## Math 6 Chapter 3 Lesson 16: Find the ratio of two numbers

## 1. Summary of theory Tóm

### 1.1. Ratio of two numbers

The quotient in dividing the number a by the number b \((b \ne 0)\) is called the ratio of a and b.

The ratio of a and b is denoted a : b (also denoted \(\frac{a}{b}\))

**Example 1:** The ratio of two numbers 3 and 5 is \(3: 5 = \dfrac{3}{5}\)

### 1.2. Percentage

To find the percentage of two numbers a and b, multiply a by 100 and then divide by b and write the % sign in the result \(\dfrac{{a\,\,.\,\,100}}{ b}\% \)

**Example 2: **A class has 40 students. Including 30 female students. What percentage of the total number of students is the number of other students?

**Solution**

The number of students who make up the percentage of the whole class is

\(\dfrac{30.100}{40} \%=75 \% \)

### 1.3. Chain ratio

The scale T of a drawing (or a map) is the ratio of the distance a between two points on the drawing (or map) and the distance b between the actual two corresponding points:

\(T = \dfrac{a}{b}\) (a, b have the same units)

## 2. Illustrated exercise

**Question 1: **Find the percentage of

a) 5 and 8;

b) 25 kg and \(\dfrac{3}{10}\) weights.

**Solution guide**

a) 5 and 8

The percentages of 5 and 8 are : \(\displaystyle {{5,100} \over 8} = 62.5\% \)

b) 25kg and \(\dfrac{3}{10}\) weights

We have: \(\dfrac{3}{10}\) weights = 30 kg

The percentage of 25kg and 30kg or the percentage of 25kg and \(\dfrac{3}{10}\) weight is:

\(\displaystyle {{25.100} \over {30}} = 83.3\% \)

**Verse 2:** The distance from the northernmost point in Ha Giang to the southernmost point at Cape Ca Mau is 1620 km long. On a map, that distance is 16.2 cm. Find the scale of the map.

**Solution guide**

Map scale: \(\dfrac{{16.2}}{{162\,000\,000}} = \dfrac{1}{{10\,000\,000}}\)

**Question 3: **The ratio of two numbers is \(2 : 7\). If 35 is added to the first number, their ratio will be \(11 : 14\). Find two of them.

**Solution guide**

\(\dfrac{a}{b} = \dfrac{2}{7},\,\,\,\dfrac{{a + 35}}{b} = \dfrac{{11}}{{14} }\)

We have: \(\dfrac{a}{b} + \dfrac{{35}}{b} = \dfrac{{11}}{{14}}\)

\( \Rightarrow \dfrac{{35}}{b} = \dfrac{{11}}{{14}} – \dfrac{a}{b} = \dfrac{{11}}{{14}} – \dfrac{2}{7} = \dfrac{1}{2}\)

Therefore:

b = 35. 2 = 70

\(a = \dfrac{2}{7}.70 = 20\)

## 3. Practice

### 3.1. Essay exercises

**Question 1: ** A rectangular plot of land has an area of \(5000{m^2}\). On a 1:1000 scale map, how big is that land?

**Verse 2:** The difference of two numbers is 32. Knowing 25% of the large numbers is equal to 0.375 of the small numbers. Find two of them.

**Question 3: **The ratio of two numbers is \(\dfrac{3}{5}\), the difference of their squares is -64. Find two of them.

**Question 4: **Find two numbers, knowing their ratio is \(2:5\) and their product is 40.

### 3.2. Multiple choice exercises Bài

**Question 1: **The ratio of two numbers a and b is 120%. The difference of those two numbers is 16. Find the sum of those two numbers.

A. 96

B. 167

C. 150

D. 176

**Verse 2: **In a garden, there are three kinds of trees, jackfruit, persimmon and apple. The number of apple trees accounts for 30% of the total number of trees, the number of persimmon trees accounts for 50% of the total number of trees, the number of jackfruit trees is 40. What is the total number of trees in the garden?

A. 20 trees

B. 200 plants

C. 100 trees

D. 240 plants

**Question 3: **A class has less than 50 students. At the end of the year, 30% of students got good grades, \(\dfrac{3}{8}\) got good grades, the rest were average. Calculate the average number of students

A. 15 students

B. 13 students

C. 20 students

D. 9 number of students

**Question 4: **The ratio between male and female students is 80%. Calculate the number of male students, knowing that class 6A has 36 students

A. 20 students

B. 15 students

C. 18 students

D. 16 students

**Question 5: **The difference of two numbers is 21. Knowing that 37.5% of the large numbers are equal to 0.6 of the small numbers. Those two numbers are:

A. 56; 35

B. 45; 56

C. 60; 39

D. 56; 45

**Question 6: **Two fields harvested all 990kg of rice. Assume that \(\frac{2}{3}\) the number of paddy harvested in the first field is equal to \(\frac{4}{5}\) the number of paddy harvested in the second field. How much rice does the second field yield?

A. 450 kg

B. 540 kg

C. 600 kg

D. 300 kg

## 4. Conclusion

Through this lesson, you should know the following:

- Know the types of ratios (ratio of two numbers, percentages, scale ratios).
- Use the knowledge to do some related exercises.

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