Order of Operations & Positive & Negative Numbers
Simplify -13 + -2
-13 + -2
-15
Ezekiel and three friends work for for 177 3/5 hours. What is the average number of hours each friend works?
(177 3/5) /4 = (888/5)/4=(888/5) * 1/4 = (888/20)=44 8/20=44 2/5
Evaluate the expression for the given value of the variable (plug in the number) 7(n + 3) if n = -4
7(-4 + 3) if n = -4
7(-4+3) = 7(-1)
-7
Pizzas are $19 each. You need 4 pizzas for a party. What is the cost of 4 pizzas before tax? Solve without a calculator using the distributive property.
$76
4 (19) = 4 (10 + 9) = 40 + 36 OR
4(19)= 4(20-1) = 80-4 = $76
548/4=137/1
heart beat 548 times in 4 minutes
Simplify -15 - 36 div 3^2
-15 - 36 div 3^2
-15 - (36div9)
-15-4 = -19
Casey buys 12 gel pens for $15.00. What is the unit rate?
$1.25 per pen 15/12 = 1.25
12 gel pens for $15.00
Simplify 3x + 5x^2 - 7x^2
3x + 5x^2 - 7x^2
3x + -2x^2
Solve for the variable r/238 =3
r= 714
r/238 =3
238(r/238) =3(238)
To make 4 large pizza pockets, Jeremiah needs 14 cups of cheese. How much cheese does he need for just 1 large pizza pocket?
3.5 cups per 1 pizza pocket 3.5/1
cups/# of pizzas = 14/4
14/4 = 3.5/1
Simplify 2(4+3)^2 - 8
2(4+3)^2 - 8
2(7)^2 - 8
2(49) - 8
98 - 8 = 90
Add
1/3 + 2/5
1/3 + 2/5
5/15 + 6/15
11/15
Write as an algebraic expression: The quotient of a number and 12
The quotient of a number and 12
n/12
Solve for the variable
3.6m = 25.2
m = 7
Divide both sides by 3.6 to isolate m
(3.6 m)/3.6 =( 25.2)/3.6
Are these ratios proportional? 8/24, 6/20
No. 8/24 simplifies to 1/3 while 6/20 simplifies to 3/10 These fractions are are not equal. We could also turn both ratios into decimals (0.3333 does not equal .3) or use cross products
To join a gym, Simon pays a $75 enrollment fee and $32 per month. Write an algebraic expression to represent the total cost of m months, including the enrollment fee.
$75 +32m
$75 enrollment fee and $32 per month
Subtract
-4/11 - 4/44
-4/11 - 4/44
-4/11 - 1/11
-5/11
Write as an algebraic expression: 20 minus the product of 8 and a number
20 minus the product of 8 and a number
20-(8*n)
20 - 8n
d/(8) =12
d = 96 Multiply both sides by 8 to "undo" division
8(d/8)=12(8)
d = 96
Solve using cross products p/6=10/3
p= 20
p/6=10/3
10 * 6 = p*3
60/3=(3p)/3
20=p
Draw this shape and write an expression for the perimeter of a trapezoid with a base of n + 4, the second base is n+ 6, and the two sides are 3n.
base of n + 4, the second base is n+ 6, and the two sides are 3n.
(n +4) + (n + 6) + (3n) +( 3n)
8n +10
If distance = rate x time, and Khloe drives 65 mph for 4.3 hours, how far does she travel?
d = rt Khloe drives 65 mph for 4 hours and 12 minutes (12/60 minutes = 1/5 of an hour= 0.2)
d = 65(4.2) = 273 miles
Solve for the variable d -15 = 45
d =60
d -15 = 45
d -15 + 15 = 45 + 15
Collin earned $230 for 40 hrs of work while Hazel earned $192 for 32 hours of work. Are their pay rates proportional?
No. Collin's hourly rate is ($230)/(40hr)=$5.75/(1hr)
while Hazel's hourly rate is ($192)/(32hr)=$6/(1hr) ($192)/(32hr)=$6/(1hr)
Thus, Hazel make's $0.25 more per hour than Collin does. (Collin should work for whomever Hazel is working for!)
Density is the ratio of a substance's mass to its volume d = (mass)/(volume). The density of ice is 0.92 grams per 1 mL. What is the mass of (or how many grams are in) 3 mL of ice?
mass of 3 mL of ice = 2.76 grams
d = (mass)/(volume) set up proportion with mass (grams) as numerator, volume (mL) as denominator
(0.92 grams)/(1 mL) = (m grams)/ (3 mL)
use cross products m*1=3*0.92
m = 2.76 grams