## Fractions to Decimals

4/15/2013

There are two official ways to convert fractions to decimals, and an alternate of one of the ways. The first way is to convert the fraction to an equivalent multiple of ten. After that, the conversion is easy: 3/10=.3, 55/100=.55, etc. However, the first step is often hard to do. For example, if one has the fraction 3/4 and wants to use the first way, then they would first multiply the fraction by 10/10, or 1 in a different form. The fraction 30/40 could then be multiplied by .25/.25, still one. This would then make the decimal over ten. But the number thirty doesn't quarter as easily. Long division, extensive mental math, or a calculator would be required to make the fraction equivalent, and many problems are more complex.

However, there is a second way. The second way also requires long division, extensive mental math, or a calculator, but it doesn't have any of the extra "multiple of 10" steps. This method is to simply divide the denominator into the numerator, or divide the numerator by the denominator. This method always works, but is sometimes complicated. Nevertheless, it is often easier than the multiples of 10 method, except when the fraction is already in that form.

## Restaurant Supplies: Ratios Or percentages?

4/8/2013

When deciding between ratios and percents to find the amount of food necessary to restock a restaurant,  ratios would be the better choice. Let's say that a restaurant has a popular dish, and a less popular dish. It restocks ingredients for both those dishes, but wants to have twice as much of the popular dish (D1) than the less popular one (D2), or have the ratio 2:1. Now, let's say that D1 requires fish (I1) and salt (I2), and D2 requires bacon (I3) and pepper (I4). If the restaurant is left with 20 units of I1 and 10 units of I2, and knows they want to restock fully to 100 units of I1 and 50 of I2, but lost the information about D2, then the ratio 2:1 can be used to come up with the solution of 50 units of I3 and 25 of I4.

That can be done like this. For I1, 100 is the one that is going to be larger, so we'll put it over the unknown: 100/?. Two is greater than one, so: 2/1. Then a proportion can be written: 100/?=2/1. Using cross-multiplication, which in this case says that the product of the outside numbers must be equal to the product of the inside. So, 100*1=100, but what times two equals 100? 50, of course. So, 100/50=2/1. From that, it can be discovered that 50 units of I3 are needed. Also, the same process can be used to find the answer of 25 units of I4.

The same ratio could also be used in a different situation. Let's say that everything is the same, except for the fact that the restaurant lost the information on D1, instead of D2. Then, the proportion would have to be set up like this: ?/50=2/1. Since 50*2=100, ?*1 must equal 100. Because anything times one is itself, ?, and the number of I1, must be 100. The same can be done to find the

## JJ s.

These are requests given by the Computech math teachers that I respond to every Monday.