Multiplication with Fractions

Today's lesson was pretty easy! It was basically overview of simple multiplication only in a fraction form. Basically when multiplying two fractions together the product is made by just multiplying the two numerators together and the two denominators together.


For Example: a/b * c/d = a * c/b * d

• 3/4 * 1/3 = 3/12 <-- this is also known as 1/4 
• 2/5 * 1/3 = 2/15
• 3/2 * 1/4 = 3/8

Another way of showing this besides just doing it in your head is by making a grid and shading each fraction to get your answer. For instance, if you were using the equation 3/4 * 1/3 you would make a grid with 3 across and 4 down creating a grid of 12 boxes. This is because you base the grid off of the two denominators. (the first denominator is always the amount going down, the second is always the amount going across) Next you should shade in 3/4 of the grid (9 boxes), then you should shade in 1/3 of the boxes (4 boxes). This leaves exactly 3 out of the 12 boxes shaded by both fractions. That makes your answer 3/12.

 Through multiplication familiar property rules apply:

• closure: fraction * fraction = fraction
• commutative: a/b * c/d = c/d * a/b
• associative: (a/b * c/d) * e/f  = a/b * (c/d * e/f)
• distributive: a/b (c/d + or - e/f) = a/b * c/d + or - a/b * e/f
• inverse: for every fractions a/b, a & b do NOT = 0; there exists an b/a so that a/b * b/a = 1 (reciprocal) ---> practice the inverse operation
• identity: a/b * 1 = a/b * 1/1 = a/b 

Intergers

 Today in class we went over Integers, and different ways to understand them or solving simple math equations. When using Integers i learned you use a debt (-) for a negative number, and a credit (+) for a positive number. First, we practiced multiplication, and how to set up a array with the equation. For example, we used 5 x -3 so we made five columns and 3 rows of debts. This can also be said as 5 debts of size 3. After we mastered that we covered division. There are a few different ways of showing division by using debts and credits. One way is the sharing method, this is used when the divisor is positive and the dividend is negative. The other method is measurement, this is used when the divisor and dividend are both negative. When solving a multiplication or division problem, there are a few key tricks to understand.



Integers are a very fun thing to learn I believe, and I really enjoyed learning new and different methods to solving multiplication and division problems using debts and credits. There were a few more methods we went over to help us understand. I learned the number line model when dealing with temperature vs. time. That is simply just creating a number line and depending on your equation and moving up or down the number ling till you reach your correct answer. For example, The temperature is now 0 degrees, the temperature goes down 4 degrees every 3 hours, what is the temperature in 6 hours. (You would start at 0, and go down by five 6 times, leaving your answer to be -30 degrees)


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practicing multiplication with Intergers