Question

A rectangular card has an area of 120 over 1\4 square inches. The card is 6 over 1\2 inches wide. How long is the card????

Answer 1

The area of a rectangle is A=lw.  A is the area, l is length, w is width.  So, you just need to multiply length times width to get area.  BUT, you have the area--what you need to find is length.  Let's fill in what you know so far.  120 1/4 = l * 6 1/2.

But to find the length, you need to isolate it on one side of the equation.  So, you can divide both sides by 6 1/2.  l * 6 1/2 / 6 1/12 = 120 1/4 / 6 1/2.  So, l = 120 1/4  /  6 1/2.

Now, we just need to calculate 120 1/4 divided by 6 1/2.  The first thing to do when dividing fractions is to convert all fractions into improper fractions.  We need to turn 120 1/4 into an equivalent fraction, with 4 as the denominator (bottom number).  How do you do that?  Multiply 120 by the denominator, 4, and put this as the numerator to get 120*4 / 4 or 480/4.  We know this is true because if you divide 480 by 4, you get 120, so this is an equivalent fraction.  Finally, we need to add the numerators 480 and 1 together, because they are part of the same number and have the same denominator.  So, 120 1/4 = 481/4.

Same concept with 6 1/2: 6*2=12, 12+1=13, answer is 13/2.

Next, when dividing fractions, you multiply by the reciprocal.  So, since you're dividing 481/4 by 13/2, that's the same as multiplying by the reciprocal of the divisor, 13/2.  The reciprocal is basically the opposite of the fraction, where you switch the numerator and denominator.  The reciprocal of 13/2 is 2/13.  Now you just need to multiply 481/4 by 2/13.

Remember, when multiplying fractions, you multiply numerators together to get new numerator, and multiply the denominators to get the new denominator.  481*2=962, and 4*13=52.  The answer is 962/52.

After that, you need to simplify this by finding their greatest common factor and dividing by it.  The GCF is 26.  962/26=37, and 52/26=2.  So, the answer is 37/2.  Finally, you need to convert this back to a mixed number.  37/2 = 36+1 / 2 = 36/2 + 1/2 = 18 1/2.  Since the area is in square inches, the length must be in inches.

Answer: 18 1/2 inches