Math Skills: Fractions

Lesson 1: Lesson 1: Fractions Pretest and Terminology

Pretest on Fractions Answers

Here are the answers and how to get them:

1. 24/64 = 3/8. Reduce by dividing the numerator, 24, and the denominator, 64, by 8. Eight is the Greatest Common Factor (GCF) of 24 and 64.

2. 15/4 = 3 3/4. Divide 4 into 15. You get an answer of 3 with a remainder of 3. Take the remainder 3 and express it as a fraction, 3 divided by the divisor 4. So you get 3 3/4.

3. 4 7/20 + 9 1/2 = 13 17/20. Since the denominators are not alike you cannot add these fractions as they are; you must find a common denominator. To find the common denominator, find a number that both 20 and 2 go into evenly, and try to find the LOWEST they both go into evenly. That number is 20, the "least common multiple", and, therefore, the lowest common denominator.

You don't have to change 7/20, but you do have to change 1/2. 1/2 is ?/20. This is a proportion--remember how to solve proportions? 1/2 = 10/20.

Thus, 4 7/20 + 9 10/20 = 13 17/20.

4. 3 1/3 + 1 5/9 + 2 5/6 = 7 13/18.

The least common multiple ((LCM)or the lowest common denominator) for 3, 6, and 9 is 18. Thus: 1/3 = 6/18; 5/9 = 10/18; 5/6 = 15/18.

So, 3 6/18 + 1 10/18 + 2 15/18 = 6 31/18. This answer must be reduced because you can't leave it 31/18! Since 18 goes into 31 1 13/18 times, you add 6 and 1 13/18 to get 7 13/18. Thus, 7 13/18 is the answer. Remember with fractions you must reduce to lowest terms!

5. 9 1/2 - 4 3/8 = 5 1/8. As with addition of fractions, to subtract fractions you must have a common denominator. The common denominator of 2 and 8 is 8 (LCM). 1/2 is the same as 4/8; so 9 4/8 - 4 3/8 = 5 1/8.

6. 12 1/4 - 10 7/16 = 1 13/16. The LCM of 4 and 16 is 16, the common denominator. Thus 1/4 becomes 4/16. So we get 12 4/16 - 10 7/16. But we can't subtract 4/16 - 7/16!

Thus we come to that most dread element of subtraction of fractions, borrowing! It took me literally years to get this straight, and it took my son, who I homeschool, also years to get this straight! There are all kinds of ways to explain why you do such and such to borrow with fractions, but I'll give you "the skinny": when you borrow with fractions, you simply add the numerator and denominator of the fraction you need to borrow in, put that number over the denominator, then take one away from the whole number. If you are interested in why you do this, ask me in the discussion section!

Thus: 12 1/4 - 10 7/16 = 12 4/16 - 10 7/16 = 11 20/16 - 10 7/16 = 1 13/16.

7. 4/5 x 5/6 = 20/30 = 2/3. In multiplication of fractions, multiply the numerators together and the denominators together--you don't need a common denominator. Just slice the 0's off the numerator and denominator to reduce.

8. 12 x 4 1/2 x 2 2/3 = 12 x 9/2 x 8/3 = 144 (after turning all mixed numbers into improper fractions--nobody multiplies mixed numbers the old fashioned way anymore, and, in fact, I haven't sued the old-fashioned way since 4th grade--about 40 years ago!).

From here you start cancelling. This cannot be demonstrated with the keyboards we have, crossing out the 2 with the 12 and the three with the nine, but what we get when we cancel is: 12 x 9/2 x 8/3 = 6 x 3 x 8 = 144, the answer.

9. 20 divided by 4/5 = 25. In division of fractions, you really multiply by the reciprocal of the divisor fraction (which in this case is 4/5). What is the reciprocal of 4/5? Simply, 5/4 (flip the fraction over!). Thus 20 divided by 4/5 = 20 x 5/4 = 100/4 = 25.

10. 6 1/4 divided by 1 7/8 = 3 1/3. Turn all mixed numbers into improper fractions first, then use reciprocal of the divisor fraction, do any cancelling you can do. Thus:

6 1/4 divided by 1 7/8 = 25/4 divided by 15/8 = 10/3, which reduces to 3 1/3 (divide 10 by 3).

11. Is 5/16 larger than 1/3? No, because when you turn these fractions into fractions with the same denominator (how else would you compare them?), 5/16 becomes 15/48 and 1/3 becomes 16/48. Thus, 1/3 is larger!

12. Change 0.45 to a fraction. Like it or not, any decimal can be expressed as a fraction. 0.45 means 45 hundredths, or 45/100. Reduce (by GCF) by 5 to get 9/20, the answer.

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