Question

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

3B.$\frac{\mathbf{5}}{\mathbf{3}}\mathbf{\cdot }\mathbf{25}\mathbf{\cdot }\mathbf{3}\mathbf{\cdot }\mathbf{2}$

Short answer

The value of the expression is 250.

Step-by-step solution

– 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:

localid="1648218764262" $a\cdot \frac{1}{a}=\frac{1}{a}\cdot a=1$

– Write the given information

The expression given is

$\frac{5}{3}\cdot 25\cdot 3\cdot 2$

- DESCRIPTION OF STEP

To solve given expression use commutative property and associative property to solve it as:

$\begin{array}{c}\frac{5}{3}\cdot 25\cdot 3\cdot 2=25\cdot \frac{5}{3}\cdot 3\cdot 2\text{commutativeproperty}\\ =25\cdot \left(\frac{5}{3}\cdot 3\right)\cdot 2\text{associativeproperty}\\ =25\cdot \left(5\cdot 1\right)\cdot \text{2inverseproperty}\\ =25\cdot 5\cdot 2\\ =25\cdot 10\\ =250\end{array}$

Hence,$\frac{5}{3}\cdot 25\cdot 3\cdot 2=250$