[size=150]The [b]variables[/b] [math]a[/math] through [math]h[/math] all represent [i]different[/i] numbers. Mentally find numbers that make each equation true.[/size][br][br][math]\frac{3}{5}\cdot\frac{5}{3}=a[/math]
[math]7\cdot b=1[/math][br]
[math]c\cdot d=1[/math][br]
[size=150]The members increased their elevation 290 feet during their hike this morning. Now they are at an elevation of 450 feet.[/size][br][br]Explain how to find their elevation before the hike.
Han says the equation [math]e+290=450[/math] describes the situation. What does the variable [math]e[/math] represent?
Han says that he can rewrite his equation as [math]e=450+-290[/math] to solve for [math]e[/math]. Compare Han's strategy to your strategy for finding the beginning elevation.
[size=150]The temperature fell 4 degrees in the last hour. Now it is 21 degrees. Write and solve an equation to find the temperature it was 1 hour ago.[/size]
[size=150]There are 3 times as many students participating in the hiking trip this year than last year. There are 42 students on the trip this year.[/size][br][br]Explain how to find the number of students that came on the hiking trip last year.
Mai says the equation [math]3s=42[/math] describes the situation. What does the variable [math]s[/math] represent?
Mai says that she can rewrite her equation as [math]s=\frac{1}{3}\cdot42[/math] to solve for [math]s[/math]. Compare Mai's strategy to your strategy for finding the number of students on last year’s trip.
[size=150]The cost of the hiking trip this year is [math]\frac{2}{3}[/math] of the cost of last year's trip. This year's trip cost $32. [/size][size=150]Write and solve an equation to find the cost of last year's trip.[/size]
The numbers 0 and 1 are marked on the line, as are two other rational numbers [math]a[/math] and [math]b[/math].[br][br][img]data:image/png;base64,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[/img][br]Decide if [math]a-1[/math] is positive or negative.
Decide if [math]a-2[/math] is positive or negative.
Decide if [math]-b[/math] is positive or negative.
Decide if [math]a+b[/math] is positive or negative.
Decide if [math]a-b[/math] is positive or negative.
Decide if [math]ab+1[/math] is positive or negative.
What do you notice about the numbers and their inverses?