Mastering Mathematics – Fractions Are Key – Part I

If you study mathematics, you simply cannot and will not escape fractions. Thus a mastery of this topic is essential. Fractions and their closely related cousins, percents and decimals, spawn problem after problem for many students attempting to make headway in arithmetic, pre-algebra, algebra, pre-calculus, and yes—even calculus. These two-headed monsters pop up everywhere. So love them or hate them, you best know them. Here in this multi-part series we discuss the key things you need to know to help dominate these mathematical bugbears.First of all, let’s talk about some basic concepts. What is a fraction? A fraction, or rational number, as it is more formally called, is a number that is the quotient of two integers. Thus 1/2, -3/5, and 5/7 are all fractions. Students in the elementary grades learn that an improper fraction is one in which the numerator is greater than the denominator. Thus 3/2 and 5/4 are improper fractions. Because students in the earlier grades think better in terms of whole numbers rather than fractions, or partial numbers, such students are taught to convert impropers into mixed numbers. A mixed number is simply the whole portion part plus the fractional part, such that the fractional part has a numerator less than the denominator. To convert an improper fraction such as 14/5 into a mixed number, simply divide the denominator into the numerator: the quotient is the whole number part of the mixed number and the remainder is the fractional part. Thus 14/5 becomes 2 4/5 because 5 goes into 14 twice, leaving a remainder of 4.Going from a mixed number to an improper fraction is equally easy. Simply multiply the whole number by the denominator and add the numerator of the fractional part. Thus 3 6/7 becomes 3×7 + 6 or 27/7. Similarly 4 5/9 becomes 4×9 + 5 or 50/9. This applies as well to negative mixed numbers, however with one adjustment; you need to ignore the negative sign until the end. Thus -8 1/2 becomes 8×2 + 1 = 17. Now add the negative sign and place this number over the denominator to get -17/2. Similarly -5 2/3 becomes 5×3 + 2 = 17; thus the improper fraction is -17/3.Stay tuned as in Part II, we will examine reducing fractions, recognizing equivalent fractions, and multiplying and dividing fractions.