Math in Focus Chapter 1 Test Review

Greatest Common Factor

100

GCF of 4 and 10

2

200

GCF of 30 and 75

15

300

GCF of 210, 84, and 56

14

400

Express the sum of each pair as the product of the greatest common factor and another sum.

54 + 90

18(3+5)

500

Nicole has two ribbons.  The first ribbon measures 90 centimeters and the second string measures 75 centimeters.  She wants to cut the ribbons into equal lengths so she'll have a bunch of smaller ribbons that are all the same length.  What is the least number of ribbons of equal lengths that she can get? (Hint: The least number of smaller strings means each smaller piece is the largest it could possibly be.)

Each smaller ribbon will be 15 centimeters long.  The 90 cm ribbon will be cut into 6 pieces that are 15 cm each. The 75 cm ribbon will be cut into 5 pieces that are 15 cm each.  Together she will have 11 small pieces. 

Least Common Multiple

100

LCM of 9 and 21

63

200

LCM of 12 and 28

84

300

LCM of 20, 30, and 40

120

400

LCM of 48, 84, 144

1,008

500

Johnny takes 45 seconds to run around the track.  Ms. Hagan takes 60 seconds to run around the track.  If they both start at the same time, when will they both be back at the starting line, starting a new lap together?

180 seconds

<>, Prime Factorization, and Problem Solving

100

Write an inequality (<>) to compare the following numbers:

5.02   5.2

5.02 < 5.2

200

Write an inequality (<>) to compare the following numbers:

3 1/2   3.4

3 1/2 > 3.4

300

Write the number as a product of prime numbers.

54

54 = 2 x 3 x 3 x 3 Or

54 = 2 x 3³

400

Write the number as the product of prime numbers.

580

580 = 2 x 2 x 5 x 29 or

580 = 2² x 5 x 29

500

There are 40 turnips, 32 carrots, and 28 tomatoes in a basket.  The vegetables are packed into bags. An equal number of EACH vegetable is put into each bag and all of the vegetables are packed into bags meaning that while the amount of turnips, carrots, and tomatoes differ every bag is the same.  What is the LEAST possible number of bags of vegetables packed?

4 bags.  Each bag has 10 turnips, 8 carrots, and 7 tomatoes.

Squares and Square Roots

100

14²

196

200

Square Root of 576

24

300

Find two consecutive numbers whose squares produce a sum of 761

19 and 20

400

Find two consecutive numbers whose squares differ by 15

7 and 8

500

if the square root of 529 is 23, evaluate 230²

52,900

Cubes and Cubed Roots

100

Cubed Root of 1000

10

200

24³

13,824

300

7³ x 5² + 10

8585

400

Find two consecutive numbers whose cubes differ by 19.

2 and 3

500

Find two consecutive numbers whose cubes produce a sum of 1241.

8 and 9