Answer :

To solve the given problem, let's break it down step by step:


  1. Calculate the sum of [tex]-\frac{16}{35}[/tex] and [tex]\frac{14}{15}[/tex]:

    To do this, we need a common denominator. The least common multiple (LCM) of 35 and 15 is 105.

    [tex]-\frac{16}{35} = -\frac{16 \times 3}{35 \times 3} = -\frac{48}{105}[/tex]

    [tex]\frac{14}{15} = \frac{14 \times 7}{15 \times 7} = \frac{98}{105}[/tex]

    Now, add the two fractions:

    [tex]-\frac{48}{105} + \frac{98}{105} = \frac{-48 + 98}{105} = \frac{50}{105}[/tex]

    Simplify [tex]\frac{50}{105}[/tex] by dividing the numerator and the denominator by 5:

    [tex]\frac{50}{105} = \frac{50 \div 5}{105 \div 5} = \frac{10}{21}[/tex]


  2. Calculate the quotient of [tex]-\frac{12}{7}[/tex] and [tex]-18[/tex]:

    Dividing a fraction by a number means multiplying by its reciprocal:

    [tex]-\frac{12}{7} \div -18 = -\frac{12}{7} \times \frac{1}{-18}[/tex]

    The negative signs will cancel each other out:

    [tex]\frac{12}{7} \times \frac{1}{18} = \frac{12}{126}[/tex]

    Simplify [tex]\frac{12}{126}[/tex] by dividing by their greatest common divisor, which is 6:

    [tex]\frac{12 \div 6}{126 \div 6} = \frac{2}{21}[/tex]


  3. Divide the sum by the quotient:

    We have the sum as [tex]\frac{10}{21}[/tex] and the quotient as [tex]\frac{2}{21}[/tex]. To divide two fractions, multiply by the reciprocal:

    [tex]\frac{10}{21} \div \frac{2}{21} = \frac{10}{21} \times \frac{21}{2}[/tex]

    Multiply the fractions:

    [tex]\frac{10 \times 21}{21 \times 2} = \frac{210}{42}[/tex]

    Simplify the fraction by dividing by their greatest common divisor, which is 42:

    [tex]\frac{210 \div 42}{42 \div 42} = 5[/tex]

    Therefore, the final result is [tex]5[/tex].


Other Questions