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Accelerated Math 6/7
Lessons 4.1, 4.2, 4.3, 4.4 Study Guide
Vocabulary:
Prime Number – a whole number greater than one whose only factors are 1 and itself
Composite Number – a whole number greater than one with two or more factors
Factor – numbers that when multiplied together equal a larger number; the 2 numbers
that are multiplied together to equal a larger number
Multiple – the product of the number and any nonzero whole number; you multiply the
original number by 1, then by 2, then by 3, then by 4, etc.
Relatively Prime – if the greatest common factor of 2 numbers is “1”, then the numbers
are called “relatively prime”
Equivalent Fraction – fractions that represent the same amount
Numerator – the top number in a fraction
Denominator – the bottom number in a fraction
Simplest Form – when the greatest common factor of the numerator and denominator is
“1”; when both the numerator and denominator cannot be divided by the same number
4.1 Prime Factorization
Write the first 8 prime numbers: __2__, ___3_, __5__, __7__, __11_, __13_, __17_, __19_
Write the prime factorization of the following numbers by making a factor tree (give your
answer using exponents if possible);
100
22 x 52
54
144
64
2 x 33
24 x 32
26
4.2 Greatest Common Factor
Find the GCF of the following numbers using any method:
75, 285 (GCF= ___15___)
98, 140 (GCF= ___14___)
65, 112 (GCF= ___1___) Relatively Prime
63, 84, 126 (GCF= __21____)
110, 132, 176 (GCF= ___22___)
You are decorating a Rose Bowl float. There are 108 red roses, 144 white roses, 48 yellow
roses, and 72 purple roses. If the number of total roses in each bunch is the same and
there are no leftover roses, what is the greatest number of bunches of roses that can be
made? How many roses of each color are in each bunch? (Total number of bunches =
_______12______)
# of red roses in each bunch ____9____
# of white roses in each bunch ____12____
# of yellow roses in each bunch ___4_____
# of purple roses in each bunch ____6____
4.3 Equivalent Fractions
During the 1800’s, there were 22 different Presidents of the United States, and 6 of them
were born in Virginia. Write a fraction comparing the number of Presidents born in
Virginia with the total number of Presidents in the 1800’s. Put the fraction in simplest
form. ____6/22 = 3/11_____
The U.S. Highway speed limit in 20 states is 60 miles per hour. In simplest form, what
fraction of states have a speed limit of 60 miles per hour? __20/50 = 2/5____
4.4 Least Common Multiple
Find the LCM of the following numbers using any method:
16, 20 (LCM= ___80__)
25, 70 (LCM= ___350__)
9, 14, 21 (LCM= ___126)
7, 20, 35 (LCM= ____140_)
Three tour buses leave the visitor’s center at 9:00 a.m. Bus A returns to the visitors
center every 60 minutes, Bus B returns every 40 minutes, and Bus C returns every 75
minutes. What is the next TIME the buses will all return to the visitor’s center at the same
time? ____600 minutes or 10 hours; so 7:00 p.m._____________