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

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Introduction

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

Problem 1

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 multiplied by a proper fraction.

Problem 2

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 multiplied by a fraction which is equal to 1.

Problem 3

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 multiplied by an improper fraction.