Question

How do you solve and check your solution given `b-1 1/2=4 1/4`?

Answer 1

`4*6/8`

Explanation:

We have :
`c-1*1/2=4*1/4`
For simplicity we can convert the mixed fraction into a simple fraction , we get

`c-3/2=17/4`

if u shift `-3/2` to the right side and we change the signof `-3/2` to `+3/2` we get

`c=3/2+17/4`
now by cross multiplication

we get `46/8=4*6/8`

Answer 2

`b=23/4`

Explanation:

`color(blue)("Important facts")`

A fraction consists of two parts and the function of these parts are:

`("count")/("size indicator of what is being counted")->("numerator")/("denominator")`

You can NOT DIRECTLY add or subtract the counts unless the size indicators are the same.

If you multiply a number by 1 you do not change its true value. However, one comes in many forms so you can change the way a number looks without changing its 'intrinsic value'.
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`color(blue)("Answering your question")`
Given:`" "b-1 1/2=4 1/4`

I choose to make all the denominators 4

Write as: `" "b-3/2=17/4`

`color(green)([bcolor(red)(xx1)]-[3/2color(red)(xx1)]=17/4`

`color(green)([bcolor(red)(xx4/4)]-[3/2color(red)(xx2/2)]=17/4`

`" "(4b)/4" "-" "6/4" "=17/4`

Multiply both sides by 4

`4b-6=17" "larr" Directly dealing with the counts!"`

Add 6 to both sides

`4b=23`

divide both sides by 4

`b=23/4`
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Check: consider the left hand side

`b-3/2" "->" "23/4-6/4" "->" "17/4=4 1/4`

This matches the right hand side so true