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7th Grade Math Year in Review Part 1



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okay we're gonna start with just some

sign numbers so when you add a negative

and a positive you're going to take the

difference between those two which is

three and nine the difference is six and

then you take the sign of the larger

value in this case nine is positive and

it's greater than three so that's gonna

be a positive six okay now let's look at

adding two negative numbers well when

you have two negative numbers and you're

adding them you're literally just going

to add the two numbers and that value is

negative so four plus seven is 11 carry

the one one plus two is three plus one

more is four so that adds up to negative

41 so add and keep the sign now let's

look at subtraction we have 72 minus a

negative five when you have a double

negative you can make those into

positive because two negatives make a

positive

so now we're going to add those together

and we get 77 so those are the first

three sign number problems now let's try

another subtraction problem what if we

have negative 24 minus a positive 48 I

like to rewrite this as addition so I'm

gonna write it as negative 24 plus a

negative 48 now I can apply my addition

rules I'm adding they're both negatives

so I add and take the sign so 8 plus 4

is 12 carry the 1 4 plus 2 is 6 plus 1

is 7 and I carry the sign so that's a

negative 72 okay let's look at

multiplying okay multiplying if you

multiply two negatives you get a

positive so negative times a negative is

a positive and 4 times 16 is 64 so

that's a positive

64

now let's look at division we've got a

negative divided by a positive so let's

go ahead and decide on the sign a

negative divided by a positive is a

negative because positive negative

values always come in pairs so if you

have a negative and a positive the other

term must be negative when you're

multiplying and dividing so my answer is

going to be negative now I'm gonna go

over here and just for a second I'm

gonna long to buy so I'm gonna put 24.5

on the outside and 93.1 on the inside

and how many times will 24 go into 93 24

is close to 25 so I'm gonna estimate 24

plus 24 or 25 plus 25 is 50 plus another

25 is 75 plus 1/4 one would be a hundred

what I don't have a hundred so it has to

be three so let's try that 3 times 5 is

15 carry the 1 that's 12 plus 1 is 13

carry the 1 3 times 2 is 6 plus 1 is 7

now let's subtract 1 minus 5 is 6 I had

to borrow or 11 that was 11 minus 5 is 6

12 minus 3 is 9 I had to borrow well 8

minus 1 is or 8 minus 7 is 1 so now I

need to ask myself ok how many times

does 24 point 5 go into 196 well it's

gonna go see 2 goes into 2 oh I forgot

to bring with them I zero so bring down

this 0 and that looks to be about what

24 doesn't go into 19 so I'm gonna have

to look at 24 going into 196 and go

several times I'm gonna estimate because

25 would be 25 50 75 100 125 150 175 I'm

gonna estimate 8 maybe so let's take 8

times 5 is 40 carry the 4

8 times 4 is 32 33 34 35 36 carry the 3

8 times 2 is 16 17 18 19 and lo and

behold it comes out nice and evenly so

when I divide I'm getting negative 3.8

with long division so I hope that one

that was a little longer because I had

to do my long division okay let's look

at another one where we are multiplying

okay

so what have we talked about so far when

you have multiply and divide you've got

to have two negatives so this is a

positive times a negative so the answer

is going to be negative so that's the

sign now since we're a long divided our

long multiplying I'm gonna go over here

and stack it and that's going to be 12

point seven times seven point two I'm

gonna ignore the sign because I've

already figured out this is negative now

let's go ahead and multiply 2 times 7 is

14 carry the 1 2 times 2 is 4 plus 1 is

5 2 times 1 is 2 I've put my placeholder

as 0 because now I'm in the 10th

position so 7 times 7 is 49 carry the 4

7 times 2 is 14 plus 4 is 18 carry the 1

7 times 1 is 7 plus 1 is 8 draw my line

I'm gonna add up so 4 9 + 5 is 14 carry

the 1 8 + 2 is 10 plus 1 is 11 carry the

1 and that's 9 okay so I've got 9 144

but remember I had some decimals how

many decimal places did I have I had 1 2

decimal places

one in seven point two in one and 12

point seven so I'm gonna move my decimal

in two places so the answer is negative

91.44 so there we go and multiplying now

let's look at this one okay I'm gonna

divide 84 or 86

for by 13.5 and when I divide those I'm

gonna have to set up my bracket again so

let's do this we got or what let's do

the sign first when we divide I know I

have to have two negatives so I only

have one so the answer is negative now

let's set up on the outside thirteen

point five on the inside I'm gonna have

eighty six point four so let's think for

a second when I divide 86.4 by 13.5 I've

got to look how many times does 13 go

into 86 let's see 13 if I double that

that's 26 if I double 26 that's 54 I'm

up to four of them well it's more than

that so if I add another 26 that puts me

right around 86 so I'm getting close to

86 I'm gonna try 6 so let's try 6 so 6

times 5 is 30

carry the 3 6 times 3 is 18 19 20 21

carry the 2 6 times 1 is 6 plus 2 more

it's 8 okay so notice I came in under

just under 80 6.4 I got 81.0 so now

let's subtract so that's 4 and 5 so

let's bring down a 0 how many times just

13.5 go into 54 because I've got to

think about this without a decimal okay

or 3 if you want to think about bringing

the oh I've already brought down my zero

so let's see 13 and 13 is 26 but it's

really 13.5 what 13 13 26 how many of

those it looks like I'm gonna have 4

about 4 so let's try 4 4 times 5 is 20

carry the 2 4 times 3 is 12 13 14

carry the one four times one is four

plus one more it's five and bingo I

subtract and I don't have a remainder

