burtonmath9

What I Have Learned About Gr.9 Exponents

~ emilys2017 ~ Leave a comment

  • What are exponents? what does it tell you?

Exponents are an indicator of how many times a number is being copied, it is an alternative to multiplication.Example) 3^3 would equal 3 x 3 x 3 = 9 x 3 = 27 and that is the final answer for 3^3

  • How do brackets affect evaluating a power?

a really common example of brackets in a power equation is if you have (-8)^3 the 2 will see the brackets and copy the whole equation, but if you have -8^3 the exponent only sees the 8 so only copies the 8 not the whole equation, therefore the answer will be positive, not negative

Answer) (-8)^3 = (-8)(-8)(-8)= (64)(-8)= -512

  • Multiplication law of exponents

the rule for multiplying exponents is really easy, if the bases are the same ( 10^2 x 10^7 ) all you have to do is add the exponents together. ( 10^2 + 10^7 = 10^9

but when the bases are different you use a different rule, if we use the same example of 10^2 but we switch the second equation to 9^4 the rule is you do 10 x 10 = 100 and 9 x 9 x 9 x 9 = 6,561 + 100 = 6,661 and your answer would be 6,661

  • Division Law of exponents

to do the division law you first have to see if the bases are the same, if they are all you need to do is subtract the exponents, with division it tells you subtraction so if we have 7^4  ÷ 7^6 =  7^2

But if the bases are different you use a different rule, all you need to do is figure out the powers answer, if we use an example of 6^2 ÷ 3^8 = 6 x 6 = 36 and 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6,561÷ 36 = 182.25 an that is how you would do the division law them the bases are different.

  • zero power law

any base to the power of 0 will always equal to 1 an example is 6^0 is equal to 1 (no matter what the base is the answer will always be one from 1-100000000000…….etc. )

another example is  3^4 divided by 3^4 will equal to 3^0 (which is equal to 1, this example is using a mixture of division law and the zero exponent law)

  • Power of a power law

what you would need to do in the power of a power law is you  use the example of (7^2)^3 is all you need to do is multiply the exponents together (2 x 3 = 6) so our answer would me 7^6

this is used with all numbers, weather it’s negative, positive, or maybe even a fraction.

  • BEDMAS

when is a question really a bedmas question? we use the order of operation when there is an equation in brackets an example would be if we have {4\cdot 3 + 3}^2 +1 the first thing to do would be the multiplication 4 x 3 =12 and followed by +3 = 15 so now our equation would be {15}^2 + 1 15 x 15= 225 + 1 = 226

to do a question like this all you need to know is Bedmas.

Image result for bedmas

 

 

 

 

What I have learned about Gr.9 fractions

~ emilys2017 ~ Leave a comment

Numberlines

  • Before you start placing the fractions on the numberline, always make sure you have a common denominator Ex: 1\frac{1}{4} and \frac{7}{12} you would have to change 1\frac{1}{4} to 1\frac{12}{48} and \frac{7}{12} to \frac{84}{48}then you can place it on the numberline- after you reduce, if you can

Comparing fractions

  • to compare fractions you have to make a common denominator, \frac{-4}{8} and \frac{-7}{8} which one is bigger? \frac{-4}{8} is bigger than \frac{-7}{8} because \frac{-7}{8} -7 is further down the number line (to the left) than \frac{-4}{8}

Adding and subtracting fractions

  • for both adding and subtracting you need to find a common denominator ex. \frac{8}{6} and \frac{12}{18} you would need to change it to \frac{12}{18} and \frac{24}{18}

Subtraction

  • \frac{12}{18} –  \frac{24}{18} all you have to do is subtract the numerators, so in our case it will end up as  \frac{12}{18} and you can reduce it to  \frac{2}{3}

Addition

if we use the same fractions ( \frac{12}{18} and \frac{24}{18} ) this time all you need to do is simply add the numerators \frac{12}{18} + \frac{24}{18} =  \frac {36}{18} and you can reduce it if you divide them both by 6 so now our final answer is \frac{6}{3}= can also equal 2

Multiplying and dividing fractions

multiplication

  • to multiply fractions, do DO NOT need a common denominator, multiplication is a just do it question!! ex. \frac{-14}{19} x \frac{7}{12} you start by multiplying te numerators, then the denominators \frac{-14}{19} x \frac{7}{12}= \frac{-98}{228} you can reduce this fraction by dividing it by 2 so now you get \frac{-49}{114} that is our final answer.

division

  • if we use the same example as the last question ( \frac{-14}{19} / \frac{7}{12} you need to use the reciprocal, which means our question is now a multiplication, \frac{-14}{19} x \frac{12}{7} our answer is now \frac{-168}{133} we can not reduce it

 

this is all of the things we have learned about in Gr.9 fractions, hop you found it helpful!