Question

How do you evaluate the following expression using decimals?
\[4.56 - \dfrac{4}{5} + 3.21 + \dfrac{17}{32}\].

Answer 1

Hint:In this question, we need to evaluate the given expression \[4.56 - \dfrac{4}{5} + 3.21 + \dfrac{17}{32}\] and we need to find the value of the expression in terms of decimals. First, we need to convert the fractions in the given expression to decimals. In order to make the given fraction over \[100\] , we can multiply both numerator and denominator by the same number to get \[100\] in the denominator and then on simplifying we can get the value of the given expression.

Complete step by step solution:
Given expression,
\[4.56 - \dfrac{4}{5} + 3.21 + \dfrac{17}{32}\]
The best way to evaluate the expression is to convert each fraction to decimal form. On seeing the given expression, two of them are already in decimal form. We need to convert the remaining two fractions into decimals.
First let us consider the term \[\dfrac{4}{5}\] ,
We need to make the fraction over \[100\] to make conversion much easier.
By multiplying both the numerator and denominator by \[20\] ,
We get,
\[\Rightarrow \dfrac{4 \times 20}{5 \times 20}\]
On multiplying,
We get,
\[\Rightarrow \dfrac{80}{100}\]
On simplifying,
We get,
\[\Rightarrow \ 0.80\] which is also equal to \[0.8\]
Then we can consider the next term \[\dfrac{17}{32}\]
Here we can’t make the fraction over \[100\] since \[100\] is not the multiple of \[32\] , thus we can make the fraction over \[100000\] to make conversion much easier.
By multiplying both the numerator and denominator by \[3125\] ,
\[\Rightarrow \dfrac{17 \times 3125}{32 \times 3125}\]
On multiplying,
We get,
\[\Rightarrow \dfrac{50125}{100000}\]
On simplifying,
We get,
\[\Rightarrow \ 0.50125\]
Thus we have converted all the fraction terms into decimals.
The given expression is \[4.56 - \dfrac{4}{5} + 3.21 + \dfrac{17}{32}\]
On rewriting all the terms in fraction,
We get,
\[\Rightarrow \ 4.56 – 0.8 + 3.21 + 0.50125\]
On simplifying,
We get,
\[\Rightarrow \ 7.47125\]
Thus we get the value of the expression \[4.56 - \dfrac{4}{5} + 3.21 + \dfrac{17}{32}\] is \[7.47125\]
The value of the expression \[4.56 - \dfrac{4}{5} + 3.21 + \dfrac{17}{32}\] is \[7.47125\] .

Note:
To solve these types of questions, we should proceed by converting the given fraction into the decimals. In order to convert the fraction into decimal , generally there are two ways to convert. First one is that if the denominator of the fraction can be converted to \[100\] by multiplying some number then we can multiply both numerator and denominator by the same number to get \[100\] in the denominator . Another method is that we can just divide the numerator by denominator to get the quotient in decimal.