now where does my decimal go I've lined

it up so it's gonna go right up here and

that makes the sense thirteen times six

is about 86 so that makes sense that the

decimal would fall here so my final

answer is negative six point four that

wouldn't went nice and easily okay so

now let's do some multiplying okay we're

multiplying a fraction times the mixed

number now there are a couple ways to do

it but the way I like to do it is I like

to go ahead and make this mixed number

into an improper fraction that's means

where the top is larger than the bottom

so I'm gonna do what I call the circle

trick I'm going to multiply and then add

so 3 times 1 is 3 plus 2 more is 5 so 1

and 2/3 becomes 5/3 so I now have 3/4

times 5/3 now I can multiply when you

multiply you go straight across and

multiply the top and the bottom now some

people like to go ahead and cross cancel

so let's look is there any value I can

cross cancel and I can a 3 and a 3

so really I'm left with just a 1 and a 1

here because 3 over 3 is 1 cancels out

so now we can multiply across 1 times 5

is 5 and 4 times 1 is 4 so the answer is

5/4 now if you're asked to write it as a

mixed number you're going to divide so

how many times does 4 go into 5 once 1

times 4 is 4

and what's my remainder 1 what do you do

with that one that is your dena

numerator it goes on the top and what

you're dividing by is on the bottom so

the answer is 1 and 1/4 if you need a

mixed number okay now let's try dividing

two fractions so we have negative 1 & 3

fits me straighten this out for you

negative 1 and 3/5 divided by 1 and 9/10

ok so I'm back to sign numbers again I

have a negative divided by a positive

negatives always come in pairs so I know

my answer is negative okay so we've got

that decided I like to do that first now

again I have mixed numbers so I'm going

to do my circle trick again so let's see

5 times 1 is 6 6 plus 3 is 9 so that's

negative 9 fifths divided by another

circle trick so not a 10 times 1 is 10

plus 9 more is 19 tenths so I have

negative 9 fifths divided by 19 tenths

but it's division what do we do with

division I like to use the process of

keep the first fraction change it to

multiplication and flip which is a call

to math reciprocal let's find the

reciprocal so I'm going to flip that

over now I can multiply across but let's

check and see if we can cross cancel we

can take out a 5 5 goes into 5 once 5

goes to into 10 twice so now I can

multiply across the top negative 9 times

2 is negative 18 and then we have a 1

times 9 which is 19 so the answer is

negative 18 over 19 or negative 18 19 so

there's a little view on division now

let's try some converting okay we're

going to convert a few decimals decimals

we're going to convert a fraction to a

decimal okay well that's just dividing

whenever you have a fraction that

actually means divide top / bottom so

let's take five and see how many times

we can divide it into 3 well 3 goes 5

dozen to 3 none so we don't have any so

I'm gonna have to add a decimal and look

at 5 into 30 well 5 into 30 goes 6 times

put the 6 here bring out my decimal 6

times 5 is 30 there's no

Mandor so the answer is just point six

okay now let's look at converting five

eighths to a decimal okay we're going to

take 8 and see how many times it goes

into five because a fraction is really

just top / bottom or 5/8 so let's set it

up how many times does 8 go into five

well it doesn't so we need to add a

decimal and a zero now how many times

does 8 go into 50 well that goes six

times and we have a decimal right in

front so 8 tower 6 times 8 is 48 so

let's bring down the 48 draw the line

and subtract so 50 minus 48 is 2 and

then we have another 0 we can bring down

so how many times does 8 go into 20 well

that's 4 I'm sorry to 2 times 8 is 16

draw the line and subtract 20 minus 16

is 4 bring down yet another 0 how many

times does 8 go into 40 well the answer

is 5 5 times 8 is 40 draw the line

subtract we have zero so our answer is

point six two five

that's the decimal okay now let's look

at converting a decimal to a person

percent okay when you take a decimal to

a percent you're basically saying per

100 so I'm going to multiply 0.625

times 100 all we're gonna do then is

just move the decimal two places because

this is a base 10 problem or base 10 we

learn a base tens so we're gonna move it

over twice so that's gonna be 62 point

five percent so just move the decimal

twice to the right now let's look at

converting let's say we have 20 percent

and we want to convert it to a fraction

well percent

means per 100 that's what I mean is a

cent there's a hundred cents in a dollar

so that means per 100 so we're just

gonna bit 20 over 100 and we're going to

reduce that fraction well if you notice

they both end in zero so we can just

divide them both by 10 by crossing out

zeros then we have 22 over 10 well 2

goes into itself once and 2 goes into 10

five so that reduces to 1/5 okay and the

last one we're going to do is convert

3/4 to a percent okay so what we're

gonna have to do first so we're gonna

have to take it to a decimal and then

take the decimal to the percent so let's

take 3/4 and we're going to divide sorry

3/4 we put the 3 on the inside the 4 on

the outside so 3 goes into our 4 goes

into 3 it doesn't so we have to add the

0 so 4 goes into 30 hmm 7 times and our

decimals here 7 times 4 is 28 let's

subtract 30 minus 28 is to bring down a

0 and then 4 goes into 25 times 5 times

4 is 20 and there is no remainder so our

answer is 0.75 well that's the decimal

now how did we go from a decimal to a

percent we multiply it by 100 so when we

multiply it by 100 we move the decimal

twice so that ends up being 75% which is

0.34 as a decimal there you go there's

the first part of seventh-grade math &

review

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