Question

Find the value of \[\left( {64.3 - 32.7} \right)\].

Answer 1

Hint: Here, we need to find the value of the given expression. We will rewrite the decimals as a sum of an integer and a decimal, and then rearrange the expression. Then, we will use addition and subtraction to find the value of the expression.

Complete step-by-step answer:
A decimal is a number where the integer part and fractional part are separated by a point, called a decimal.
For example: The numbers \[11.5,11.2,11.1\] are decimal numbers. The integer part of the numbers \[11.5,11.2,11.1\] is 11. The fractional part of the numbers \[11.5,11.2,11.1\] is \[0.5 = \frac{1}{2}\], \[0.2 = \frac{2}{{10}} = \frac{1}{5}\], and \[0.1 = \frac{1}{{10}}\] respectively.
First, we will rewrite the given numbers by separating their integer and fractional part.
The integer part of the number \[64.3\] is 64.
The fractional part of the number \[64.3\] is \[0.3\].
Writing the number \[64.3\] as a sum of its integer and fractional part, we get
\[64.3 = 64 + 0.3\]
The integer part of the number \[32.7\] is 32.
The fractional part of the number \[32.7\] is \[0.7\].
Writing the number \[32.7\] as a sum of its integer and fractional part, we get
\[32.7 = 32 + 0.7\]
Substituting \[64.3 = 64 + 0.3\] and \[32.7 = 32 + 0.7\] in the given expression \[\left( {64.3 - 32.7} \right)\], we get
\[ \Rightarrow 64.3 - 32.7 = \left( {64 + 0.3} \right) - \left( {32 + 0.7} \right)\]
Rewriting the expression, we get
\[ \Rightarrow 64.3 - 32.7 = \left( {64 + 0.3} \right) - 1\left( {32 + 0.7} \right)\]
Multiplying \[ - 1\] by \[32 + 0.7\] using the distributive law of multiplication, we get
\[ \Rightarrow 64.3 - 32.7 = 64 + 0.3 - 32 - 0.7\]
Rearranging the terms in the expression, we get
\[ \Rightarrow 64.3 - 32.7 = 64 - 32 + 0.3 - 0.7\]
Subtracting the number 32 from 64, we get
\[ \Rightarrow 64.3 - 32.7 = 32 + 0.3 - 0.7\]
Subtracting the decimal \[0.7\] from the decimal \[0.3\], we get
\[ \Rightarrow 64.3 - 32.7 = 32 - 0.4\]
Finally, subtracting the decimal \[0.4\] from the number 32, we get
\[ \Rightarrow 64.3 - 32.7 = 31.6\]
\[\therefore \] We get the value of the expression \[\left( {64.3 - 32.7} \right)\] as \[31.6\].

Note: We have used the distributive law of multiplication to multiply \[ - 1\] by \[32 + 0.7\]. The distributive law of multiplication states that \[a\left( {b + c} \right) = a \cdot b + a \cdot c\].
We can also use the same method by rewriting the number \[64.3\] as \[64.3 = 64 + 0.3\] and rewriting the number \[32.7\] as \[32.7 = 33 - 0.3\].