  ### Home > CC2 > Chapter 3 > Lesson 3.3.3 > Problem3-120

3-120.

Hilda was simplifying some numerical expressions and made each of the following sequences of calculations. Name the mathematical property, operation, or idea that justifies how Hilda went from each step to the next step.

1. $\begin{array}{l} 5\cdot\left(-\frac{4}{3}\right)\cdot \left(\frac{2}{5}\right) \\ =\left(-\frac{4}{3}\right)\cdot5\cdot \left(\frac{2}{5}\right) \\ =\left(-\frac{4}{3}\right)\cdot \left(5\cdot\left(\frac{2}{5}\right)\right) \\ =\left(-\frac{4}{3}\right)\cdot \left(\frac{2}{1}\right) =-\frac{8}{3}=-2\frac{2}{3} \end{array}$

If you are having trouble, review the mathematical properties in problems 3-113 and 3-116 before checking the answers.

Commutative Property of Multiplication

Associative Property of Multiplication

Multiplied the terms together

1. $\begin{array}{l} 17+29+3+1 \\ =17+3+29+1 \\ =\left(17+3\right)+\left(29+1\right) \\ =20+30 \\ =50 \end{array}$

For each step, think about what Hilda did to the expression. Was she grouping terms differently? Did she move any terms?