Question

1. 9/10 x 4/7

1 point
your answer

1. 3 1/2 x 2 1/5

1 point
your answer

1. 2 3/5 x 3 1/2

1 point
your answer

1. 2 4/5 x 4 1/4

1 point
your answer

Explanation:

Question 5

Step1: Multiply numerators and denominators

To multiply two fractions \(\frac{a}{b} \times \frac{c}{d}\), we use the rule \(\frac{a}{b} \times \frac{c}{d}=\frac{a\times c}{b\times d}\). For \(\frac{9}{10} \times \frac{4}{7}\), we multiply the numerators \(9\times4 = 36\) and the denominators \(10\times7=70\). So we get \(\frac{36}{70}\).

Step2: Simplify the fraction

We can simplify \(\frac{36}{70}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \(\frac{36\div2}{70\div2}=\frac{18}{35}\).

Step1: Convert mixed numbers to improper fractions

A mixed number \(a\frac{b}{c}\) can be converted to an improper fraction as \(\frac{a\times c + b}{c}\). For \(3\frac{1}{2}\), we have \(\frac{3\times2 + 1}{2}=\frac{7}{2}\). For \(2\frac{1}{5}\), we have \(\frac{2\times5+1}{5}=\frac{11}{5}\).

Step2: Multiply the improper fractions

Using the rule for multiplying fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\), we multiply \(\frac{7}{2}\times\frac{11}{5}=\frac{7\times11}{2\times5}=\frac{77}{10}\).

Step3: Convert back to mixed number (optional, but common)

\(\frac{77}{10}=7\frac{7}{10}\) (since \(77\div10 = 7\) with a remainder of 7).

Step1: Convert mixed numbers to improper fractions

For \(2\frac{3}{5}\), convert to improper fraction: \(\frac{2\times5 + 3}{5}=\frac{13}{5}\). For \(3\frac{1}{2}\), convert to improper fraction: \(\frac{3\times2+1}{2}=\frac{7}{2}\).

Step2: Multiply the improper fractions

Multiply \(\frac{13}{5}\times\frac{7}{2}=\frac{13\times7}{5\times2}=\frac{91}{10}\).

Step3: Convert back to mixed number

\(\frac{91}{10}=9\frac{1}{10}\) (since \(91\div10 = 9\) with a remainder of 1).

Answer:

\(\frac{18}{35}\)

Question 6