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today we'll be solving one-step

equations

and in this one-step equation we will

notice that our coefficient

is a fraction the coefficient is that

number that's in front of the letter

the letter is also known in math as the

variable

so when i go ahead and multi using the

multiplication property of equality

which means whatever i do on the left

side i am going to

make this equation equal

i'm going to do the same on the right

side

so when we have 3 over 5 when we have 3

over 5 that means that we are going to

multiply it

by its reciprocal of five

over three now because i do it on the

left side

i'm gonna have to multiply by five

over three on the right side

now this six is a whole number and that

to make it

equivalent as a fraction i'm going to

make that six over one

so now that i can either do one of two

things i could multiply across

15 over 5 times 3 is 15

and 3 times 5 is 15 so

15 over 15 is equal to 1.

therefore i'll have one w and i would

have my variable by

itself but another way i can do it

is by cross multiplying or cross

canceling

and in cross canceling i'm going to go

ahead and say the 5

goes into the 5 one time

and the three will go into the three one

time because they're factors of each

other

they're the same number so through the

identity property they are the same

therefore one times one and one times

one gives me 1 over 1

so that gives me w by itself

now 6 times 5 on the right hand side

will equal 30

and 1 times 3 in the denominator

would be 3. now if i simplified 30 how

many times does 3 go into 30

and the answer is 10 times so

my correct answer is w equals 10.

let's go ahead and give that another

shot another try

with another sample problem

here we go have something hidden right

here for you

so our next one is 7 8 t equals 14.

now when i get rid of this fraction i'm

gonna multiply it by its reciprocal

which is going to be eight over seven

and what i do on the right side i'm

going to multiply

14 by 8 over 7.

yes and you're right i'm going to go

ahead and put the 14 over 1

because i'm going to create this whole

number into a fraction

now as we look at the 8 over 7

multiplied by 7 over 8

it is going to cancel

each out so 1 times 1 is going to bring

the t

my variable all by itself and now i can

go 14 times 8

and that's going to be a big number

divided by

1 times 7. so i know that 1 times 7

would be easy but i really want to look

and see if i can do any canceling

and which i can so the 7 goes into

itself

once and the 7 because it's multiples of

14 it goes into it 2 times

so now i could easily say 2 times 8

is 16 over

1 times 1 is 1. so my final answer

t is going to equal 16.

so just remember when we have fractions

in our equations not to necessarily

freak out

we remember that we'll take that

fraction and take its reciprocal

and which the when i take the reciprocal

or multiply the reciprocal by the

original fraction

it will come out to be one and so i'll

have one t

and i'll have my variable by itself and

then i'll be able to find

my answer

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you