Practice on solving math

**Lesson 1:** A class has 40 students, in which there are \(\frac{1}{{10}}\) the number of students who are good at Math, \(\frac{3}{{10}}\) the number of students who are good at Vietnamese . How many students are good at Math and Vietnamese in that class?

**Solution**

Number of students who are good at Math

\(40\,\,x\,\,\frac{1}{{10}} = 4\) (student)

Number of students who are good at Vietnamese

\(40\,\,x\,\,\frac{3}{{10}} = 12\) (student)

Number of students who are good at Vietnamese and Math

4 +12 = 16 (student)

**Lesson 2:** A rectangle has an area equal to \(\frac{{15}}{{48}}{m^2}\). Find the perimeter of a rectangle whose width is equal to \(\frac{3}{8}m.\)

**Solution**

The length of the rectangle is:

\(\frac{{15}}{{48}}\,\,:\,\,\frac{3}{8} = \frac{5}{6}\) (m)

Perimeter of the rectangle is:

\(\left( {\frac{3}{8} + \frac{5}{6}} \right)x\,\,2 = \frac{{29}}{{12}}\) (m )

**Lesson 3:** A cement dealer sold all the cement they had in 4 days. The first day sold \(\frac{1}{5}\) of cement and 10 quintals. On the second day sell \(\frac{4}{9}\) the remaining amount of cement and 10 quintals. On the third day sell \(\frac{2}{7}\) the remaining amount of cement and 10 quintals. On Wednesday sell \(\frac{8}{9}\) the remaining amount of cement and the last 10 quintals. How many quintals of cement did this agent sell in all?

**Solution**

On Wednesday sell \(\frac{8}{9}\) the remaining cement and the last 10 quintals, so \(\frac{1}{9}\) equals 10 quintals of cement.

So the amount of cement left after the third day (or the number of cement sold on the fourth day) is:

\(10\,\,:\,\,\frac{1}{9} = 90\) (weight)

(90 + 10) quintal is \(\frac{5}{7}\) the amount of cement left after the second day, so the remaining cement after the second day is:

\(100\,\,:\,\,\frac{5}{7} = 140\) (weight)

(140 + 10) quintal is \(\frac{5}{9}\) the amount of cement left after day 1, so the amount of cement left after day 1 is:

\(150\,\,:\,\,\frac{5}{9} = 270\) (weight)

(270 + 10) quintal is \(\frac{4}{5}\) the number of cement in stock, so the number of cement this dealer has in all is:

\(280\,\,:\,\,\frac{4}{5} = 350\) (weight)

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