Ask a New Question
Menu

Use the properties of operations and rules for multiplying and dividing to solve:

(−3/5) x (5/16) x (7/12) ÷ (−3/16) x (−5/7)

1 answer

To solve the expression

\[ \left(-\frac{3}{5}\right) \times \left(\frac{5}{16}\right) \times \left(\frac{7}{12}\right) \div \left(-\frac{3}{16}\right) \times \left(-\frac{5}{7}\right) \]

we can simplify it step by step by using the properties of multiplication and division.

  1. Changing the division to multiplication: Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, we rewrite the division part:

    \[ \div \left(-\frac{3}{16}\right) = \times \left(-\frac{16}{3}\right) \]

So, the expression becomes:

\[ \left(-\frac{3}{5}\right) \times \left(\frac{5}{16}\right) \times \left(\frac{7}{12}\right) \times \left(-\frac{16}{3}\right) \times \left(-\frac{5}{7}\right) \]

  1. Rearranging the Expression: We can rearrange the multiplication as follows:

\[ \left(-\frac{3}{5} \times -\frac{16}{3}\right) \times \left(\frac{5}{16}\right) \times \left(\frac{7}{12}\right) \times \left(-\frac{5}{7}\right) \]

  1. Calculating Individual Parts: Let's calculate the first pair:

\[ -\frac{3}{5} \times -\frac{16}{3} = \frac{3 \times 16}{5 \times 3} = \frac{16}{5} \]

Next, we calculate the product of the second pair, which includes \(\frac{5}{16}\) and \(-\frac{5}{7}\):

\[ \frac{5}{16} \times -\frac{5}{7} = -\frac{25}{112} \]

  1. Combining All Parts: Now, we can combine the values:

\[ \frac{16}{5} \times \frac{7}{12} \times -\frac{25}{112} \]

Computing the multiplication step by step:

  1. Calculate \(\frac{16}{5} \times \frac{7}{12}\):

\[ \frac{16 \times 7}{5 \times 12} = \frac{112}{60} = \frac{28}{15} \quad (\text{after simplifying by dividing numerator and denominator by 4}) \]

  1. Now multiply this by \(-\frac{25}{112}\):

\[ \frac{28}{15} \times -\frac{25}{112} = -\frac{28 \times 25}{15 \times 112} \]

Calculating the numerator:

\[ 28 \times 25 = 700 \]

And the denominator:

\[ 15 \times 112 = 1680 \]

Thus, we have:

\[ -\frac{700}{1680} \]

  1. Final Simplification: Let’s simplify \(-\frac{700}{1680}\):

Both 700 and 1680 can be divided by 140:

\[ -\frac{700 \div 140}{1680 \div 140} = -\frac{5}{12} \]

Thus, the result of the original expression is:

\[ \boxed{-\frac{5}{12}} \]