[tex]5\frac{3}{7}[/tex] Kilometers of thread.
The key to solve this problem is using the rule of three.
We have to change mixed number to improper fraction in order to solve the problem.
A mixed number is a number formed by an integer and a proper fraction (one whose quotient is less than 1).
An improper fraction is one whose denominator is less than its numerator.
To change a mixed number to an improper fraction:
1. Multiply the whole number by the denominator and add to the numerator.
2. The denominator of the mixed number is unchanged.
It takes [tex]2\frac{1}{4}[/tex] kilometers of thread to make [tex]3\frac{1}{2}[/tex] boxes of shirts. How many kilometers of thread would it take to make 8 boxes?
We need to change [tex]2\frac{1}{4}[/tex] and [tex]3\frac{1}{2}[/tex] to an improper franctions:
[tex]2\frac{1}{4}=\frac{(2)(4)+1}{4}=\frac{9}{4}[/tex]
[tex]3\frac{1}{2}=\frac{(3)(2)+1}{2}=\frac{7}{2}[/tex]
To calculate how many kilometers of thread would it take to make 8 boxes, we use the rule of three:
9/4 Km of thread -------------> 7/2 boxes of shirts
x <------------- 8 boxes of shirts
[tex]x = \frac{(\frac{9}{4})(8)}{\frac{7}{2}}= \frac{19}{\frac{7}{2}}\\x=\frac{38}{7}[/tex]
Convert the improper fraction 38/7 to a mixed number:
1. Divide the numerator by the denominator.
38÷7 = 5 and a remainder of 3
2. 5 become the whole number, the remainder is the numerator, and the denominator is unchanged.
38/7 = 5 3/7
It would take 5 3/7 kilometers of thread make 8 boxes of shirts.
