Question

Convert \[1\dfrac{3}{4}\]lb to oz?

Answer 1

Hint: We firstly convert the mixed fraction to a proper fraction. Using the conversion of pounds to ounces and unitary method we calculate the value of \[1\dfrac{3}{4}\]lb in oz.
Pound is a unit of measuring weight. It is denoted as ‘lb’.
Ounce is also a unit of measuring weight. It is denoted as ‘oz’.
1 pound has 16 ounces.
Unitary method helps us to calculate the value of multiple units by multiplying value of single unit to number of units given
General form of a mixed fraction is \[a\dfrac{b}{c}\]and it can be converted into proper fraction as \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]

Complete step by step solution:
We have to convert \[1\dfrac{3}{4}\]lb to oz.
Firstly we convert the mixed fraction in pounds in proper fraction in pounds.
Mixed fraction is \[1\dfrac{3}{4}\] … (1)
Use the formula of converting mixed fraction to proper fraction i.e. \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]
We can write the mixed fraction in equation (1) as
\[ \Rightarrow 1\dfrac{3}{4} = \dfrac{{1 \times 4 + 3}}{4}\]
Multiply the terms in the numerator of RHS
\[ \Rightarrow 1\dfrac{3}{4} = \dfrac{{4 + 3}}{4}\]
Add the terms in the numerator of RHS
\[ \Rightarrow 1\dfrac{3}{4} = \dfrac{7}{4}\]
So, the mixed fraction in equation (1) becomes \[\dfrac{7}{4}\]
Now we have to convert \[\dfrac{7}{4}\]pounds into ounces.
Since we know 1 pound \[ = 16\]ounces
i.e. 1 lb \[ = 16\]oz
Use unitary method and multiply both sides by \[\dfrac{7}{4}\]
\[ \Rightarrow \dfrac{7}{4}\] lb \[ = 16 \times \dfrac{7}{4}\]oz
Cancel possible factors from numerator and denominator on right hand side
\[ \Rightarrow \dfrac{7}{4}\] lb \[ = 4 \times 7\]oz
\[ \Rightarrow \dfrac{7}{4}\] lb \[ = 28\]oz
Since we know \[1\dfrac{3}{4} = \dfrac{7}{4}\]
\[ \Rightarrow 1\dfrac{3}{4}\] lb \[ = 28\]oz
\[\therefore \]The value of \[1\dfrac{3}{4}\] lb is 28oz.

Note: Alternate method:
We can write \[1\dfrac{3}{4}\] lb as 1lb and \[\dfrac{3}{4}\]lb
So, using conversion of pounds to ounces i.e. 1 lb \[ = 16\]oz we can write
\[ \Rightarrow 1\dfrac{3}{4}\] lb \[ = 1\]lb and \[ + \dfrac{3}{4}\]lb
Multiply both terms on right hand side by 16
\[ \Rightarrow 1\dfrac{3}{4}\] lb \[ = 1 \times 16\]oz and \[ + \dfrac{3}{4} \times 16\]oz
Cancel common factors in right hand side
\[ \Rightarrow 1\dfrac{3}{4}\] lb \[ = 16\]oz and \[ + 3 \times 4\]oz
\[ \Rightarrow 1\dfrac{3}{4}\] lb \[ = 16\]oz and \[ + 12\]oz
\[ \Rightarrow 1\dfrac{3}{4}\] lb \[ = 28\]oz
\[\therefore \]The value of \[1\dfrac{3}{4}\] lb is 28oz.