IM 7.5.13 Lesson: Expressions with Rational Numbers

Decide if the statement is true or false.
[math]\left(-38.76\right)\left(-15.6\right)[/math] is negative
Explain your reasoning.[br]
Decide if the statement is true or false.
[math]10000-99999[/math]<[math]0[/math]
Explain your reasoning.[br]
Decide if the statement is true or false.
[math]\left(\frac{3}{4}\right)\left(-\frac{4}{3}\right)=0[/math]
Explain your reasoning.[br]
Decide if the statement is true or false.
[math]\left(30\right)\left(-80\right)-50=50-\left(30\right)\left(-80\right)[/math]
Explain your reasoning.[br]
Group the expressions below into pairs that have the same value.
For each set of values for a and b, evaluate the given expressions and record your answers in the table.
[size=150]When [math]a=-\frac{1}{2}[/math] and [math]b=6[/math], which expression:[br][/size][br]has the largest value?
has the smallest value?[br]
is the closest to zero?[br]
[size=150]When [math]a=\frac{1}{2}[/math] and [math]b=-6[/math], which expression:[/size][br][br]has the largest value?
has the smallest value?
is the closest to zero?
[size=150]When [math]a=-6[/math] and [math]b=-\frac{1}{2}[/math], which expression:[/size][br][br]has the largest value?
has the smallest value?
is the closest to zero?
[size=150]Are there any values you could use for [math]a[/math] and [math]b[/math] that would make all of these expressions have the same value? Explain your reasoning.[/size]
[size=150]A seagull has a vertical position [math]a[/math], and a shark has a vertical position [math]b[/math].[/size][br][img]data:image/png;base64,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[/img][br][br]In the applet below, you may choose to start by clicking on the open circles on the seagull and shark to drag them to new vertical positions. Once you have them in place, drag each of the other animals to the vertical axis to show its position, determined by the expression next to it.[br][list=1][*]A dragonfly at [math]d[/math], where [math]d=-b[/math] [br][/*][*]A jellyfish at [math]j[/math], where [math]j=2b[/math][br][/*][*]An eagle at [math]e[/math], where [math]4e=a[/math].[br][/*][*]A clownfish at [math]c[/math], where [math]c=\frac{-a}{2}[/math][br][/*][*]A vulture at [math]v[/math], where [math]v=a+b[/math][br][/*][*]A goose at [math]g[/math], where [math]g=a-b[/math][br][/*][/list]
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Information: IM 7.5.13 Lesson: Expressions with Rational Numbers