Question

question 27 of 60
multiply.
\\(\frac{3}{5} \times \frac{7}{8}\\)

question 28 of 60
multiply.
\\(-\frac{1}{9} cdot \frac{5}{4}\\)
write your answer in simplest form.

question 29 of 60
a metal rod will be cut into pieces that are each \\(\frac{1}{20}\\) meters long. the rod is \\(\frac{4}{5}\\) meters long. how many pieces will be made from the rod?
write your answer in simplest form.

question 30 of 60
multiply. write your answer as a fraction in simplest form.
\\(\frac{3}{5} \times \frac{11}{2}\\)

question 31 of 60
fill in the blank to make the two fractions equivalent.
\\(\frac{3}{4} = \frac{\\_\\_\\_}{20}\\)

question 32 of 60
find the least common multiple (lcm) of 4 and 5.

Explanation:

Question 27

Step1: Multiply numerators and denominators

To multiply fractions, we multiply the numerators together and the denominators together. So for \(\frac{3}{5} \times \frac{7}{8}\), we have \(3 \times 7 = 21\) (numerator) and \(5 \times 8 = 40\) (denominator).
\(\frac{3}{5} \times \frac{7}{8} = \frac{3 \times 7}{5 \times 8}\)

Step2: Simplify (if possible)

The fraction \(\frac{21}{40}\) cannot be simplified further as 21 and 40 have no common factors other than 1.

Step1: Multiply numerators and denominators (consider sign)

For \(-\frac{1}{9} \times \frac{5}{4}\), multiply the numerators: \(1 \times 5 = 5\) and denominators: \(9 \times 4 = 36\). The negative sign remains.
\(-\frac{1}{9} \times \frac{5}{4}=-\frac{1\times5}{9\times4}\)

Step2: Simplify (if possible)

\(\frac{5}{36}\) is in simplest form, so the result is \(-\frac{5}{36}\).

Step1: Determine the operation

To find the number of pieces, we divide the total length of the rod by the length of each piece. So we calculate \(\frac{4}{5} \div \frac{1}{20}\).

Step2: Divide fractions (multiply by reciprocal)

Dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{4}{5} \div \frac{1}{20}=\frac{4}{5} \times \frac{20}{1}\).

Step3: Multiply numerators and denominators

\(4 \times 20 = 80\) and \(5 \times 1 = 5\), so we have \(\frac{80}{5}\).

Step4: Simplify the fraction

\(\frac{80}{5}=16\) (since 80 ÷ 5 = 16).

Answer:

\(\frac{21}{40}\)

Question 28