Fractions and division of natural numbers

### 1.1. Knowledge to remember

a) There are 8 oranges, divided equally among 4 children. Each child gets:

8: 4 = 2 (orange)

b) There are 3 cakes, divided equally among 4 children. How many pieces of cake did each child get?

*Comment : *We have to do the division 3: 4. Since 3 is not divisible by 4, we can do the following:

- Divide each cake into 4 equal parts and then give each child 1 portion, i.e. \(\frac{1}{4}\) the cake.

Divide 3 cakes equally among 4 children

- After 3 times dividing the cake like that, each child gets 3 portions, we say each child gets \(\frac{3}{4}\) cake (see picture).

Each child gets \(\frac{3}{4}\) a cake

We write: \(3:4 = \frac{3}{4}\) (cake).

c) *Comment: The quotient of the division of a natural number by a (non-zero) natural number can be written as a fraction, the numerator is the divisor and the denominator is the divisor.*

Such as :

\(8:4 = \frac{8}{4};\,\,\,\,3:4 = \frac{3}{4};\,\,\,\,5:5 = \frac {5}{5}\)

### 1.2. Solving Textbook Exercises

**Lesson 1: **Write the quotient of each of the following division as a fraction

7: 9; 5: 8; 6: 19; 1: 3.

**Solution guide:**

- The quotient of division of a (non-zero) natural number can be written as a fraction, the numerator being the divisor and the denominator the divisor.

\(7:9 = \frac{7}{9}\) ; \(5:8 = \frac{5}{8}\) ; \(6:19 = \frac{6}{{19}}\); \(1:3 = \frac{1}{3}\).

**Lesson 2: **Write according to the pattern

*Template:* \(24:8 = \frac{{24}}{8} = 3\)

\(36:9;\,\,\,\,88:11;\,\,\,\,0:5;\,\,\,\,\,7:7\,\,\,\ ,\).

__Solution guide:__

- Write the division as a fraction and then calculate the value of that fraction.

\(36:9 = \frac{{36}}{9} = 4\) ; \(88:11 = \frac{{88}}{{11}} = 8\) ;

\(0:5 = \frac{0}{5} = 0\) ; \(7:7 = \frac{7}{7} = 1\).

**Lesson 3:**

a) Write each natural number as a fraction with a denominator of 11 (following the denominator).

* Template: * \(9 = \frac{9}{1}\)

6 = … ; 1 = … ; 27 = … ; 0 = … ; 3 = … .

b) Comment: Every natural number that can be written as a fraction is that natural number and has a denominator equal to 1.

__Solution guide:__

Every natural number that can be written as a fraction is that natural number and has a denominator of 11.

a) \(6 = \frac{6}{1}\); \(1 = \frac{1}{1}\); \(27 = \frac{{27}}{1}\) ;

\(0 = \frac{0}{1}\) ; \(3 = \frac{3}{1}\).

b) Comment: Every natural number that can be written as a fraction is that natural number and has a denominator equal to 1.

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