Question

Question #9ddf0

Answer 1

`128`

Explanation:

We have: `42 (2) / (3) div (1) / (3)`

`= (42 (2) / (3)) / ((1) / (3))`

`= ((42 cdot 3 + 2) / (3)) / ((1) / (3))`

`= ((128) / (3)) / ((1) / (3))`

`= (128) / (3) cdot (3) / (1)`

`= (128) / (3) cdot 3`

`= 128`

Answer 2

It is `128`

Explanation:

`42 2/3-:1/3`

`=42 2/3xx3`

`=42xx3+2/3xx3`

`=126+2`

`=128`

I used the following properties of division and multiplication:

• division by a fraction is the same as multiplication by the fraction's reciprocal

`a-:b/c=axxc/b`

• distributive property:

`axx(b+c)=ab+ac`

Answer 3

`128`

Explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dividing with fractions: `rarr` In a nutshell

Step 1 . change all mixed numbers to improper fractions

Step 2 .`div rarr xx` and flip the next fraction

Step 3 : cancel any numerator with any denominator through `xx`

Step 4 : `("top x top")/("bottom x bottom")`

Step 5 : simplify if necessary.

Step 6 : Keep improper fractions or change to mixed numbers depending on what you have been told to do.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`42 2/3 div 1/3`

`=128/3 div 1/3 " "larr` step 1

`=128/3 xx3/1" "larr` step 2

`=128/cancel3 xxcancel3/1" "larr` step 3 and step 4

`= 128" "larr` step 5. no further simplifying necessary

Answer 4

`42 2/3 -: 1/3=128`

Explanation:

`color(blue)("For a moment consider just the "42 2/3)`

write this as `42+2/3`

This is the same as:

`" "[42color(magenta)(xx1)]+2/3`

But we can write 1 as `3/3` giving:

`" "[42color(magenta)(xx3/3)]+2/3`

`" "[126/3]" "+2/3 = 128/3`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`42 2/3 -: 1/3" "=" "128/3-:1/3`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Shortcut method")`
Turn the `1/3` upside down and multiply

`128/3xx3/1 " "=" "3/3xx128/1 " "=" "1xx128" "=" "128`

Or by cancelation (which is the same thing really):

`128/(cancel(3))xx(cancel(3))/1 = 128/1=128`