College

Multiply and simplify:

[tex]-\frac{10}{28} \cdot \frac{24}{30} \cdot \left(-\frac{35}{10}\right) = \square[/tex]

Write all products as reduced fractions or integers—not mixed numbers. If the expression is undefined, use the word "undefined" in the answer box.

Answer :

We want to simplify the expression

[tex]$$
-\frac{10}{28} \cdot \frac{24}{30} \cdot \left(-\frac{35}{10}\right).
$$[/tex]

Step 1. Reduce each fraction:

- For the first fraction, simplify
[tex]$$
-\frac{10}{28} = -\frac{10\div2}{28\div2} = -\frac{5}{14}.
$$[/tex]

- For the second fraction, simplify
[tex]$$
\frac{24}{30} = \frac{24\div6}{30\div6} = \frac{4}{5}.
$$[/tex]

- For the third fraction, simplify
[tex]$$
-\frac{35}{10} = -\frac{35\div5}{10\div5} = -\frac{7}{2}.
$$[/tex]

Step 2. Multiply the first two fractions:

Multiply

[tex]$$
-\frac{5}{14} \cdot \frac{4}{5}.
$$[/tex]

Multiply the numerators and denominators:

[tex]$$
-\frac{5 \cdot 4}{14 \cdot 5} = -\frac{20}{70}.
$$[/tex]

Now simplify [tex]$-\frac{20}{70}$[/tex] by dividing numerator and denominator by 10:

[tex]$$
-\frac{20\div10}{70\div10} = -\frac{2}{7}.
$$[/tex]

Step 3. Multiply the result by the third fraction:

Now multiply

[tex]$$
-\frac{2}{7} \cdot \left(-\frac{7}{2}\right).
$$[/tex]

Multiply the numerators and denominators:

[tex]$$
\frac{(-2)(-7)}{7 \cdot 2} = \frac{14}{14}.
$$[/tex]

Simplify the fraction:

[tex]$$
\frac{14}{14} = 1.
$$[/tex]

Thus, the simplified result is

[tex]$$
1.
$$[/tex]

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