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
Wednesday, December 14, 2011
Wednesday, December 7, 2011
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.
Tuesday, November 29, 2011
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)
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)
Monday, November 21, 2011
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!
and
Our Earth Science foldable will be done/finished by Tuesday too!
Tuesday, November 8, 2011
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
- 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
Monday, October 24, 2011
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
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
Monday, October 17, 2011
Strategies for finding common denominators (also see video links for more help!)
Finding common denominators - Reasons:
(1) To accurately compare the relative value of 2 fractions (when denominator is same - same sized pieces- the one with the bigger numerator is larger...has more of these same sized pieces!) or
(2) to add & subtract fractions finding common denominators becomes essential because you need to be adding up (or subtracting) the same sized pieces or your answer won't make any sense!
Strategy/Example #1:
1/3 + 2/9 = _____
- Hmmm, well, since the denominator of the 1st fraction is a FACTOR of the second I should be able to use multiplication to create my common denom. because 3x3=9! Don't forget, to get an EQUIVALENT fraction (we don't want to add up a non-equivalent fraction, that would change the actual value of the problem!) we need to multiply the numerator and the denominator by the same #
1 x 3
__ = 3/9 and now we just substitute 3/9 into our original problem for 1/3
3 x 3
3/9 + 2/9 = 5/9 (remember, only add the denominators because that is how many pieces you
are adding - if you added the denominators you'd be changing the size of
your pieces which would, in effect, be making your sum of less value!)
Strategy/example #2:
1/5 + 2/4 = ____ well, neither denominator is a factor of the other so we have to find a
common multiple of both - easiest way to do this is to multiply 2
numbers together!! Here, like this:
1 x 4
___ = 4/20
5 x 4
2 x 5
__ = 10/20
4 x 5
Now, we can substitute our new, fancy equivalent fractions with common denominators in for the old ones and we get
4/20 + 10/20 = 14/20 which reduces to 7/10
Note: you can also use division to reduce fractions in order to find a common denominator - make sure you divide the numerator and the denominator by the same # and that the they are both divisible by that number!
(1) To accurately compare the relative value of 2 fractions (when denominator is same - same sized pieces- the one with the bigger numerator is larger...has more of these same sized pieces!) or
(2) to add & subtract fractions finding common denominators becomes essential because you need to be adding up (or subtracting) the same sized pieces or your answer won't make any sense!
Strategy/Example #1:
1/3 + 2/9 = _____
- Hmmm, well, since the denominator of the 1st fraction is a FACTOR of the second I should be able to use multiplication to create my common denom. because 3x3=9! Don't forget, to get an EQUIVALENT fraction (we don't want to add up a non-equivalent fraction, that would change the actual value of the problem!) we need to multiply the numerator and the denominator by the same #
1 x 3
__ = 3/9 and now we just substitute 3/9 into our original problem for 1/3
3 x 3
3/9 + 2/9 = 5/9 (remember, only add the denominators because that is how many pieces you
are adding - if you added the denominators you'd be changing the size of
your pieces which would, in effect, be making your sum of less value!)
Strategy/example #2:
1/5 + 2/4 = ____ well, neither denominator is a factor of the other so we have to find a
common multiple of both - easiest way to do this is to multiply 2
numbers together!! Here, like this:
1 x 4
___ = 4/20
5 x 4
2 x 5
__ = 10/20
4 x 5
Now, we can substitute our new, fancy equivalent fractions with common denominators in for the old ones and we get
4/20 + 10/20 = 14/20 which reduces to 7/10
Note: you can also use division to reduce fractions in order to find a common denominator - make sure you divide the numerator and the denominator by the same # and that the they are both divisible by that number!
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