Expressions with Rational Numbers: IM 7.5.13
[url=https://im.kendallhunt.com/MS/teachers/2/5/13/preparation.html]“Expressions with Rational Numbers”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table des matières
- Lesson 7.5.13
- IM 7.5.13 Lesson: Expressions with Rational Numbers
- Practice 7.5.13
- IM 7.5.13 Practice: Expressions with Rational Numbers
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]
IM 7.5.13 Practice: Expressions with Rational Numbers
The value of [math]x[/math] is [math]-\frac{1}{4}[/math]. Order these expressions from least to greatest:[br][br][math]x[/math] [math]1-x[/math] [math]x-1[/math] [math]-1\div x[/math]
[size=150]Here are four expressions that have the value [math]\frac{-1}{2}[/math]:[br][/size][br][math]-\frac{1}{4}+\left(\frac{-1}{4}\right)[/math] [math]\frac{1}{2}-1[/math] [math]-2\cdot\frac{1}{4}[/math] [math]-1\div2[/math][br][br]Write a sum that has the value [math]\frac{-3}{4}[/math].
Write a difference that has the value [math]\frac{-3}{4}[/math].
Write a product that has the value [math]\frac{-3}{4}[/math].
Write a quotient that has the value [math]\frac{-3}{4}[/math].
Write an expression that involves at least two operations that has the value [math]\frac{-3}{4}[/math].
Find the value of each expression.
[math]-22+5[/math]
[math]-22-\left(-5\right)[/math]
[math]\left(-22\right)\left(-5\right)[/math]
[math]-22\div5[/math]
[size=150]The price of an ice cream cone is $3.25, but it costs $3.51 with tax. What is the sales tax rate?[/size]
Two students are both working on the same problem: A box of laundry soap has 25% more soap in its new box. The new box holds 2 kg. How much soap did the old box hold?
[list][*]Here is how Jada set up her double number 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[/img][br][br][br][list][*]Here is how Lin set up her double number line.[/*][/list][img]data:image/png;base64,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[/img][br][br][br]Do you agree with either of them? Explain or show your reasoning.
A coffee maker’s directions say to use 2 tablespoons of ground coffee for every 6 ounces of water. How much coffee should you use for 33 ounces of water?
A runner is running a 10 km race. It takes her 17.5 minutes to reach the 2.5 km mark. At that rate, how long will it take her to run the whole race?