Mid-Term Review2012
Mid-Term Study Guide Answers
Tuesday, January 22, 2013
Model of Multiplying Fractions
I found this video to help explain why you need to convert mixed numbers into improper fractions to multiply. Hope this helps. Click here for the link to the video.
Multiplying Fractions
When you multiply fractions you do not need to find a common denominator because you are finding a part of a part. The video below is similar to the brownie pan model which helps you understand the algorithm to multiply fractions. To multiply you can simply multiply numerator to numerator and denominator to denominator. Multiplying the denominators breaks the original fractions into more pieces. Remember to always simplify the product.
A helpful strategy is to cross cancel. When you cross cancel you are simplifying the fractions before you you multiply. This makes the multiplication a bit easier and less cumbersome. To cross cancel you look for a common factor that is share by any numerator and any denominator in the problem. You can use any numerator and denominator because of the commutative property of multiplication. Once you have "pulled out" or divided by as many common factors as you can, you can then multiply the numerators and the denominators that are left. If you have cross cancelled correctly, your product is usually simplified.
A helpful strategy is to cross cancel. When you cross cancel you are simplifying the fractions before you you multiply. This makes the multiplication a bit easier and less cumbersome. To cross cancel you look for a common factor that is share by any numerator and any denominator in the problem. You can use any numerator and denominator because of the commutative property of multiplication. Once you have "pulled out" or divided by as many common factors as you can, you can then multiply the numerators and the denominators that are left. If you have cross cancelled correctly, your product is usually simplified.
When you multiply mixed numbers you need to convert the mixed numbers to improper fractions first. You need to do this because you need to account for the whole value of the set. Remember 2 * 3 means three sets of two, so 2 1/3 * 3 1/4 means three and one-fourth sets of two and a third. You can not multiply the whole numbers separately from the fractions.
Fractions and Word Problems
One of the more difficult aspects of this unit is deciphering the operation you need to do to solve a word problem. We have talked about many phrases and words that are clues, but be careful with words like "of." Though many times the word means to multiply, it often show up simply as a preposition to explain something. Sometimes there are no common words or phrases in the problem and we just have to make sense of the situation. One way to help you make sense of the situation is to substitute whole numbers or easy benchmark fractions like one-half into the problem. Use the document below as practice making sense of word problems.
Bits Pieces II Mixed Word Problem Practicex
Bits Pieces II Mixed Word Problem Practicex
Subtraction Word Problem
The following problem causes confusion for many students who do not take the time to make sense of the problem and/or their answer.
In June your new puppy weighed 10 2/3 pounds and by July the puppy weighed 19 1/5 pounds. How much weight did the puppy gain?
First makes sense of the problem by substituting easy whole numbers for the mixed numbers. Let's make 10 2/3 simply 10 pounds and 19 1/5, 20 pounds. Then you can make sense of the problem. It only makes sense to subtract 10 from 20 (20 - 10 = n) to find the difference in pounds or the weight gained. Subtracting 20 from 10 (10 - 20 = n) will give you a negative integer which does not make sense since the puppy did not lose weight from June to July.
Remember, just because a number comes first in a word problem does not mean that it will come first in a number sentence. It is important that you stop and think about the situation and make sense of it before you begin your computation.
In June your new puppy weighed 10 2/3 pounds and by July the puppy weighed 19 1/5 pounds. How much weight did the puppy gain?
First makes sense of the problem by substituting easy whole numbers for the mixed numbers. Let's make 10 2/3 simply 10 pounds and 19 1/5, 20 pounds. Then you can make sense of the problem. It only makes sense to subtract 10 from 20 (20 - 10 = n) to find the difference in pounds or the weight gained. Subtracting 20 from 10 (10 - 20 = n) will give you a negative integer which does not make sense since the puppy did not lose weight from June to July.
Remember, just because a number comes first in a word problem does not mean that it will come first in a number sentence. It is important that you stop and think about the situation and make sense of it before you begin your computation.
Subtracting Fractions
Since addition and subtraction are inverse operations, subtracting Fractions is similar to adding fractions in that you must have the same size pieces. The video from www.khanacademy.org has a useful model to show you why simplifying is important.
Be careful when subtracting mixed numbers. You may need to borrow from the whole. If you borrow one whole you need to convert that to a fraction to add to the fraction portion of the mixed number. You have not changed the value but have renamed the mixed number in a way that allows you to compute. In the second example pictured below, the one whole was converted into 27/27 to because it needed to be added to 3/27.
Be careful when subtracting mixed numbers. You may need to borrow from the whole. If you borrow one whole you need to convert that to a fraction to add to the fraction portion of the mixed number. You have not changed the value but have renamed the mixed number in a way that allows you to compute. In the second example pictured below, the one whole was converted into 27/27 to because it needed to be added to 3/27.
The video below shows the algorithm step by step.
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