Factor Masters (GCF)
Find the greatest common factor (GCF) of 12 and 18.
6
Find the least common multiple (LCM) of 8 and 12.
24
Write the ratio of 15 apples to 12 oranges as a fraction in simplest form.
5:4
A grocery store sells a pack of 5 pens for $6.25. Write this rate as a unit rate in dollars per pen.
$1.25 per pen
Determine if these two rates are equivalent: $135 raised for washing 15 cars, and $225 raised for washing 25 cars. Explain your reasoning.
Yes, they are equivalent.
Find the GCF of the set of numbers: 16, 24, and 40.
8
Find the least common multiple (LCM) of 15 and 20.
60
A pet shelter has 6 puppies, 15 kittens, 5 birds, and 4 hamsters. Find the ratio of kittens to the total
number of animals. Write your ratio in simplest form.
1:2
A delivery truck travels 345 miles in 5 hours. At this rate, how far does the truck travel per hour?
69 miles per hour
If 15 identical boxes of crayons contain a total of 360 crayons, how many crayons are in 8 of these boxes?
192 crayons
A baker has 36 chocolate chip cookies and 48 sugar cookies. She wants to pack them into identical bags with no cookies left over. What is the greatest number of bags she can make?
12 bags
Maya visits the library every 6 days, goes swimming every 4 days, and plays tennis every 8 days. If
she did all three today, in how many days will she do them all on the same day again?
24 days
In a school club, the ratio of boys to girls is 3:5. If there are 40 girls, how many boys are there? How
many total members are in the club?
24 boys and 64 total members
Explain the difference between a rate and a unit rate in your own words, and give an example of each.
A rate is a comparison of two quantities measured in different units (e.g., 120 miles in 2 hours). A unit rate is a simplified rate where the second quantity is exactly 1 unit (e.g., 60 miles per 1 hour, or 60 mph).
After working for 12 hours, Sophia earned $180. After working for 20 hours, she earned $300. Predict how much she would earn after 35 hours of work at this rate.
$525
Three ribbons have lengths of 24 cm, 36 cm, and 60 cm. If they are cut into equal pieces of the maximum possible length with no ribbon left over, how many total ribbon pieces will there be?
10 Pieces
A red light flashes every 10 seconds, a blue light flashes every 12 seconds, and a green light flashes
every 15 seconds. If they all flash together at exactly 12:00 PM, how many times will they flash
together between 12:00 PM and 12:10 PM (excluding the 12:00 PM flash)?
10 times
An artist is creating a mosaic using red, blue, and white tiles. The ratio of red to blue to white tiles is 3:5:8. If she uses 40 blue tiles, how many red and white tiles does she need, and what is the total number of tiles?
24 red, 64 white, and 128 total tiles
Brand A sells an 18-ounce box of cereal for $4.50. Brand B sells a 24-ounce box of the same cereal
for $5.76. Which brand is the better buy? Explain by finding the unit rate for each.
Brand B is the better buy
To make a certain shade of orange paint, a painter mixes 3 drops of red paint for every 5 drops of yellow paint. First, if she uses 45 drops of yellow, how many drops of red does she need? Second, if she wants to make a total of 120 drops of orange paint, how many drops of each color does she need?
First: 27 drops of red. Second: 45 drops of red and 75 drops of yellow
Leo is asked to find the GCF of $24$ and $36$. He writes: "The GCF is 6 because 6 goes into both 24 and 36 evenly.
The Scenario: Sarah is asked to find the LCM of 6 and 8. She writes: "To find the least common multiple of 6 and 8, I just multiply them together: $6 x 8 = 48. So the LCM is 48.
A class has 12 boys and 18 girls. Jack is asked to write the ratio of boys to the total number of students in simplest form. Jack writes: "The ratio of boys to girls is 12 to 18, which simplifies to 2 to 3."
The Scenario: Emily is finding the unit rate for a store selling 4 notebooks for $5.00. She divides 4 by 5 and says: "The unit rate is $0.80 per notebook."
Lamar earns $375$ for 25 hours of work4. To predict how much Lamar would make in 10 hours, Marcus writes: "Since 25 hours minus 15 hours is 10 hours, he will make $375 minus $15, which is $360."