Many people believe that mathematics is mainly doing calculations with numbers and formulas – but in reality mathematics has more to do with thinking in a systematic way. Nevertheless, there are some topics in mathematics that do indeed involve a lot of numerical and algebraic computations
Many people believe that mathematics is mainly doing calculations with numbers and formulas – but in reality mathematics has more to do with thinking in a systematic way. Nevertheless, there are some topics in mathematics that do indeed involve a lot of numerical and algebraic computations. Mathematics that we use in everyday financial transactions is like that – there are certain formulas and calculations that you need to master, and there is no way to get around it. It is important to develop a fairly good understanding of these formulas and calculations, so that you can decide for yourself what is in your best financial interest without having to rely on someone else.
Percentages pop up all the time in our financial dealings – in making shopping purchases, computing bank and credit card interest, paying sales and income taxes, calculating discounts and surcharges, and just about everywhere. Anyone without a good basic understanding of percentages in today’s world has not much hope of capably managing his or her finances.
A percentage represents parts per one hundred. For instance, if you take 35% (35 percent) of a pile of rice, that is equivalent to dividing up the rice into 100 equal parts, and then taking 35 of those parts.
If a store clerk charges you 4% sales tax on a $200 purchase, that means the clerk divides the $200 into 100 equal parts of $2 each, and then takes 4 of those parts for a total of $8. Of course, the clerk does not physically divide up the money into 100 equal stacks and take 4 stacks, but instead uses a mathematical formula to accomplish the same result. If A is the amount of a general purchase, and the clerk divides this amount into 100 equal parts, then each part is worth the quotient A/100. When the clerk takes 4 of those parts, the amount of the tax comes to
Thus, to compute 4% of an amount A, you multiply A by.04. The number.04 is the decimal equivalent of 4% – it is obtained by dividing 4 by 100. If we write 4 as 4.0, then dividing 4 by 100 just moves the decimal point two places to the left. To denote that.04 is the decimal equivalent of 4%, we write
4% =.04.
Naturally, the same reasoning applies to any given percentage – to take 37% of a number you multiply it by.37, and in general to take a percentage p of a number you multiply the number by the decimal equivalent of p, obtained by moving the decimal point two places to the left in p and dropping the percentage sign.
A percentage does not have to be a whole number, nor does it have to be less than 100. If you take 23.5% of a pile 