constant of proportionality
scaled factoring
tax, tip, discount
6th grade math
rational numbers
100
Based on the graph, how much would it cost for 5 pizzas?
$9.00 (because 18/10 = 1.80 x 5 = 9.00
100
Jimmy is creating an enlargement of the image shown for an art gallery.
Note: Figure not drawn to scale.
He needs the enlargement to follow the scale of 1/2 of a foot to 3 feet. This will result in an image with a length of 6 feet and width of 4 feet.
What is the scale factor for the area of the enlarged image?
72 ft.
Because 1/2 x 2/3 =1/3 and 6 x 4 = 24
so 24 / 1/3 = 72
100
Pierre bought a box of cookies originally priced at $35. He used a 25% discount on the original price. What is the total amount that Pierre paid for the box of cookies after the discount?
$26.25
because 35 x 0.75 (which is 100-25) = 26.25
or 35 x 0.25 =8.75, then subtract 35 - 8.75
100
What is the distance between the points (-1, 3) and (9, 3) in the coordinate plane?
10 units
because l-1 + l9l=10
100
Simplify the expression.
(-19 - 9) - (9 + 9)
-46,
because (-19 - 9) = -28 - and (9 + 9)=18
then -28 - 18 = -28 + -18 = -46
200
Randy drove to the mountains at a constant rate of speed (r) for a vacation. In the equation below, r is the miles per hour that Randy drove to get to his destination.
2.5r = 105
What was Randy's rate of speed?
42 miles per hours. Because 105/2.5 = 42
200
Figure KLMN is a scaled version of figure PQRS. The two figures are shown below.
If KN = 6 cm, MN = 27 cm, RS = 108 cm, and PS = 24 cm, what is the scale factor of figure PQRS to figure KLMN?
1/4 cm
because RS =108 and MN = 27
and 108 x 1/4 = 27
Big to small is fractional. Small to big is a whole number
200
Mr. Davies opened a new retail store. During the first week, 300 customers visited the store. During the second week, 250 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
A. a 16.7% decrease
B. a 16.7% increase
C. a 20% decrease
D. a 20% increase
A.
because 300-250= 50 and 50/300
200
There are 30 students in the 6th grade at Garden Valley Middle School. Eight of them have freckles. What percentage of 6th graders have freckles?
26 2/3 %
because 30 / 8 = 0.2666666... and we don't write percentages with repeating decimals. and 6 repeating is 2/3
200
simplify
2 1/4 - (- 9 1/2)
11 3/4 or 11.75
because 2 1/4 + 9 1/2= 11 3/4
or 2.25 + 9.5 =
300
A blueprint for a house shows the height of the house to be 1 1/2 inches. The actual house is 26 2/5 feet tall. What is the unit rate in feet per inch?
A. 56/1000 feet per inch
B. 396/10 foot per inch
C. 17 3/5 foot per inch
D. 39 6/10 feet per inch
C.
because 26 2/5 / 1 1/2
300
If the area of the smaller rectangle is 24 inches2, what is the area of the larger rectangle?
A. 33 inches2
B. 216 inches2
C. 240 inches2
D. 72 inches2
B 216
because when a side length is tripled the are is multiplied by 9, so 24 x 9 = 216
300
Gia opened two savings accounts at two different banks. One account earns an annual 3.4% simple interest, and the other earns half as much.
If she deposited $500 in each account, how much total interest will she have earned in 2 years?
A. $34.00
B. $102.00
C. $51.00
D. $510.00
C.
because 500 x 0.034 = 34 and 500 x 0.017 = 17, then 17 + 34 =51
300
Of the students at Milton Middle School, 190 are girls. If 50% of the students are girls, how many total students are there at Milton Middle school?
A. 190
B. 475
C. 380
D. 285
C
because 190 represents 50% then 190 represents the other 50%, so 190 + 190 = 380
300
A submarine is 255 feet below the surface of the water. The sub can ascend upwards at 50 foot stages. How many stages will it take him to get back to the surface?
6 stages
because l-255l / l50l = 5.1 round up to the nearest whole stage, because its still under water, just saying.
400
At the school fall festival, the student council sold sodas as a fundraiser. The table below shows the number of sodas they sold and the cumulative total money.
Sodas Sold Money Collected
0 $0.00
2 $6.60
5 $16.50
9 $29.70
10 $33.00
Based on the information, what is the price for 12 sodas?
$39.60
because 6.60/2 = 3.30 x 12 = 39.60
400
The dimensions of an office conference room are 8 feet by 16 feet. If the conference room blueprint dimensions are 4 centimeters by 8 centimeters, what is the scale of the blueprint?
A. 1 centimeter = 4 feet
B. 1 centimeter = 6 feet
C. 1 centimeter = 8 feet
D. 1 centimeter = 2 feet
D
because 4 x 2 = 8 and 8 x 2 = 16
400
Eloise bought a pair of shoes originally priced at $105. She used a 30% discount on the original price, and then she paid a 5% sales tax on the purchase price. What is the total amount that Eloise paid for the shoes?
$ 77.18
Because 105 x .70 =73.50, then 73.50 x 1.05= 77.18
400
Pounds ounces
6 96
7 112
? 176
What is the missing value in the table above when comparing ounces and pounds?
11 pounds
because 96 x 1/16 = 6 and 176 x 1/16 = 11
400
Simplify the following complex fraction.
3 + 4/5
_______
1/3
57/5 or 11.4 or 11 2/5
because 3 + 4/5 = 19/5 x 3 (which is the reciprocal of 1/3) = 57/5. You could also do 3.8 x 3
500
The students at Bain Elementary school sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with tickets selling for d dollars.
How much did each ticket cost?
$746.75 = 103d
$7.25 per ticket
because 746.75 / 103 = 7.25
500
Note: Picture is not drawn to scale.
Triangle A is a scaled version of triangle B. The dimensions of triangle B are three times the dimensions of triangle A. The area of triangle A is 4 sq cm.
What is the area of triangle B?
A. 12 sq cm B. 16 sq cm C. 24 sq cm D. 36 sq cm
D
because triangle areas are 9 times the area when scaled by 3 times or 4 x 9 =36
500
A family of six went out to dinner at Char-bar. All 6 of them ordered the buffet and drink at $11.95 per person. They left a 20% gratuity (tip) for the waitress, they ended up paying a total of $ __________for their dinner.
$86.04
because 11.95 x 6 = 71.70, then 71.70 x 1.2
or 71.70 x 0.20 = 14.34, then 71.70 + 14.34 = 86.04
500
A robot packs boxes in a factory. It runs at a constant speed, and packs 5 boxes in 9 minutes. If the robot operated for 144 minutes on Monday, how many boxes did it pack?
80 boxes,
because 144 / 9 = 16 and 16 x 5 = 80
500
Mr. Rico's small business is starting to make a profit. His costs last week were -$1560. His profit last week was $195. How many times are his costs than his profit?
A. -8 times
B. -195 times
C. 1365
D. -1755
A. -8
because -1560 / 195 = -8
and -8 x 195 = -1560