Determining if a Quantity is Increased or Decreased When Multipped by a Fraction

The product of a number multipped by a fraction is not always smaller than the original number. A number multipped by a fraction can also give an equal number or a number greater than the original number.

Multiply 2 × $frac{1}{3}$ and determine if 2 is decreased/increased/same on multiplying by $frac{1}{3}$

Solution

Step 1:

2 × $frac{1}{3}$ = $frac{2}{1}$ × $frac{1}{3}$ = $frac{(2 × 1)}{(1 × 3)}$ = $frac{2}{3}$

Step 2:

Comparing 2 and $frac{2}{3}$

$frac{2}{3}$ (the product)   <   2 (the original number)

Step 3:

So, in this case the number is decreased when multipped by a proper fraction.

Multiply 3 × $frac{4}{4}$. and determine if 3 is decreased/increased/same on multiplying by $frac{4}{4}$.

Solution

Step 1:

3 × $frac{4}{4}$ = $frac{3}{1}$ × $frac{4}{4}$ = $frac{(3 × 4)}{(1 × 4)}$ = $frac{12}{4}$ = $frac{3}{1}$

Step 2:

Comparing 3 and $frac{3}{1}$

$frac{3}{1}$(the product) = 3 (the original number)

Step 3:

So, in this case the number is same (neither decreased or increased) when multipped by a fraction which is equal to 1.

Multiply 3 × $frac{3}{2}$. and determine if 2 is decreased/increased/same on multiplying by $frac{3}{2}$.

Solution

Step 1:

2 × $frac{3}{2}$ = $frac{2}{1}$ × $frac{3}{2}$ = $frac{(2 × 3)}{(1 × 2)}$ = $frac{6}{2}$ = $frac{3}{1}$ = 3

Step 2:

Comparing 2 and 3

3 (the product)   >   2 (the original number)

Step 3:

So, in this case the number is increased when multipped by an improper fraction.