Practice on fractions

### 1.1. Solve textbook exercises on pages 148, 149

**Lesson 1 Textbook page 148**

a) Write a fraction indicating the shaded part of each of the following figures:

b) Write a mixed number for the shaded part of each of the following figures:

*Solution guide:*

a) Figure 1: \(\frac{3}{4}\)

Figure 2: \(\frac{2}{5}\)

Figure 3: \(\frac{5}{8}\)

Figure 5: \(\frac{3}{8}\)

b) Figure 1: \(1\frac{1}{4}\)

Figure 2: \(2\frac{3}{4}\)

Figure 3: \(3\frac{2}{3}\)

Figure 4: \(4\frac{1}{2}\)

Lesson 2 Textbook page 148

Simplify fractions:

\(\frac{3}{6};\frac{{18}}{{24}};\frac{5}{{35}};\frac{{40}}{{90}};\frac {{75}}{{30}}\)

*Solution guide:*

- \(\frac{3}{6} = \frac{{3:3}}{{6:3}} = \frac{1}{2}\)
- \(\frac{{18}}{{24}} = \frac{{18:6}}{{24:6}} = \frac{3}{4}\)
- \(\frac{5}{{35}} = \frac{{5:5}}{{35:5}} = \frac{1}{7}\)
- \(\frac{{40}}{{90}} = \frac{{40:10}}{{90:10}} = \frac{4}{9}\)
- \(\frac{{75}}{{30}} = \frac{{75:15}}{{30:15}} = \frac{5}{2}\)

Lesson 3 Textbook page 149

Converting the denominators of fractions:

a) \(\frac{3}{4}\) and \(\frac{2}{5}\)

b) \(\frac{5}{12}\) and \(\frac{11}{36}\)

c) \(\frac{2}{3}\), \(\frac{3}{4}\) and \(\frac{4}{5}\)

*Solution guide:*

a) \(\frac{3}{4} = \frac{{3 \times 5}}{{4 \times 5}} = \frac{{15}}{{20}}\)

\(\frac{2}{5} = \frac{{2 \times 4}}{{5 \times 4}} = \frac{8}{{20}}\)

b) \(\frac{5}{{12}} = \frac{{5 \times 3}}{{12 \times 3}} = \frac{{15}}{{36}}\)

Keep the fraction \(\frac{{11}}{{36}}\)

c) \(\frac{2}{3} = \frac{{2 \times 4 \times 5}}{{3 \times 4 \times 5}} = \frac{{40}}{{60}} \)

\(\frac{3}{4} = \frac{{3 \times 3 \times 5}}{{4 \times 3 \times 5}} = \frac{{45}}{{60}}\)

\(\frac{4}{5} = \frac{{4 \times 3 \times 4}}{{5 \times 3 \times 4}} = \frac{{48}}{{60}}\)

Lesson 4 Textbook page 149

Put >, <, = in the dot:

\(\begin{array}{l}

\frac{7}{{12}}….\frac{5}{{12}}\\

\frac{2}{5}…..\frac{6}{{15}}\\

\frac{7}{{10}}….\frac{7}{9}

\end{array}\)

*Solution guide:*

- \(\frac{7}{{12}} > \frac{5}{{12}}\) (because 7 > 5)
- We have: \(\frac{2}{5} = \frac{{2 \times 3}}{{5 \times 3}} = \frac{6}{{15}}\)

So \(\frac{2}{5} = \frac{6}{{15}}\)

- \(\frac{7}{{10}} < \frac{7}{9}\) (because 10 > 9)

Lesson 5 Textbook page 149

Write the appropriate fraction on the line between \(\frac{1}{3}\) and \(\frac{2}{3}\) on the number line:

*Solution guide:*

We see: from line 0 to line 1 is divided into 66 equal. Combining two fractions \(\frac{1}{3}\) and \(\frac{2}{3}\) with a common denominator of 66 we have:

\(\frac{1}{3} = \frac{{1 \times 2}}{{3 \times 2}} = \frac{2}{6};\frac{2}{3} = \frac {{2 \times 2}}{{3 \times 2}} = \frac{4}{6}\)

Which \(\frac{2}{6} < \frac{3}{6} < \frac{4}{6}\)

Thus the line between \(\frac{1}{3}\) and \(\frac{2}{3}\) corresponds to the fraction \(\frac{3}{6}\) or the fraction \ (\frac{1}{2}\) (because of the reduction of the fraction \(\frac{3}{6}\) we get the simplest fraction \(\frac{1}{2}\)).

