1
Prime, composite, or neither
97
Prime
Prime, composite, or neither
141
composite
Compare the fractions using <, >, or =
9/16 _____ 8/15
9/16 > 8/15
Write the prime factorization of each number in exponential form.
100
2^2 x 5^2
Write the prime factorization of the number in exponential form.
945
3^3 x 5 x 7
Find the GCF using prime factorizations.
54 = 2 x 3^3
30 = 2 x 3 x 5
2 x 3 = 6
Find the GCF of 84 and 120 using prime factorization.
84 = 2^2 x 3 x 7
120 = 2^3 x 3 x 5
GCF = 2^2 x 3 = 12
When are two numbers relatively prime?
when the GCF = 1
Identify the pair of relatively prime numbers within each set of numbers.
9, 20, 36
9 = 3^2
20 = 2^2 x 5
36 = 2^2 x 3^2
9 and 20 have a GCF of 1 meaning they are relatively prime.
Find the LCM of 10 and 15 using lists of multiples.
10, 20, 30, 40, 50
15, 30, 45, 60
LCM = 30
Find the LCM using prime factorizations.
108 = 2^2 x 3^3
72 = 2^3 x 3^2
2^3 x 3^3 = 8 x 27 = 216
Find the LCM using prime factorizations.
12, 24, and 80
12 = 2^2 x 3
24 = 2^3 x 3
80 = 2^4 x 5
LCM = 2^4 x 3 x 5 = 240
11/33
1/3
Reduce to lowest terms
24/108
2/9
Write each mixed number as an improper fraction.
6 4/5
34/5
-2 7/16
-39/16
Write the improper fraction as a mixed number.
49/4
12 1/4
Write the rational number as a reduced fraction.
4.2
42/10 = 21/5
Write the fraction as a decimal.
79/50
158/100 = 1.58
Find the missing number.
n/42 = 5/7
n = 30
20/n = 80/100
n = 25
Jim has three lawn jobs that are done every 7 days, 10 days, and 6 days. How often will he have to do all three jobs on the same day?
6 = 2 x 3
7 = 7
10 = 2 x 5
LCM = 2 x 3 x 5 x 7 = every 210 days
Kevin has a cactus that needs to be watered every 8 days and rotated every 12 days. How often will he have to do both on the same day?
8 = 2^3
12 = 2^2 x 3
LCM = 2^3 x 3 = every 24 days
When making up gift bags for a party, you have 110 hard candies, 90 packs of gum, and 40 candy bars. How many gift bags can you make if the contents of each gift bag are identical? How many of each item will be in each bag?
110 = 2 x 5 x 11
90 = 2 x 3^2 x 5
40 = 2^3 x 5
GCF = 2 x 5 = 10 bags
110 divided by 10 = 11 hard candies
90 divided by 10 = 9 packs of gum
40 divided by 10 = 4 candy bars
Amita is making up packages of electronic parts for sale at her store and has 84 batteries, 60 earbuds, and 12 car adapters. How many packages can be made with identical contents? How many of each item will be in each package?
84 = 2^2 x 3 x 7
60 = 2^2 x 3 x 5
12 = 2^2 x 3
GCF = 2^2 x 3 = 12 packages
84 divided by 12 = 7 batteries
60 divided by 12 = 5 earbuds
12 divided by 12 = 1 car adapter