Question

How do you simplify the given sum $3\left( 2-0.9h \right)+\left( 1.3h-4 \right)$?

Answer 1

Hint: We start solving the problem by equating the given sum to a variable. We then recall the distributive property as multiplication distributes over addition which is represented as $a\left( b\pm c \right)=ab\pm ac$. We make use of distributive for one of the terms present in the given sum. We then make use of the associative property of multiplication $a\times \left( b\times c \right)=\left( a\times b \right)\times c$, to proceed through the problem. We then make the necessary calculations involving multiplication, addition and subtraction operations to get the required answer.

Complete step by step answer:
According to the problem, we are asked to simplify the given sum $3\left( 2-0.9h \right)+\left( 1.3h-4 \right)$.
Let us assume $S=3\left( 2-0.9h \right)+\left( 1.3h-4 \right)$ ---(1).
Let us recall the distributive property.
From the distributive property, we know that multiplication distributes over addition which is $a\left( b\pm c \right)=ab\pm ac$. Let us use this in equation (1).
$\Rightarrow S=\left( 3\times 2 \right)-3\left( 0.9h \right)+1.3h-4$ ---(2).
From associative property of multiplication, we know that $a\times \left( b\times c \right)=\left( a\times b \right)\times c$. Let us use this result in equation (2).
$\Rightarrow S=6-\left( 3\times 0.9 \right)h+1.3h-4$.
$\Rightarrow S=2-2.7h+1.3h$.
$\Rightarrow S=2-1.4h$.
So, we have found the simplified form of the given sum $3\left( 2-0.9h \right)+\left( 1.3h-4 \right)$ as $2-1.4h$.

$\therefore $ The simplified form of the given sum $3\left( 2-0.9h \right)+\left( 1.3h-4 \right)$ is $2-1.4h$.

Note: Whenever we get this type of problems, we try to make use of standard properties of the real numbers to get the required result. We should not make mistakes while performing the subtraction of coefficients of the terms h while solving this problem. We should keep in mind that the subtraction of the coefficients of the terms h and constant terms has to be performed individually. Similarly, we can expect problems to find the simplified result of $\left( a+bx \right)x-2\left( c+dx+e{{x}^{2}} \right)$.