Question

It takes 2 1/4 kilometers of thread to make 3 1/2 boxes of shirts. How many kilometers of thread would it take to make 8 boxes?

Answer 1

`5(3)/(7)` 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
`2(1)/(4)` kilometers of thread to make
`3(1)/(2)` boxes of shirts. How many kilometers of thread would it take to make 8 boxes?

We need to change
`2(1)/(4)` and
`3(1)/(2)` to an improper franctions:

`2(1)/(4)=((2)(4)+1)/(4)=(9)/(4)`

`3(1)/(2)=((3)(2)+1)/(2)=(7)/(2)`

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

`x = (((9)/(4))(8))/((7)/(2))= (19)/((7)/(2))\\x=(38)/(7)`

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.