Question

. Find the value of each expression. Show your work. (a) 1.42 (b) 300 = 2(0.5 +4.5) ? 3 ) te) -23

Answer 1

For the first expression, we have 1.4², this can be expressed as 1.4×1.4 and then we get:

$1.4^2=1.4\times1.4=1.96$

For the second expression, 300 ÷ 2(0.5 + 4.5)² we must start by solving the sum inside the parenthesis, then we get:

300 ÷ 2(0.5 + 4.5)² = 300 ÷ 2(5)²

Then, solve the exponent on the right of the division symbol:

300 ÷ 2(5)² = 300 ÷ 2×25

Now, solve the multiplication

300 ÷ 2×25 = 300 ÷ 50

Now, we can solve the division

300 ÷ 50 = 6

Then, 300 ÷ 2(0.5 + 4.5)² = 6

For the last expression, we must start with the exponent:

$\begin{gathered} \frac{1}{3}\div2(\frac{1}{2})^3 \\ \frac{1}{3}\div2\times\frac{1}{2^3} \\ \frac{1}{3}\div2\times\frac{1}{8}^{} \end{gathered}$

Now we can solve the multiplication:

$\frac{1}{3}\div2\times\frac{1}{8}^{}=\frac{1}{3}\div\frac{2}{8}^{}$

In order to divide one fraction by another one we just have to keep the first fraction unchanged, change the ÷ for a × and flip the second fraction, like this:

$\frac{1}{3}\div\frac{2}{8}^{}=\frac{1}{3}\times\frac{8}{2}=\frac{1\times8}{3\times2}=\frac{8}{6}=\frac{4}{3}$

Then, the value of the last expression is 4/3