Question

iii. multiplication by cancelling
a) canceling with same number in numerator and denominator
example: $\frac{5}{6}\times\frac{6}{8}$
since the numerator of the second fraction and the denominator of the first fraction both have the same number, 6, you can cancel both.
divide both by the common factor 6.
cross out both 6’s, then place the number 1 above the 6 in the numerator and below the 6 in the denominator.
$\frac{5}{1,6}\times\frac{6^1}{8}=$
the 5 and 8 do not have a common factor so won’t cancel.
multiply the numerators 5 x 1, and the denominators, 1 x 8,
$\frac{5}{1,6}\times\frac{6^1}{8}=\frac{5\times1}{1\times8}$
exercises: multiply the following, canceling common factors. 1 - 6 are marked. complete marking and canceling 7 - 12.

1. $\frac{4}{5}\times\frac{1}{4}$
2. $\frac{3}{5}\times\frac{5}{8}$
3. $\frac{3}{7}\times\frac{7}{10}$
4. $\frac{9}{11}\times\frac{5}{9}$
5. $\frac{6}{7}\times\frac{5}{6}$
6. $\frac{3}{5}\times\frac{1}{3}$

Explanation:

Step1: Identify common factors

For each fraction - multiplication problem, find the common factors in the numerators and denominators.

Step2: Cancel common factors

Divide the numerators and denominators by the common factors.

Step3: Multiply remaining factors

Multiply the remaining numerators together and the remaining denominators together.

1. For $\frac{4}{5}\times\frac{1}{4}$:

• The common factor of 4 in the numerator of the second - fraction and denominator of the first - fraction is 4.
• After canceling, we have $\frac{1}{5}\times\frac{1}{1}=\frac{1\times1}{5\times1}=\frac{1}{5}$.

1. For $\frac{3}{5}\times\frac{5}{8}$:

• The common factor of 5 in the numerator of the second - fraction and denominator of the first - fraction is 5.
• After canceling, we have $\frac{3}{1}\times\frac{1}{8}=\frac{3\times1}{1\times8}=\frac{3}{8}$.

1. For $\frac{3}{7}\times\frac{7}{10}$:

• The common factor of 7 in the numerator of the second - fraction and denominator of the first - fraction is 7.
• After canceling, we have $\frac{3}{1}\times\frac{1}{10}=\frac{3\times1}{1\times10}=\frac{3}{10}$.

1. For $\frac{9}{11}\times\frac{5}{9}$:

• The common factor of 9 in the numerator of the second - fraction and denominator of the first - fraction is 9.
• After canceling, we have $\frac{1}{11}\times\frac{5}{1}=\frac{1\times5}{11\times1}=\frac{5}{11}$.

1. For $\frac{6}{7}\times\frac{5}{6}$:

• The common factor of 6 in the numerator of the second - fraction and denominator of the first - fraction is 6.
• After canceling, we have $\frac{1}{7}\times\frac{5}{1}=\frac{1\times5}{7\times1}=\frac{5}{7}$.

1. For $\frac{3}{5}\times\frac{1}{3}$:

• The common factor of 3 in the numerator of the second - fraction and denominator of the first - fraction is 3.
• After canceling, we have $\frac{1}{5}\times\frac{1}{1}=\frac{1\times1}{5\times1}=\frac{1}{5}$.

Answer:

1. $\frac{1}{5}$
2. $\frac{3}{8}$
3. $\frac{3}{10}$
4. $\frac{5}{11}$
5. $\frac{5}{7}$
6. $\frac{1}{5}$