The missing factor is 1 5/8
<u>Step-by-step explanation:</u>
Let us consider the missing factor has 'x'
The given expression is 4 1/2 - x = 2 7/8
<u>To find x :</u>
The first step is to bring all the constant terms on on side and x on the other side,
⇒ 4 1/2 - 2 7/8 = x
Now, the numbers are in improper fraction (mixed fraction). So you have to convert them into proper fraction.
To convert the improper fraction 4 1/2 into proper fraction,
Multiply the denominator 2 with 4 and the result 8 is added with the numerator 1.
⇒ 4 1/2 = 9/2.
To convert the improper fraction 2 7/8 into proper fraction,
Multiply the denominator 8 with 2 and the result 16 is added with the numerator 7.
⇒ 2 7/8 = 23/8.
Now replace them in the given expression. The expression becomes as :
⇒ (9/2) - (23/8) = x
Cross multiply 2 and 8,
⇒ (72 - 46) / 16 = x
⇒ 26 / 16 = x
⇒ 13/8 = x
The x value is 13/8. You have to convert it into mixed fraction (since the question is given in the form of mixed fraction).
<u>To convert into mixed fraction,</u>
Divide 13 by 8 and write them in the form of Quotient (Reminder / Divisor).
⇒ 13 ÷ 8
⇒ 1 (quotient)
⇒ 5 (remainder)
The divisor is 8.
Therefore, x = 13/8 can be written as 1 5/8.
The missing factor is 1 5/8.
![x^{2} - 4 [(x-4)^{2}] =16 ](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-%204%20%5B%28x-4%29%5E%7B2%7D%5D%20%3D16%0A%20)