About Fractions
The denominator of a fraction tells you this.
How many parts make up one whole?
Percents are always "out of" this value.
100
Greg is mixing batter for some pancakes. He adds 2 cups of water for every 3 scoops of pancake mix.
What is the ratio of pancake mix to water shown in three formats?
[3 : 2] [3 to 2] [3/2]
Galinda and Elphie are begrudgingly sharing a pizza in their dorm room. Galinda eats 1/3 and Elphie eats 2/5.
They ate this much pizza altogether.
11/15
If a pizza is cut into 10 slices and you eat 30% of it, this is how many slices you ate.
What is 3 slices?
Division.
Explain your strategy for converting fractions to percentages. Provide an example.
1) Use multiplication to find an equivalent fraction that is out of 100.
2) Divide numerator by denominator, then multiply final answer by 100.
Rene ran for 16 minutes and was able to make it around his neighborhood park 4 times. Name the ratio that demonstrates the relationship between laps run and minutes spent.
1 lap : 4 minutes
Giulio has 11/12 of a bag of flour at home. For a fresh pasta recipe, he needs to use 1/2 the bag for the pasta dough, and then 1/5 of the bag for dusting the counter, rolling it out, and preparing it properly.
After he prepares his pasta, he will have this much of the original bag of flour.
**Create an operation to express this problem for 50 bonus points.**
What is 13/60 of the bag?
A store is having a 25% off sale on a $40 jacket. This is how much money you save.
What is $10?
When a fraction has a higher value in the numerator than the denominator we call it this.
Improper fraction.
This is the difference between a part-to-part ratio, and a part-to-whole ratio. Provide an example.
A PTP ratio compares part of a group to another part of the group. A PTW ratio compares a part of the group to the whole group.
Examples will vary.
After the Winter holidays, candy canes are being sold for a special price. The local candy store is offering 25 candy canes for $3.00.
At this price, what is the unit rate?
$ 0.12 per candy cane
When finding a fraction of a fraction, we use this operation.
What is multiplication?
Out of 60 students in a class, 40% like soccer as their most preferred team sport to play. This is how many students like soccer the most.
What is 24 students?
When adding fractions, why must denominators match? Explain with a picture model.
Because to combine the values correctly, you need to be working with all the same size parts--so you must find a common denominator to make sure your wholes are divided in the same way.
A "unit rate" provides this information. Give an example.
The cost/value of one item/unit when priced by group.
Charlotte has been taking measurements in her garden to track plant growth. She noticed that every time her catnip plant grows 3 inches, her basil plant only grows 2.
If her catnip plant is now 15 inches tall, her basil plant is this tall.
What is 10 inches?
Margaret knows that 1/4 of the students at her school play a sport. Of those students, 2/3 of them play team sports.
This fraction of the total student body plays on a team.
A pro-level jersey originally costs $180. Justina's mom said she can't buy it until it goes on sale with a discount.
Finally, Justina finds a coupon for a 30% discount. With the coupon, this is the new price of the jersey.
What is $126?
A fraction is typically this type of ratio.
Part to Whole
How is a percentage like a fraction/PTW ratio?
Main point: They each compare two values where one of the values is a subset/group within the whole group and the other value is the size of the whole group. In a percent, the value that represents the whole group is 100.
Hailey and her parents have struck a deal about screen-time at his house. Hailey is allowed to spend 5 minutes gaming for every 3 minutes she spends on chores.
If Hailey spent a total of 160 minutes on chores and gaming yesterday, she spent this much time on just chores.
What is 60 minutes?
Fabiana is doing a study of musical theatre's popularity in her cohort. She took several polls to do this and found:
1/2 of her peers have seen Wicked the movie.
3/5 of those students have also seen the musical on stage.
Of the students that have seen BOTH, 1/3 know the lyrics to all the songs.
Assume that the students who have never seen either do not know the music.
This fraction of students know all the songs' lyrics.
What is 1/10 of the students?
A school's population increased from 400 students to 500 students.
This is the percent increase in the population.
What is 25%?