a remaining volume of water equal to 13/20 of the tank capacity. How many liters of water can this tank hold?

**Solution guide**

350 liters of water for \(1-\dfrac{13}{20}=\dfrac {7}{20}\)( tank capacity )

This tank can hold the number of liters of water: \(350:\dfrac {7}{20}=350.\dfrac {20}{7}=1000\) ( liters of water)

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Grade 6 of the school has 4 classes. The number of students in class 6A is equal to \(\frac{9}{{25}}\) the total number of students in the remaining three grades. The number of students in class 6B is equal to \(\frac{{21}}{{64}}\) the total number of students in the remaining three grades. The number of students in class 6C is equal to \(\frac{4}{{13}}\) the total number of students in the remaining three grades. The number of students in class 6D is 43 students. What is the total number of 6th grade students in that school and the number of students in each class?

**Verse 2:** A man brought a basket of oranges to sell. After selling \(\frac{4}{7}\) the number of oranges and 2, the number of oranges left is 46. Calculate the number of oranges he brought to sell.

**Question 3: **Two teams of workers repair two road sections with a total length of 200m. We know that \(\frac{1}{6}\) the first team’s track is fixed by \(\frac{1}{4}\) the second team’s track. Calculate the length of the track each team has corrected.

### 3.2. Multiple choice exercises Bài

**Question 1: **There are 50 oranges in the basket. The number of apples is equal to \(\frac{9}{{10}}\) the number of oranges and the number of oranges is equal to \(\frac{10}{{11}}\) the number of mangoes. How many oranges, apples and mangoes are there in all?

A. 150 balls

B. 100 fruits

C. 145 fruits

D. 130 fruit

**Verse 2: **A store imported 42kg of flour. The store sold out \(\frac{5}{7}\) that flour. How many kilograms of flour are left in the store?

A. 12 kg

B. 18 kg

C. 25 kg

D. 30 kg

**Question 3: **Class 6A has 24 boys. The number of boys is equal to \(\frac{4}{5}\) the number of students in the class. How many girls are there in class 6A?

A. 30 students

B. 8 students

C. 6 students

D. 16 students

**Question 4: **There are a total of 840 kg of rice, including three types of \(\frac{1}{6}\) of which are eight aromatic rice, \(\frac{3}{8}\) of which are glutinous rice, the rest are rice meager. Calculate the amount of rice

A. 390 kg

B. 120 kg

C. 270 kg

D. 385 kg

**Question 5: **On the map draw a rectangle with length 5cm and width 3cm. Calculate the actual perimeter of the rectangle in meters. Know that the map is drawn at a scale of 1:1000

A. 150 m

B. 140 m

C. 150m

D. 160 m

**Question 6: **Minh read the book in 4 days. On the first day Minh read \(\frac{2}{5}\) the number of pages in the book. On the second day Minh read \(\frac{3}{5}\) the remaining number of pages. On the third day read 80% of the remaining pages after the second and fourth day read the last 30 pages. Ask how much that book pages?

A. 375 pages

B. 625 pages

C. 500 pages

D. 650 pages

## 4. Conclusion

Through this lesson, you should know the following:

- Know the rule to find a number given its fractional value.
- Apply the rule to solve related exercises.

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