Equal fractions

**Lesson 1:** Write the correct number in the dot

\(\begin{array}{l}

\frac{4}{5} = \frac{{4 \times 4}}{{5 \times 4}} = \frac{{…}}{{…}};\,\,\ ,\,\,\frac{1}{5} = \frac{{1 \times 5}}{{5 \times 5}} = \frac{{…}}{{…}}; \,\,\,\,\,\frac{9}{{15}} = \frac{{9:3}}{{15:3}} = \frac{{…}}{{. ..}};\\

\frac{2}{7} = \frac{{2 \times 2}}{{7 \times …}} = \frac{{…}}{{…}};\,\ ,\,\,\,\frac{8}{3} = \frac{{8 \times …}}{{3 \times …}} = \frac{{40}}{{.. .}};\,\,\,\,\,\frac{{21}}{{14}} = \frac{{21:…}}{{14:…}} = \frac {{…}}{{…}}.

\end{array}\)

**Solution guide:**

Apply the basic property of fractions:

- If you multiply both the numerator and the denominator of a fraction by the same non-zero natural number, you get a fraction equal to the given fraction.
- If both the numerator and the denominator of a fraction are divisible by the same non-zero natural number, then a fraction equal to the given fraction is obtained.

\(\begin{array}{l}

\frac{4}{5} = \frac{{4 \times 4}}{{5 \times 4}} = \frac{{16}}{{20}};\,\,\,\,\ ,\frac{1}{5} = \frac{{1 \times 5}}{{5 \times 5}} = \frac{5}{{25}};\,\,\,\,\, \frac{9}{{15}} = \frac{{9:3}}{{15:3}} = \frac{3}{5};\\

\frac{2}{7} = \frac{{2 \times 2}}{{7 \times 2}} = \frac{4}{{14}};\,\,\,\,\,\ frac{8}{3} = \frac{{8 \times 5}}{{3 \times 5}} = \frac{{40}}{{15}};\,\,\,\,\, \frac{{21}}{{14}} = \frac{{21:7}}{{14:7}} = \frac{3}{2}.

\end{array}\)

**Lesson 2:** Write the correct number in the dot

a) \(\frac{{28}}{{20}} = \frac{{14}}{{…}} = \frac{7}{{…}}\)

b) \(\frac{3}{5} = \frac{{…}}{{10}} = \frac{{…}}{{15}} = \frac{{… }}{{20}}\)

c) \(\frac{{24}}{{36}} = \frac{8}{{…}} = \frac{2}{{…}}\)

d) \(\frac{7}{6} = \frac{{…}}{{12}} = \frac{{…}}{{18}} = \frac{{… }}{{30}}\)

**Solution guide:**

a) \(\frac{{28}}{{20}} = \frac{{14}}{{10}} = \frac{7}{5}\)

b) \(\frac{3}{5} = \frac{6}{{10}} = \frac{9}{{15}} = \frac{{12}}{{20}}\)

c) \(\frac{{24}}{{36}} = \frac{8}{{12}} = \frac{2}{3}\)

d) \(\frac{7}{6} = \frac{{14}}{{12}} = \frac{{21}}{{18}} = \frac{{35}}{{30} }\)

.

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