By George Boole
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Extra info for A Treatise on Differential Equations
Erase three small circles from the third circle. 4. Two small circles are left in the third circle. You have two whole circles 2 3 2 and two-fifths (5 ) of the last circle, so 3 – 5 = 2 5 . 5. Use the circle method and the method in the Tips and Tricks box to solve the following problems: 1 7–4 4 10 – 7 3 14 – 8 T o subtract a fraction from a whole number, follow these three simple steps. The 2 problem in this example is 6 – 3. 1. Reduce the whole number by 1 and convert the 1 you took away into a fraction that has the same numerator and denominator as the denominator of the fraction 3 you are subtracting.
7/0 is undefined. 1/0 is undefined. No matter what the numerator is, if the denominator is 0 the fraction is always undefined. ZERO 37 PartII 12/6/00 9:25 AM Page 38 PartIII 11/28/00 9:22 AM Page 39 III ADDING AND SUBTRACTING FRACTIONS N ow that you know fraction basics, it is time to learn how to add and subtract fractions. You’ll learn how to add and subtract fractions that have common denominators and fractions that have different denominators. You’ll add mixed numbers to mixed numbers, mixed numbers to proper fractions, and fractions to whole numbers.
If you are not sure which fraction is larger, convert both fractions to their lowest common denominator, then compare their numerators. The “lowest common denominator” is the smallest number that can be evenly divided by both denominators. For example, to 28 T H E FA C T S O N F R A C T I O N S find the lowest common denominator of 3/5 and 5/12, multiply the denominators: 5 × 12 = 60. Can both denominators divide evenly a number lower than 60? They cannot. So 60 is the lowest common denominator.