Question

Howard needs 576 square inches of cardboard for a school project, but the store only sells cardboard by the square foot. How many square feet of cardboard does he need?

Answer 1

Hint: First find the relation between the 2 measurements, then try to find the way to substitute the latter measurement in the given measurement to get its value in required measurement, which is the required result.

Complete step-by-step answer:
Given the condition in the question is written in the form of, Howard needs 576 square inches cardboard. He needs to ask in square feet to get it from the shop there.
Measurements: Measurement is the assignment of a member to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of the measurement are dependent on the context and discipline.
Units: A unit of measurement is a definite magnitude of the quantity defined and adopted by convention by law, that is used as a standard of measurement of the same kind of quantity. Any other quantity of that kind can be expressed as multiple of the unit of measurement.
Here we have 2 types of units of same measurement:
Unit-1 = Inches, Unit-2 = feet.
Relation between these two can be written as:
1 foot = 12 inches
By dividing with 12 on both sides we get it as
$1\text{ inch}=\dfrac{1}{12}\text{feet}.................\left( 1 \right)$
The measurement of cardboard given the question is 576 square inch. By writing it mathematically, we can write it in form of
$576inc{{h}^{2}}$
By writing the unit as product, we get it in form of:
$576inch\times inch$
By substituting equation (i) in the above equation we get it as below
$576\times \dfrac{1}{12}\times feet\times \dfrac{1}{2}\times feet$
By combining similar terms together, we get it in form of:
$\left( 576\times \dfrac{1}{12}\times \dfrac{1}{12} \right)\times \left( feet\times feet \right)$
By simplifying them, we can write it in the form of
$\dfrac{576}{144}fee{{t}^{2}}$
By simplifying the above term, we write it in form of
$4fee{{t}^{2}}$
In words we can write in the form of 4 square feet. So, to 576 square inch cardboard he must ask for 4 square feet of cardboard.

Note: Be careful while substituting the value of inch in feet, some students multiply by 12 instead of dividing by 12. This is a very common mistake but you must take care which unit is greater. Just verify at the last step which one is greater than you can avoid this mistake.