Q3. - Algebra 1

Question

Evaluate each expression using the properties of numbers. Name the property used in each step.

3A. $\mathbf{2}\mathbf{.9}\mathbf{\cdot }\mathbf{4}\mathbf{\cdot }\mathbf{10}$

Step-by-Step Solution

Answer

The value of the expression is 116.

Step 1 –Write the formulae used

Associative property of multiplication:

$\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

Commutative property of multiplication:

$a\cdot b=b\cdot a$

Inverse property of multiplication:

$a\cdot \frac{1}{a}=\frac{1}{a}\cdot a=1$

Step 2 – Write the given information

The expression given is

$2.9\cdot 4\cdot 10$

Step 3 - DESCRIPTION OF STEP

To solve given expression first rewrite it as:

$2.9\cdot 4\cdot 10=\frac{29}{10}\cdot 4\cdot 10$

Now use commutative property and associative property to solve it as:

$\begin{array}{c}\frac{29}{10}\cdot 4\cdot 10=4\cdot \frac{29}{10}\cdot 10\\ =4\cdot \left(\frac{29}{10}\cdot 10\right)\\ =4\cdot \left(29\cdot 1\right)\text{ inverse property}\\ =4\cdot 29\\ =116\end{array}$

Hence, $2.9\cdot 4\cdot 10=116$