Multiplying fractions

Whoohoo! No need to find common denominators when multiplying fractions! Just multiply straight across - numerator x numerator and denominator x denominator! Remember though, that WHOLE numbers can be viewed as a fraction with a denominator or 1!

example #1:

1/2 x 3/4 = ____

For the above problem...

Numerator x Numerator: 1 x 3 = 3
Denominator x Denominator: 2 x 4= 8

so 1/2 x 3/4 = 3/8

Example #2 (with whole number):

1/3 x 2 = _____

well, 2 is the same as 2/1 so NOW we can multiply!!!

1/3 x 2/1 = 2/3

Some more tidbits for estimation...

multiplying one factor by another factor SMALLER than 1 will give you a product smaller than that the "original" factor

"original" factor x Factor smaller than 1 = value less than original factor

Examples:

10 x 1/2 = 5

10 x 1/5 = 2

10 x 1/3 = 3.33

"Rules" for manipulating addition and subtraction number sentences to solve for the variable

If your variable is in an addition number sentence:

Addend1 + Addend2 = Sum (original problem format)
Addend2 + Addend1 = Sum
Sum - Addend1 = Addend2
Sum - Addend2 = Addend1

If your variable is in a subtraction number sentence:

Minuend - Subtrahend = Difference (original problem format)
Minuend - Difference = Subtrahend
Subtrahend + Difference = Minuend
Difference + Subtrahend = Minuend

Example:

1/3 - B = 5/24

let's label each piece....

1/3 (min.) - B (sub.) = 5/24 (diff.)

so, we want to solve for our variable, B. In other works, we want to "isolate" our variable all by itself after the equal sign! So, our subtrahend (which is what the variable B is in our original problem) will follow the equal sign if we subtract our difference form our minuend!

1/3 - 5/24 = B

Now find common denominators and solve!!!

1/3 = 8/24 so 8/24 - 5/24 = 3/24 so B=3/24

Welcome Trimester 2!

Welcome to trimester #2! Off to a fresh start so let's make a good beginning of it! I've purged the homework page of last trimesters assignments and started fresh.

Adding and subtracting mixed #'s - step 1: create common denominators if they are not there! (2) Step 2: Add or subtract (you can add/subtract the whole #'s first and then the fractions or the fractions and then the whole #'s or vice-versa...doesn't matter).
NOTE: You may need to borrow "from the wholes" on some of the subtraction problems (see example below!)

Example: 1 1/2 - 7/8 = _____

step 1 - common denominators: 1 4/8 -7/8 = _____

Ok, so you can't take 7/8 away from 4/8 so we're going to have to borrow some 8ths from our 1 whole...1=8/8 which we can combine with the 4/8 we already have....this would make our number sentence look like this:

12/8 - 7/8= 5/8 (the 12/8 is is the 8/8 + 4/8 from above)

Should be DONE in journal....

By tomorrow (11/22) the following assignments should be DONE in your math journal: (1) Bits & Pieces II: Investigation 1.2 A-D; (2) ACE Questions 16-30 on page 10; Bits & Pieces II: Investigation 2.1 A-F and ACE Question #1 on pg. 24

and

Our Earth Science foldable will be done/finished by Tuesday too!

Percents

- Percent as "out of 100"

- Three equivalencies:
1/4 = .25 x 100 = 25%

- so from fraction to percent just 2 steps:
step 1: numerator divided by denominator = decimal value
step 2: decimal value x 100 = % value
that's it!

Using percents....

strategy 1:
use the definition of percents to make equivalent fractions
18% of people like chocolate ice cream best. How many people out of 200 like chocolate ice cream best?

18/100 = 36/200 so 36 people

strategy 2 (same problem);
multiply decimal equivalent by proposed total of people
0.18 x 200= 36 people

Fraction to decimal

We've been working on converting fractions into their decimal equivalents! We've been specifically looking at the meaning of place value and how to convert fractions with denominators of 10, 100, 1000, etc. into decimals using place value! The denominator determines where the numerator goes using place value...



Example 1:
1/100 = .01 the 1 is in the hundredths place (we have no tenths so the 0 "holds"
the 1 in the correct, hundredths place)

Example 2:
25/1000 = .025 the last digit in the numerator goes in the place value indicated by the denominator, which in this case is the thousandths place...then just back-fill until you get to the decimal. The decimal is read like a whole number but you then add the place value the last digit is in (twenty-five thousandths.....just like the fraction!)

Example 3:
101/100 = 1.01 (this is an improper fraction so we know that we have a value greater than 1 whole - not by very much in this case!)

example 4:
sometimes you have to create and equivalent fraction with a denominator of 10, 100, 1000, etc. before you can use our wonderful base-ten decimal system....if we had 4 fingered hands we've have a base-8 decimal system!!

4/25 = 16/100 (I multiplied the numerator and denominator both by 4)

16/100=0.16