Practice on fractions

**Lesson 1: **Choose a letter that has a right answer

\(\frac{2}{5}\) is a fraction of the colored part of which shape ?

A. Figure 1 B. Figure 2

C. Figure 3 D. Figure 4

**Solution guide:**

- Observe the figure and find the fraction of the shaded portion of each figure.

*Solution :*

The fraction indicating the shaded part of figure 1 is \(\frac{1}{6}\) ;

The colored part of figure 2 fraction is \(\frac{3}{5}\) ;

The shaded fraction of figure 3 is \(\frac{4}{{10}} = \frac{2}{5}\) ;

The fraction indicating the shaded part of figure 4 is \(\frac{2}{6} = \frac{1}{3}\).

So \(\frac{2}{5}\) is a fraction indicating the shaded part of figure 3.

Choose answer C.

**Lesson 2: **Continue to write the appropriate fraction in the dot

__Solution guide:__

- Look at the picture and fill in the appropriate fraction in the dot.

**Lesson 3: **Simplify fractions

\(\frac{{12}}{{18}};\frac{4}{{40}};\frac{{18}}{{24}};\frac{{20}}{{35} };\frac{{60}}{{12}}\)

__Solution guide:__

When reducing fractions, you can do the following:

- Consider whether the numerator and the denominator are divisible by the larger natural number.
- Divide the numerator and denominator by that number.
- Keep doing this until you get the simplest fraction.

\(\begin{array}{l}

\frac{{12}}{{18}} = \frac{{12:6}}{{18:6}} = \frac{2}{3};\,\,\,\,\,\ ,\,\,\,\,\,\,\,\,\,\,\frac{4}{{40}} = \frac{{4:4}}{{40:4}} = \ frac{1}{{10}};\\

\frac{{18}}{{24}} = \frac{{18:6}}{{24:6}} = \frac{3}{4};\,\,\,\,\,\ ,\,\,\,\,\,\,\,\,\,\,\frac{{20}}{{35}} = \frac{{20:5}}{{35:5}} = \frac{4}{7}\\

\frac{{60}}{{12}} = \frac{{60:12}}{{12:12}} = \frac{5}{1} = 5.

\end{array}\)

**Lesson 4: **Denominator of fractions

a) \(\frac{2}{5}\) and \(\frac{3}{7}\) ; b) \(\frac{4}{{15}}\) and \(\frac{6}{{45}}\) ; c) \(\frac{1}{2};\frac{1}{5}\) and \(\frac{1}{3}\).

__Solution guide:__

When reducing the denominator of two fractions, we can do the following:

- Multiply the numerator and denominator of the first fraction by the denominator of the second.
- Multiply the numerator and denominator of the second fraction by the denominator of the first fraction.

a) Choose a common denominator of 5 × 7 = 35.

We have : \(\frac{2}{5} = \frac{{2 \times 7}}{{5 \times 7}} = \frac{{14}}{{35}};\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{3}{7} = \frac{{3 \times 5}}{{7 \times 5}} = \frac{{15}}{{35}}\)

b) Choose a common denominator of 45.

We have : \(\frac{4}{{15}} = \frac{{4 \times 3}}{{15 \times 3}} = \frac{{12}}{{45}}\) ; Keep the fraction \(\frac{6}{{45}}\).

c) Choose a common denominator: 2 × 5 × 3 = 30.

\(\begin{array}{l}

\frac{1}{2} = \frac{{1 \times 15}}{{2 \times 15}} = \frac{{15}}{{30}};\,\,\,\,\ ,\,\,\,\,\,\,\,\frac{1}{5} = \frac{{1 \times 6}}{{5 \times 6}} = \frac{6}{{ 30}};\\

\frac{1}{3} = \frac{{1 \times 10}}{{3 \times 10}} = \frac{{10}}{{30}}.

\end{array}\)

**Lesson 5: **Sort the fractions \(\frac{1}{3};\frac{1}{6};\frac{5}{2};\frac{3}{2}\) in ascending order.

__Solution guide:__

- Compare the given fractions and then arrange the fractions in order from smallest to largest.

Comment :

\(\frac{1}{3} < 1;\,\,\,\frac{1}{6} < 1\) and \(\frac{1}{6} < \frac{2}{6 } = \frac{1}{3}\)

\(\frac{5}{2} > 1;\,\,\,\frac{3}{2} > 1\) and \(\frac{3}{2} < \frac{5}{2 }\)

So \(\frac{1}{6} < \frac{1}{3} < \frac{3}{2} < \frac{5}{2}\)

So the given fractions in ascending order are: \(\frac{1}{6};\frac{1}{3};\frac{3}{2};\frac{5}{2 }\)

.

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