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

Question

Isaiah Anthony · Accepted Answer

#4*6/8#

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#

Nathan Axel · Answer

#b=23/4#

#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'. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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

Ethan Adkins · Answer

undefined To solve for $ b $, add $ 1 \frac{1}{2} $ to both sides of the equation. Then, check the solution by substituting it back into the original equation.