Question

1. circle each expression that is equivalent to 38 × 45.

(38 + 40) × (38 + 5)
(38 × 40) + (38 × 5)
45 × (40 + 2)
45 thirty - eights

1. true or false? explain how you know:

57 × 2 × 10 × 10 × 10 = 570 × 2 × 10

Explanation:

3)

Step1: Simplify each expression

• For \((38 + 40)\times(38+5)\):

$$
LATEXBLOCK0
$$

• For \((38\times40)+(38\times5)\):

Using the distributive property \(a\times(b + c)=a\times b+a\times c\) (here \(a = 38\), \(b=40\), \(c = 5\)), \((38\times40)+(38\times5)=38\times(40 + 5)=38\times45\)

• For \(45\times(40 + 2)\):

$$
LATEXBLOCK1
$$

• For \(45\) thirty - eights: \(45\) thirty - eights means \(45\times38\) (by the definition of multiplication as repeated addition, \(n\) times \(m\) is \(n\times m\))

Answer:

The expressions \((38\times40)+(38\times5)\) and \(45\) thirty - eights are equivalent to \(38\times45\)

4)

Step1: Simplify both sides

• Left - hand side: \(57\times2\times10\times10\times10=57\times2\times10^{3}=114\times1000 = 114000\)
• Right - hand side: \(570\times2\times10=(57\times10)\times2\times10=57\times(10\times2\times10)=57\times200 = 11400\)