Question

6 compute products of positive fractions, including mixed numbers with procedural fluency. (l4)
what is the value of the product $\frac{5}{6} \times 3\frac{1}{2}$?
what is the value of the product $\frac{9}{10} \times 4\frac{2}{3}$?
7 nso.2.2 with or without models, compute quotients of positive fractions, involving at least one unit fraction. (l3)
what is the quotient of $\frac{5}{8} \div \frac{2}{5}$?
what is the quotient of $\frac{9}{10} \div \frac{3}{4}$?

Explanation:

Step1: Solve \(\frac{5}{8} \div \frac{2}{5}\)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of \(\frac{2}{5}\) is \(\frac{5}{2}\). So we have \(\frac{5}{8} \times \frac{5}{2}\).
Multiply the numerators: \(5\times5 = 25\).
Multiply the denominators: \(8\times2 = 16\).
So \(\frac{5}{8} \div \frac{2}{5}=\frac{25}{16}=1\frac{9}{16}\).

Step2: Solve \(\frac{9}{10} \div \frac{3}{4}\)

Again, use the reciprocal. The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\). So we calculate \(\frac{9}{10} \times \frac{4}{3}\).
Simplify before multiplying: 9 and 3 have a common factor of 3, so \(9\div3 = 3\) and \(3\div3 = 1\). 10 and 4 have a common factor of 2, so \(10\div2 = 5\) and \(4\div2 = 2\).
Now we have \(\frac{3}{5} \times \frac{2}{1}=\frac{6}{5}=1\frac{1}{5}\).

Step3: Solve \(\frac{5}{6} \times 3\frac{1}{2}\)

First, convert the mixed number \(3\frac{1}{2}\) to an improper fraction. \(3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}\).
Then multiply: \(\frac{5}{6} \times \frac{7}{2}=\frac{35}{6}=5\frac{5}{6}\).

Step4: Solve \(\frac{9}{10} \times 4\frac{2}{3}\)

Convert the mixed number \(4\frac{2}{3}\) to an improper fraction: \(4\frac{2}{3}=\frac{4\times3 + 2}{3}=\frac{14}{3}\).
Multiply: \(\frac{9}{10} \times \frac{14}{3}\). Simplify: 9 and 3 have a common factor of 3, so \(9\div3 = 3\) and \(3\div3 = 1\). 10 and 14 have a common factor of 2, so \(10\div2 = 5\) and \(14\div2 = 7\).
Now we have \(\frac{3}{5} \times \frac{7}{1}=\frac{21}{5}=4\frac{1}{5}\).

Answer:

• \(\frac{5}{8} \div \frac{2}{5}=\boldsymbol{\frac{25}{16}}\) (or \(1\frac{9}{16}\))
• \(\frac{9}{10} \div \frac{3}{4}=\boldsymbol{\frac{6}{5}}\) (or \(1\frac{1}{5}\))
• \(\frac{5}{6} \times 3\frac{1}{2}=\boldsymbol{\frac{35}{6}}\) (or \(5\frac{5}{6}\))
• \(\frac{9}{10} \times 4\frac{2}{3}=\boldsymbol{\frac{21}{5}}\) (or \(4\frac{1}{5}\))