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

May 24, 2017

$4 \cdot \frac{6}{8}$

#### Explanation:

We have :
$c - 1 \cdot \frac{1}{2} = 4 \cdot \frac{1}{4}$
For simplicity we can convert the mixed fraction into a simple fraction , we get

$c - \frac{3}{2} = \frac{17}{4}$

if u shift $- \frac{3}{2}$ to the right side and we change the signof $- \frac{3}{2}$ to $+ \frac{3}{2}$ we get

$c = \frac{3}{2} + \frac{17}{4}$
now by cross multiplication

we get $\frac{46}{8} = 4 \cdot \frac{6}{8}$

May 24, 2017

$b = \frac{23}{4}$

#### Explanation:

$\textcolor{b l u e}{\text{Important facts}}$

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

$\left(\text{count")/("size indicator of what is being counted")->("numerator")/("denominator}\right)$

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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$\textcolor{b l u e}{\text{Answering your question}}$
Given:$\text{ } b - 1 \frac{1}{2} = 4 \frac{1}{4}$

I choose to make all the denominators 4

Write as: $\text{ } b - \frac{3}{2} = \frac{17}{4}$

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

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

$\text{ "(4b)/4" "-" "6/4" } = \frac{17}{4}$

Multiply both sides by 4

$4 b - 6 = 17 \text{ "larr" Directly dealing with the counts!}$

$4 b = 23$

divide both sides by 4

$b = \frac{23}{4}$
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Check: consider the left hand side

$b - \frac{3}{2} \text{ "->" "23/4-6/4" "->" } \frac{17}{4} = 4 \frac{1}{4}$

This matches the right hand side so true