Unit 1
Fraction Times
Fraction Times
Of the 180 students in the 7th grade, 2/3 of them are on a sports team and 1/4 of those on a sports team are on the basketball team.
The fraction of 7th graders on the basketball team is this...
What is 1/6?
We are looking for 1/4 of the 2/3 that play sports, because 1/4 of them play basketball so that means we have to multiply.
1/4 x 2/3 = 2/12 which is 1/6 in simplest form.
The percents 75 and 33 1/3, when written as fractions, are these....
What are 3/4 and 1/3 ?
Dave has a car and it gets 28 miles per gallon.
If he drove 112 miles, the total gallons of gas Dave used, is this.....
What is 4 gallons?
112 miles / 28 mpg = 4 gallons of gas
Computing 50 - 5 x 4 (3 + 2) will give you this answer...
What is - 50?
50 - 5 x 4 (3 + 2)
50 - 5 x 4 (5)
50 - 5 x 20
50 - 100
-50
Sharon left Laguardia Airport in New York at 4pm on a 6-hour flight to San Diego, California.
The time in California when she arrives, will be this...
What is 7pm Pacific Standard Time (PST)?
If it is a 6-hour flight, then leaving in NY at 4pm means she'll land when it is 10pm in NY.
Since California is 3 hours behind NY in time zones, 10 - 3 = 7pm PST.
Of the 200 students in 6th grade, 3/4 participate in sports and 2/5 of those students who are active in sports are on the swim team.
The number of 6th graders on the swim team is this....
What is 60?
3/4 of 200 participate in sports. We multiply 200 x 3/4 and get 150.
Since 2/5 of those 150 are on the swim team, we multiply 150 x 2/5 and get 60.
60% of 240 is this.....
What is 144?
240 x 0.60 = 144
Carter drove 1,990 miles over the course of 25 hours.
His average rate of speed, was this...
What is 79.6 mph?
1,990 / 25 = 79.6
Designing an arithmetic tree to solve the following expression, 12 + 18 - 6 x 2 , will give you this...
What is 18?
12 18 6. 2
x
12
+
30
-
18
The temperature in Helsinki, Finland overnight was -5o Celsius. By the end of the next day, the temperature was 2o Celsius. The total change in temperature was this....
What is 7 degrees?
To go from -5o up to +2o means you had to cross 0o
That is a total distance of 7o
24 teachers were interviewed and asked what is their favorite type of music.
0 chose Rap. 10 chose Classical. 5 chose Jazz. 9 chose Rock. 0 chose Alternative.
The percentage of teachers whose favorite type of music is Rock is this....
What is 37.5%?
9/24 = .375
.375 x 100 = 37.5%
The original recipe for Grandma's famous apple pie had a total calories count of 1,200 calories per serving.
We found a healthier alternative by substituting butter with apple sauce. This makes each serving 1/5 less calories, or this total amount of calories....
What is 960 calories?
1/5 less the calories of 1,200 means that we have to find 1/5 of 1,200 (multiply) and then subtract it from 1,200 ("less").
1/5 of 1,200 = 240.
1,200 - 240 = 960 calories.
Christopher was looking at a map of a state he was interested in visiting.
The map legend showed it was 50 miles for every 1/2 inch on the map.
The total mileage for 7.5 inches on the map, is this...
50m per 1/2inch is the same as 50/0.5
50/0.5 = 100
100 = x / 7.5
x = 750
A cell phone company created a formula to explain their charges per month. The variable m means "mintues".
The formula is : Total Cost = $60.00 + $1.75m
The numbers in this formula represent this....
What is $60.00 for the flat monthly rate plus $1.75 for each minute.
The temperature one week in NYC was as follows:
Sun Mon Tues Wed Thurs Fri Sat
-2 4 -4 5 -3 -2 1
The mean temperature that week to the nearest degree, was this....
What is 0 degrees?
Adding all of these up gives us a -1o answer.
-1o / 7 = -0.142857.....
To the nearest degree on a temperature scale, it is closer to 0o than -1o
Mr. M has 24 students very interested in music.
1/2 of the students play one instrument.
1/4 of the students play two instruments.
1/6 of the students play three or more instruments.
The fraction of students who play two or more instruments is this...
What is 5/12?
1/4 + 1/6 = 3/12 + 2/12 = 5/12
Joe is making a poster for his history class. He first sketched it out in a drawing that measure 8.5 x 11 inches.
The poster will be 150% of this drawing size.
The poster dimensions will be this.....
What is 12.75 x 16.5 inches?
150% larger means we multiply each measurement by 1.5
8.5 x 1.5 = 12.75
11 x 1.5 = 16.5
Two different items are being looked at underneath 2 different microscopes.
Item 1 and Item 2 are both the same size to the eye right now, but were magnified at different sizes to get that size.
Item 1 was magnified 1,000x and Item 2 was magnified 10,000x.
The item that is bigger in real life, is this....
What is item 1?
A magnification means it has to be enlarged.
The higher the magnification number is, the smaller the item really is in real life.
A magnification of 1,000x is not as much of an enlargement than an item of 10,000x magnification.
Joe's Construction Company called "JCC", charges their customers $45 travel cost for each worker plus each worker gets $75 per hour.
The amount JCC would charge a customer for 4 employees to do a 6 hour job, is this....
What is $1,980?
1 employee is $75 x 6 + $45 = $450 + $45 = $495
4 employees = $495 x 4 = $1,980
True or False:
A positive number added to a negative number always gives a positive number.
What is FALSE?
When the negative number is larger than the positive number, the answer will be a negative number.
10 - 12 = -2
75 - 100 = -25
The price of 3 items at $1.76 each and 4 items at $2.31 each is this....
What is $14.52?
3($1.76) + 4($2.31)
$5.28 + $9.24 = $14.52
Elaine's grandparents started a college fund for her on her 12th birthday. They put $500 in a savings account that earns 5% interest every year.
The balance she has after 4 years, is this....
What is $607.75 ?
For 4 years, we would have a 5% interest on top of the 100% value of the $500.
So its 1.05 x 1.05 x 1.05 x 1.05 x 500 = $607.75
Another way to write this is
y = $500 x (1.05)4
The school basketball team has won 10 games and lost 5 games.
The ratio of wins to losses is 10:5
If they end up playing a total of 60 games, the ratio of total wins : total losses will be this...
What is 40:20?
They have won 10 games out of 15, so the fraction 10/15 has to be equal to x / 60
10/15 = x/60
2/3 = x/60
120 = 3x
x = 40
If they win 40, they lost 20
Write an arrow string, starting with hours worked & ending with total cost, if a company charges a $75 travel fee per worker, plus $95 per hour on a job that requires 5 workers and 8 hours to finish it....
x95 +75 x5
8 ---> $760 ---> $835 --->$4,175
Triangle ABC has coordinates:
A (0, 0) B (4, 0) C (0, 4)
If we have this preimage and dilate it +3, the coordinates of A'B'C' will be this...
What is
A'(0 , 0)
B'(12, 0)
C'(0, 12) ?
A dilation means that is how much bigger or smaller an image will be. A dilation of +3 means Triangle A'B'C' will be 3 times larger. We must multiply 3 by every coordinate's (x,y) values.