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4TO AÑO
Matemáticas - 1er BIMESTRE

FICHA DE TRABAJO
ADICIÓN Y SUSTRACCIÓN DE FRACCIONES HOMOGÉNEAS

1. En la casilla en blanco, marca con "X" la respuesta que consideres Verdadera (V) o Falsa (F).

[tex]
\begin{array}{l}
\frac{9}{20} = \frac{18}{20} - \frac{4}{20} - \frac{5}{20} \\
\frac{10}{5} = 3 \frac{2}{5} + 1 \frac{2}{5} \\
2 \frac{1}{13} = \frac{25}{13} + \frac{12}{13} - \frac{9}{13} \\
5 \frac{3}{7} \neq 6 \frac{2}{7} + 1 \frac{3}{7} - 2 \frac{2}{7} \\
1 \frac{9}{12} = \frac{45}{12} - \frac{27}{12} + \frac{3}{12}
\end{array}
[/tex]

[tex]
\frac{7^7}{\frac{24}{2}}
[/tex]

[tex]
\begin{array}{|c|c|}
\hline
\text{Pregunta} & \text{V/F} \\
\hline
1 & \_\_\_\_ \\
\hline
2 & \_\_\_\_ \\
\hline
3 & \_\_\_\_ \\
\hline
4 & \_\_\_\_ \\
\hline
5 & \_\_\_\_ \\
\hline
\end{array}
[/tex]

Answer :

Sure, let's go through each statement step-by-step and see if it's true or false.

### Statement 1:
[tex]\(\frac{9}{20} = \frac{18}{20} - \frac{4}{20} - \frac{5}{20}\)[/tex]

First, let's simplify the right-hand side:
[tex]\(\frac{18}{20} - \frac{4}{20} - \frac{5}{20} = \frac{18 - 4 - 5}{20} = \frac{9}{20}\)[/tex]

So, the left-hand side matches the right-hand side.

True: [tex]\(\frac{9}{20} = \frac{9}{20}\)[/tex]

### Statement 2:
[tex]\(\frac{10}{5} = 3 \frac{2}{5} + 1 \frac{2}{5}\)[/tex]

First, let's simplify [tex]\(\frac{10}{5}\)[/tex]:
[tex]\(\frac{10}{5} = 2\)[/tex]

And now let's convert [tex]\(3 \frac{2}{5}\)[/tex] and [tex]\(1 \frac{2}{5}\)[/tex] to improper fractions:
[tex]\(3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}\)[/tex]
[tex]\(1 \frac{2}{5} = 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5}\)[/tex]

Adding these improper fractions together:
[tex]\(\frac{17}{5} + \frac{7}{5} = \frac{24}{5}\)[/tex]

[tex]\(\frac{24}{5} \neq 2\)[/tex]

False: [tex]\(\frac{10}{5} \neq 3 \frac{2}{5} + 1 \frac{2}{5}\)[/tex]

### Statement 3:
[tex]\(2 \frac{1}{13} = \frac{25}{13} + \frac{12}{13} - \frac{9}{13}\)[/tex]

First, let's convert [tex]\(2 \frac{1}{13}\)[/tex] to an improper fraction:
[tex]\(2 \frac{1}{13} = 2 + \frac{1}{13} = \frac{26}{13} + \frac{1}{13} = \frac{27}{13}\)[/tex]

Now let's simplify the right-hand side:
[tex]\(\frac{25}{13} + \frac{12}{13} - \frac{9}{13} = \frac{25 + 12 - 9}{13} = \frac{28}{13}\)[/tex]

[tex]\(\frac{27}{13} \neq \frac{28}{13}\)[/tex]

False: [tex]\(2 \frac{1}{13} \neq \frac{25}{13} + \frac{12}{13} - \frac{9}{13}\)[/tex]

### Statement 4:
[tex]\(5 \frac{3}{7} \neq 6 \frac{2}{7} + 1 \frac{3}{7} - 2 \frac{2}{7}\)[/tex]

First, let's convert [tex]\(5 \frac{3}{7}\)[/tex], [tex]\(6 \frac{2}{7}\)[/tex], [tex]\(1 \frac{3}{7}\)[/tex], and [tex]\(2 \frac{2}{7}\)[/tex] to improper fractions:
[tex]\(5 \frac{3}{7} = 5 + \frac{3}{7} = \frac{35}{7} + \frac{3}{7} = \frac{38}{7}\)[/tex]
[tex]\(6 \frac{2}{7} = 6 + \frac{2}{7} = \frac{42}{7} + \frac{2}{7} = \frac{44}{7}\)[/tex]
[tex]\(1 \frac{3}{7} = 1 + \frac{3}{7} = \frac{7}{7} + \frac{3}{7} = \frac{10}{7}\)[/tex]
[tex]\(2 \frac{2}{7} = 2 + \frac{2}{7} = \frac{14}{7} + \frac{2}{7} = \frac{16}{7}\)[/tex]

Now let's add [tex]\(6 \frac{2}{7}\)[/tex], [tex]\(1 \frac{3}{7}\)[/tex], and subtract [tex]\(2 \frac{2}{7}\)[/tex]:
[tex]\(\frac{44}{7} + \frac{10}{7} - \frac{16}{7} = \frac{44 + 10 - 16}{7} = \frac{38}{7}\)[/tex]

[tex]\(\frac{38}{7} = \frac{38}{7}\)[/tex]

True: [tex]\(5 \frac{3}{7} = 6 \frac{2}{7} + 1 \frac{3}{7} - 2 \frac{2}{7}\)[/tex]

### Statement 5:
[tex]\(1 \frac{9}{12} = \frac{45}{12} - \frac{27}{12} + \frac{3}{12}\)[/tex]

First, let's convert [tex]\(1 \frac{9}{12}\)[/tex] to an improper fraction:
[tex]\(1 \frac{9}{12} = 1 + \frac{9}{12} = \frac{12}{12} + \frac{9}{12} = \frac{21}{12}\)[/tex]

Now let's simplify the right-hand side:
[tex]\(\frac{45}{12} - \frac{27}{12} + \frac{3}{12} = \frac{45 - 27 + 3}{12} = \frac{21}{12}\)[/tex]

[tex]\(\frac{21}{12} = \frac{21}{12}\)[/tex]

True: [tex]\(1 \frac{9}{12} = \frac{45}{12} - \frac{27}{12} + \frac{3}{12}\)[/tex]

### Summary
Based on our calculations, the answers are:
1. True (V)
2. False (F)
3. False (F)
4. True (V)
5. True (V)

Therefore, the responses are:

- [tex]\(\frac{9}{20} = \frac{18}{20}-\frac{4}{20}-\frac{5}{20} \ \text{(F)}\)[/tex]
- [tex]\(\frac{10}{5}=3 \frac{2}{5}+1 \frac{2}{5} \ \text{(F)}\)[/tex]
- [tex]\(2 \frac{1}{13}=\frac{25}{13}+\frac{12}{13}-\frac{9}{13} \ \text{(F)}\)[/tex]
- [tex]\(5 \frac{3}{7} /=6 \frac{2}{7}+1 \frac{3}{7}-2 \frac{2}{7} \ \text{(V)}\)[/tex]
- [tex]\(1 \frac{9}{12}=\frac{45}{12}-\frac{27}{12}+\frac{3}{12} \ \text{(V)}\)[/tex]

Thank you for your question. If you need more help or further clarification, feel free to ask!

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Rewritten by : Barada