### 1.2. Solving textbook exercises on pages 149, 150

Lesson 1 Textbook page 149

Circle the word in front of the correct answer:

The fraction indicating the colored portion of the tape is:

\(\begin{array}{l}

A.\frac{3}{4}\\

B.\frac{4}{7}\\

C.\frac{4}{3}\\

D.\frac{3}{7}

\end{array}\)

*Solution guide:*

The dc paper tape is divided into 7 equal parts, of which 3 parts are colored, from which the colored part index fraction is \(\frac{3}{7}\)

So the colored part index fraction is \(\frac{3}{7}\).

Choose answer D.

Lesson 2 Textbook page 149

Choose a letter that has a right answer:

There are 20 marbles, including 3 brown marbles, 4 green marbles, 5 red marbles, and 8 yellow marbles. Thus, \(\frac{1}{4}\) the number of colored marbles:

A. Brown B. Red C. Blue D. Yellow

*Solution guide:*

\(\frac{1}{4}\) the number of marbles including the number of marbles is:

\(20 \times \frac{1}{4} = 5\) (marble)

So \(\frac{1}{4}\) the number of marbles is red

Choose the answer NO

Lesson 3 Textbook page 150

Find equal fractions in the following fractions:

\(\frac{3}{5};\frac{5}{8};\frac{{15}}{{25}};\frac{9}{{15}};\frac{{20} }{{32}};\frac{{21}}{{35}}\)

*Solution guide:*

\(\frac{{15}}{{25}} = \frac{{15:5}}{{25:5}} = \frac{3}{5}\)

\(\frac{9}{{15}} = \frac{{9:3}}{{15:3}} = \frac{3}{5}\)

\(\frac{{20}}{{32}} = \frac{{20:4}}{{32:4}} = \frac{5}{8}\)

\(\frac{{21}}{{35}} = \frac{{21:7}}{{35:7}} = \frac{3}{5}\)

So \(\frac{3}{5} = \frac{{15}}{{25}} = \frac{9}{{15}} = \frac{{21}}{{35}};\ frac{5}{8} = \frac{{20}}{{32}}\)

Lesson 4 Textbook page 150

Compare fractions:

a) \(\frac{3}{7}\) and \(\frac{2}{5}\)

b) \(\frac{5}{9}\) and \(\frac{5}{8}\)

c) \(\frac{8}{7}\) and \(\frac{7}{8}\)

*Solution guide:*

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

Since \(\frac{{15}}{{35}} > \frac{{14}}{{35}}\) \(\frac{{3}}{{7}} > \frac{{) 2}}{{5}}\)

b) We have: \(\frac{{5}}{{9}} < \frac{{5}}{{8}}\)

c) Because \(\frac{8}{7} > 1\); \(\frac{7}{8} < 1\) so \(\frac{8}{7} > \frac{7}{8}\)

Lesson 5 Textbook page 150

a) Write the fractions \(\frac{6}{{11}};\frac{{23}}{{33}};\frac{2}{3}\) in order from smallest to largest.

b) Write the fractions \(\frac{8}{9};\frac{8}{{11}};\frac{9}{8}\) in order from largest to smallest.

*Solution guide:*

a) Reduce the denominators of the fractions. Select MSC as 33.

\(\frac{6}{{11}} = \frac{{6 \times 3}}{{11 \times 3}} = \frac{{18}}{{33}};\frac{2} {3} = \frac{{2 \times 11}}{{3 \times 11}} = \frac{{22}}{{33}}\)

Keep the fraction \(\frac{{22}}{{33}}\)

Since \(\frac{{18}}{{33}} < \frac{{22}}{{33}} < \frac{{23}}{{33}}\) \(\frac{{) 6}}{{11}} < \frac{{2}}{{3}} < \frac{{23}}{{33}}\)

So the fractions are written in order from smallest to largest as follows: \(\frac{6}{{11}};\frac{2}{3};\frac{{23}}{{33}} \)

b) Since \(\frac{9}{8} > \frac{8}{9};\frac{8}{9} > \frac{8}{{11}}\) so \(\frac{ 9}{8} > \frac{8}{9} > \frac{8}{{11}}\)

So we write the fractions in order from largest to smallest as follows:\(\frac{9}{8} ; \frac{8}{9} ; \frac{8}{{11}}\)

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