Question

Solve.

Express the answer in simplest form.

1/5+ w =7 1/3

w=

Answer 1

\[\frac{ 1 }{5 } + w =7\frac{ 1 }{ 3 }\]
Is this it?

Answer 2

The first thing we can do is find the least common multiple of the denominators of the fractions so we can work with them.

Answer 3

yes

Answer 4

ok

Answer 5

what r the lcm?

Answer 6

If we write down multiples of 3 and 5, we need the smallest multiple that they share in common:

3: 3, 6, 9, 12, 15, 18, 21
5: 5, 10, 15, 20, 25, 30

Answer 7

Which number from this list is the first and smallest multiple that both 3 and 5 share

Answer 8

15

Answer 9

Good job :), now we can convert the fractions so that they are over 15

Answer 10

For \[\frac{ 1 }{ 5 }\]
What do we have to multiply 5 by to get to 15?

Answer 11

5*3

Answer 12

So we can do:
\[\frac{ 1* 3 }{ 5 * 3 }\]

Answer 13

3/15

Answer 14

Now we have \[\frac{ 3 }{ 15 } + w = 7\frac{ 1 }{ 3 }\]

Answer 15

We need to convert 7 1/3 into 15ths now

Answer 16

so what nxt?

Answer 17

We could just convert 7/1 into 15ths, 1/3, and add them together

Answer 18

So for 7/1 what do we have to multiply 1 by to get to 15

Answer 19

15*1 right?

Answer 20

Yep :), so we have to do:
\[\frac{ 7 * 15 }{ 1 * 15 }\]

Answer 21

105/15

Answer 22

Now we have to add 105/15 to 1/3 in 15ths.
So what does the denominator of 3 need to be multiplied by to get 15?

Answer 23

3 * ? = 15

Answer 24

is it 5? im confused a bit

Answer 25

Yes, you did it :)

Answer 26

Since 3 * 5 = 15 we can do this to get 1/3 as a fraction over 15:
\[\frac{ 1*5 }{ 3*5 }\]

Answer 27

5/15

Answer 28

Yep :), so now I can write out what we have so far:

Answer 29

ok

Answer 30

\[\frac{ 3 }{ 15 } + w = \frac{ 105 }{ 15 }+\frac{ 5 }{ 15 }\]

Answer 31

We could first simplify the right side of the equation

Answer 32

By adding the two fractions

Answer 33

\[\frac{ 105 }{ 15 }+\frac{ 5 }{ 15 } = \frac{ ? }{ 15 }\]

Answer 34

We would simply add across

Answer 35

110/15

Answer 36

\[\frac{ 3 }{ 15 } + w = \frac{ 110 }{ 15 }\]

Answer 37

What might we do to get w alone on one side of the equation

Answer 38

oh man! gtg

Answer 39

We can get rid of the\[\frac{ 3 }{ 15 } \]
by subtracting from both sides

Answer 40

\[w = \frac{ 107 }{ 15 }\]

Answer 41

ok is my answer 2 2/15?

Answer 42

It would be \[\frac{ 107 }{ 15 }\]
As an improper fraction or:
\[7\frac{ 2 }{ 15 }\]
As a mixed number

Answer 43

so 7 2/15 is the answer?

Answer 44

I would use the mixed number, yep :)

Answer 45

thanks!!!

Answer 46

\[7\frac{ 2 }{ 15 }\]