Prime Factorization and Exponents
A number that has only two factors: 1 and itself.
Use front end estimation to find the product:
7.8903 x 2
7 x 2 = 14
List all the factors for 28.
1, 2, 4, 7, 14, 28
Find the quotient:
224 ÷ 8
28
Find the quotient. You may write a remainder if there is any.
536 ÷ 5
107 r1
Write the following in expression and standard form (answer).
exponential form = 53
expression = 5 x 5 x 5
standard from = 125
Define front-end estimation and give an example using a multiplication problem.
Front-end estimation is used when we keep the first digit of a number the same and the rest of the place values become zero. This type of estimation always underestimates the product.
For example:
378 x 2 would become 300 x 2
378 x 2 = 756 , while 300 x 2 = 600.
The product in the front-end is lower, so we underestimated.
Other student examples are subject to teacher review.
Jen earns $22.53 each time she washes a car. She washed 6 cars today. How much money did she earn?
Jen earned $125.18 washing 6 cars.
Use front-end estimation to find the quotient.
61.531 ÷ 3
60 ÷ 3 = 20
Find the quotient. Remember to round to the 100ths place.
14.07 ÷ 7
2.01
Prime factorize 780. Write an equation and draw a factor tree.
780 = 22 x 3 x 5 x 13
Factor tree will be checked by teacher.
Steve ran a route around his neighbourhood for 7 days straight. His route is 11.25km. How many km did Steve run in the 7 days?
Steve ran 78.75 km in 7 days.
Each batch of cookie mix need 0.4 cups of sugar, and each batch can make 16 cookies. If Ashley is making 4 batches of cookies, how much sugar does she need?
Ashley needs 1.6 cups of sugar to make 4 batches of cookies.
Find the quotient:
636.18 ÷ 6
106.03
Sam paid $6.85 for 3 ice cream treats. How much did each treat cost?
Each ice cream treat costs $2.28.
What number does the following prime factorization equal to?
33 x 37
999
On Jupiter, objects weigh 2.64 times as much as they weigh on Earth. How much would a 5.6 pound radio weigh on Jupiter?
The radio would weigh 14.784 pounds on Jupiter.
There are 420 mangoes in a barrel. Each mango weighs 0.75 kg. What is the total weight of mangoes in the barrel?
The total weight of mangoes in the barrel is 315 kg.
Use reasonableness to find the quotient:
Leah bought 3 coffees for her friends at work. The coffees cost her $9.29. Approximarely how much money did each coffee cost?
Possible reasonableness solutions:
9 ÷ 3 = 3
Each coffee cost about $3.00.
9.3 ÷ 3 = 3.1
Each coffee cost about $3.10.
Freebie!!
Correctly spell the name of both of Ms. Aida's cats.
Mr. Frodo. Frodo is also acceptable.
Totoro. Toto is also acceptable.
Prime factorize Ms. Aida's age. Write the prime factorization equation and draw a factor tree.
Ms. Aida is currently 30 years old.
30 = 2 x 3 x 5
Factor tree will be checked by teacher.
DAILY DOUBLE (1000 points!!)
The price of gas per gallon in the time of dinosaurs (AKA when Ms. Aida was a toddler) was $1.27. Since then, the price of gas has gone up by 232%. How much does gas cost today?
232% = 2.32
1.27 x 2.32 = 2.9464 (how much it has gone up by)
add to price of gas per gallon before price increase:
1.27 + 2.9464= 4.2164 rounded to 4.22.
So, the price of gas today is $4.22.
Use reasonableness to find the product:
4.67 x 5.928
Find the actual product and compare your results.
Reasonableness answers may vary, but here are a few possible options:
5 x 6 = 30
4.7 x 5.9 = 27.73
4.67 x 5.93 = 27.6931
Actual product = 27.68376
Comparison: All the estimated products are greater than the actual product.
At Squeeze Bar, Jim prepares 19.8 gallons of fresh orange juice. The juice is poured into small containers, carrying 6 gallons each. What is the number of small containers used to hold the orange juice?
The number of small containers used to hold orange juice is 4.
We used 3.3 of the containers, but we need to round up because we are asking how many containers were used. Although the decimal quotient is technically correct, it is not useful to others who may actually need to fill up those small containers because such a precise amount is hard to gauge visually.
Sam wraps his return gifts and keeps them in a bag weighing 3.3 pounds. The weight of each gift is 1.65 pounds. How many gifts are in the bag?
There are two gifts in the bag.