Math Skills: Fractions

Lesson 1: Lesson 1: Fractions Pretest and Terminology

This first lesson in the course "Curing Math Anxiety: Basic Math-Fractions" will be a pretest so you will know exactly "where you are at"--how much you already know and more importantly, what you don't know, forgot, or need to relearn in order to apply fractions in your daily life without nervousness, fright, or pulling your hair out. In the second part of the lesson I will explain how to get the correct answers. Then we'll go over fraction terminology.

Pretest on Fractions

How well do you know how to reduce fractions, raise fractions to higher terms, and change mixed numbers and improper fractions. You will review the basic operations of addition, subtraction, multiplication, and division with fractions, as well as review how to compare fractions (which is larger? which is smaller?), and relate fractions to decimals and percents (fractions/decimals based on 100) in this and forthcoming sections. The problems listed below comprise a pretest of what you should know about dealing with fractions, but, since you are taking this course, maybe forgot.

Why should you take this test?

Let's say today you are using a recipe in a cookbook that serves 4 but you only need to serve 2. Since 2 is half of 4 (BTW, 2/4 = 1/2), you need to cut all the ingredient amounts in half, but how do you do that? Some ingredients are easy: take 2 cups, cut in half to 1 cup; but what about cutting 1/3 cup in half? If you are taking 1/2 "of" 1/3, note that the word "of" means multiply! So to take 1/2 "of" 1/3, you multiply 1/2 x 1/3. But can you multiply fractions? If you don't know the answer to this problem, then you need this course!

Note: All fraction bar signs are denoted by "/" - this fraction bar means the same as division, in that if you see this bar, the top number is divided by the bottom number.

Thus, three-fourths is denoted by 3/4 (three divided by four); one and one-half is denoted by 1 1/2 (this is a mixed number and means the same as 3/2); multiplication signs, unless otherwise indicated, use an "x": three-fourths times one-eighth is denoted by

3/4 x 1/8.

Since my keyboard doesn't have a division sign, I will use "divided by" instead. By the way, this test (as well as the pretest on decimals and pretest on percents) is listed in the text used for this course, "New Revised Cambridge GED Program: Mathematics, 2nd Edition," p. 87 (heretofore known as "Cambridge GED").

Here is the test:

1. Reduce 24/64 to lowest terms.

2. Change 15/4 to an improper fraction.

3. Find the sum of 4 7/20 and 9 1/2

4. Add 3 1/3 + 1 5/9 + 2 5/6.

5. Find the difference between 9 1/2 and 4 3/8.

6. Take 10 7/16 from 12 1/4.

7. Find the product of 4/5 and 5/6.

8. Find 12 x 4 1/2 x 2 2/3.

9. What is 20 divided by 4/5?

10. Divide 6 1/4 by 1 7/8.

11. What is larger, 5/16 or 1/3?

12. Change 0.45 to a fraction and reduce.

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