Mixed and Improper Fractions
Prime Factorization
(GCF) and LCM
Decimals and Fractions
Finding Common Denominators
100
Rewrite 4 5/6 as an improper fraction.
4 5/6 as an improper fraction is 29/6. Multiply 6 x 4 then add 5 = 29. Put over the original denominator.
100
How is a prime number different from a composite number?
A prime number only has 2 factors -- one and itself. Composite numbers have more than 2 factors.
100
Define "factor" and give an example.
A factor is any number multiplied by another number to get a product. For example 3 x 5 = 15; 3 and 5 are factors of 15.
100
What is the easiest way to change a decimal to a fraction?
Just say the decimal out loud and write it as a fraction.
100
To find the LCD you must first find the what?
To find the LCD you must first find the least common multiple, LCM.
200
Is 21/21 a proper or improper fraction? Explain.
An improper fraction is any fraction where the numerator is greater than or EQUAL TO the denominator. So 21/21 is Improper.
200
What do the Rules of Divisibility for 3 and 9 have in common?
You must find the sum of the digits for determining divisibility by both 3 and 9.
200
To help you remember what a multple is, what do we think of?
To help us remembe, we think of skip-counting.
200
To rewrite a fraction as a decimal you must do what?
To rewrite a fraction as a decimal you must divide the numerator by the denominator and keep dividing until it either repeats or terminates. 3/4 = 3 divided by 4 = .75
200
Complete the statement with < , > , or =. 2/3 __?__ 5/7
Find the common denominator (21). 2/3 becomes 14/21 and 5/7 becomes 15/21, so 2/3 < 5/7.
300
Put the following integers in order from least to greatest. 18/5; 3 11/15; 11/3
The LCD is 15 so 18/5 = 54/15; 3 11/15 = 56/15 and 11/3 = 55/15. So the correct order is 18/5; 11/3; 3 11/15
300
Using Factor Trees find the GCF of 45 and 60.
The prime factorization of 45 is 3 x 3 x 5. The prime factorization of 60 is 2 x 2 x 3 x 5. Common factors are 3 and 5 so the GCF is 3 x 5 or 15
300
Is 18/45 in simplest form? If not, simplify.
18/45 is not in simplest form. 3 is a common factor of both 18 and 45, so if we divide by 3/3 it makes the fraction 6/15. 6/15 is in simplest form.
300
What is 4.078 as a fraction in simplest form?
4.078 is 4 and 78/1000 which divided by 2/2 simplifies to 4 39/500.
300
Jewelry made of 14 carat gold is 14 parts gold and 10 parts other metals, or 14/24 gold. You are looking at three bracelets that are 1/2, 5/12, and 2/3 gold. Which bracelet contains the most gold?
The common denominator is 12 -- 1/2 = 6/12; 5/12 is 5/12; 2/3 = 8/12 so the bracelet made of 2/3 gold has the most gold.
400
List one fraction (improper or mixed number) that falls between 5 1/8 and 94/16.
5 1/8 is 41/8 as an improper fraction. The Least Common Denominator of 8 and 16 is 16, so 41/8 = 82/16. Any fraction between 82/16 and 94/16 is correct.
400
Test 180 for divisibility by 2, 3, 5, 6, 9, and 10.
180 is divisible by all the numbers. It is even, so works for 2, sum of digits is 9, so ok for 3, ends in 5 or 0 so 5 ok, is even and divisible by 3 or 6 is ok, sum is 9 so 9 is ok, ends in 0 so 10 ok.
400
There are 30 people in class and 21 of them buy lunch at school. Write the portion of the class that buys lunch at school as a fraction in simplest form.
The portion that buys lunch at school is 21/30. Both 21 and 30 have a common factor of 3, so it simplifies to 7/10.
400
Put the following numbers in order from least to greatest: 2.97; 18/7; 2 19/21
18/7; 2 19/21; 2.97
400
A table is 32 3/4 inches wide. Your tablecloth is 107/3 inches wide. Will the tablecloth be big enough to cover the table?
Yes because 107/3 is 36 1/3 inches and the table is only 32 3/4 inches wide.
500
The pole vault records for 3 different schools are shown below. Which school's record is the higest? Oakmont 49/3 feet; Perry is 16 9/12 feet; Central = 33/2 feet
The common denominator is 12. Oakmont is 16 1/3 = 16 4/12 feet; Perry is 16 9/12 feet; Central is 16 1/2 = 16 6/12 feet. Perry's height is the highest.
500
For your school's fair, you want to make 42 magnets and 36 key chains with your school's mascot on them. You want to display them in rows of equal size, but you do not want to mix the items. What is the greatest number of items you can have in a row?
To answer questions about things in equal rows we find the Greatest Common Factor. The GCF of 36 and 42 is 6, so the greatest number of magnets would be 42 divided by 6 or 7 in a row. The greatest number of key chains would be 36 divided by 6 or 6 in a row.
500
Pencils come in packages of 10. Rulers come in packages of 8. hannah wants exactly one pencil for every rules. What is the smallest number of packages of each she will need to buy? Be ready to explain how you got your answer.
4 packages of pencils (4 x 10 = 40) and 5 packages of rulers (5 x 8 = 40). Find the Least Common Multiple which is 40 and divide by the number of objects in each package.
500
About 23/25 of a watermelon is water. Write this fraction as a decimal. Then find what portion of a watermelon is NOT water.
23/25 is 0.92 as a decimal (23 divided by 25). 0.92 is how much of a watermelon is water. 1.00 - 0.92 = 0.08, so 0.08 of a watermelon is NOT water.
500
Jeff uses a different paintbrush for each color of a painting. For the red paint, he uses a 7/16 paintbrush. For the blue paint. he uses a 3/8 inch paintbrush. For the green paint, he uses a 1/4 inch paintbrush. Order the paintbrushes from smallest to largest.
Common Denominator is 16. red is 7/16; blue is 3/8 (6/16) and green is 1/4 (4/16), so from least to greatest it is green, blue and red.
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