Question

An airline agent checked in 10 and 1/3 kg of baggage for one passenger and another 8 and 5/6 kg of baggage for his travel companion. How many kilograms of luggage did the agent check in all?

Answer 1

Do you know how to first convert it into an improper fraction?

Answer 2

no I don't

Answer 3

Take a look at this image

Answer 4

ok

Answer 5

So we have

10 1/3

we have to multiply 10*3 and add 1
and then the denominator will be 3

what is 10*3 =

Answer 6

that means I have to make it a mixed fraction

Answer 7

we already have a mixed fraction! We need to make it an improper fraction

Answer 8

okay

Answer 9

how do I do that

Answer 10

so you know if you had a pie, if you cut it into thirds

you could get one third of the pie?

Answer 11

oh yea

Answer 12

we have

10 pies
and 1/3 of a pie

another way to write 10 pies in terms of slices would be
if we cut each pie into 3 slices, how many slices would 10 pies have?

Answer 13

each pie has 3 slices and we have 10 pies

so 10 times 3 =

Answer 14

30

Answer 15

good so

10 is the same thing as 30/3
because we have 30 whole slices
and each pie has 3 slice

so each pie has 3 slices and no one's eaten anything yet
so it would be
3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 3/3

= 30 / 3

Answer 16

still following along?

Answer 17

yes

Answer 18

now we said we had 10 pies AND 1/3 of another pie

so if 10 pies is 30 slices
and we have one more slice

what is 30 + 1

Answer 19

31

Answer 20

and so another way to write 10 1/3 would be as 31/3

make sense?

Answer 21

yes so you make it a mixed since it is a improper fraction or simplify it

Answer 22

we made it into an improper fraction

it's improper because the numerator (the top part of the fraction) is bigger than the denominator (the bottom part of the fraction)

Answer 23

oh

Answer 24

so what would you do after is that the answer

Answer 25

now can you similarly do that to 8 and 5/6

so instead of our pie being cut into 3 slices
we're going to cut out pie into 6 slices

so if we have 8 pies, how many total slices will we have?

Answer 26

basically what is 8 times 6
since each pie has 6 slices and there's 8 pies

Answer 27

48

Answer 28

good! now we said we have 8 5/6

so 8 pies is the same as 48 / 6

but we still have one more pie but this one only has 5 slices out of the 6 slices (5/6)

so we need to add it. AND REMEMBER when we add fractions, we do NOT add the bottom part. The bottom part MUST be the same number for us to be able to add the top parts. Got it?

So what is 48 + 5 =

Answer 29

64/6

Answer 30

are you sure? maybe you pressed the wrong number

just count on your fingers

48 + 6

Answer 31

54

Answer 32

there you go!

so now we have 54/6

Answer 33

Now, let's look at your question again and use these improper fractions we got

Answer 34

okay

Answer 35

An airline agent checked in 10 and 1/3 kg of baggage for one passenger and another 8 and 5/6 kg of baggage for his travel companion. How many kilograms of luggage did the agent check in all?

we had to ADD the two fractions

\(10 \dfrac{1}{3} + 8 \dfrac{5}{6}\)

but we just said that
10 1/3 is the same thing as 31/3

and 8 5/6 is the same thing as 54/6

so now we have

\(\dfrac{31}{3} + \dfrac{54}{6} = \)

Answer 36

18 6/6

Answer 37

no no
okay so we learned how to convert it into improper fractions

but let's take a step back

Answer 38

we have 10 pies and one third of a slice

we have 8 pies and 5 out of 6 slices

right?

Answer 39

mmmm?

Answer 40

ok

Answer 41

so let's just count the pies which we have that are FULL

what is 10 + 8

Answer 42

hold on

Answer 43

sure

Answer 44

you got 10 whole pies and 8 whole pies

how many total pies do you have

Answer 45

18

Answer 46

do you mean wholes are pies

Answer 47

how many wholes? or how manypies?

Answer 48

Good now we have to look at what's left

we have 1/3 and we have 5/6

Answer 49

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jesternmais
do you mean wholes are pies
\(\color{#0cbb34}{\text{End of Quote}}\)

yes, I'm just using pies because maybe you'll understand that better than wholes
because pies are circular so it can help you think about the fractions

Answer 50

1/3+5/6=6/6=1/1

Answer 51

or

Answer 52

now now

are you sure?

doesn't that 1/3 look much bigger than whatever is left in the 5/6 pie

Answer 53

1/3+5/6=7/6=1 1/1

Answer 54

now there you go!!!!

Answer 55

wait

Answer 56

so the answer is 1 1/1

Answer 57

7 / 6 = 1 1/6

Answer 58

oh

Answer 59

the denominator stays the same

Answer 60

at all times

Answer 61

I got thank you

Answer 62

Yes! The denominator stays the same when you're adding and subtracting

Answer 63

so what did you get as the final answer? (:

Answer 64

well I add the numerators and then I got 7/5 but left the denominator the same and when I saw it was a improper fraction I changed it to a mixed number and how I did that I divided the denominator into the numerator it went 1 time and the remainder was one which would be the numerator for the mixed number and then the denominator would be the same .

Answer 65

7/6*

Answer 66

wonderful!

so we had 18 wholes
and then we have 1 whole and 1/6

so how many wholes do we have now?

Answer 67

1 /16

Answer 68

1 1/6*

Answer 69

18 whole pies

and then we have 1 whole pie and 1/6 of a pie

so 18 + 1 1/6

Answer 70

18 +1 1/6 = 19 1/6

Answer 71

And that's your final answer!!

Answer 72

19 1/6

Answer 73

Good job!

Answer 74

thank you

Answer 75

You're most welcome!