-- II COMMON FRACTIONS 32. Meaning of Fractions.-Any part of a group of objects is called a fraction. One parts into which an apple is divided is one-h while six apples are one-half of a dozen appl Common fractions are written thus, . T low the line is called denominator and tells i equal parts the object or group of objects names the fraction with which we are dealin ber above the line is called numerator and tell the equal parts of an object or group of objec represents; it is the numberer of the fraction. tor and denominator are called the terms. 33. Integers.-Whole numbers are also cal EXERCISES 1. What part of a foot is 3 in.? 6 in.? In a foot there are how many in. ? 3. A quarter is what part of $2? of $5? 2. 4. A dime is what part of $1? of $3? What part of dozen are 6 cbinets 2 4 ject or of 34. Equivalent Fractions.-Fractions of the same valu may have different numerators and different denominators Such fractions are called equivalent fractions. One of the 2 equal parts of an object and 5 of 10 equal parts of the same object represent the same amount. Hence, = 10. two equal an apple Similarly,==, etc. How? 35. Reduction of Fractions.-Fractions may be reduced to equivalent fractions by multiplying or dividing both terms by the same number. Why? 36. Lowest Terms.-Fractions whose terms have n common divisor are said to be in their lowest terms. Re duce all final fractions to their lowest terms. EXERCISES Use pencil and paper only when necessary. 1. Show by objects that = += 1; } = 2. 1. Give three fractions equivalent to each of the follow ing: 1, 3, 1, 4, 3, 1, 1, 1. 2 3 2 5 6 3. Reduce to their lowest terms: t, 35, 18, 21, 15, 20 18, 11, 11, 11. 4. Reduce the results found in exercises on page 28 t their lowest terms. 5. Which is the larger, or ? or ? 6. Change and so that you can see which is th 10 having the same denominator may be added at once. To add and is the same as addin 1 apple. In the first case we get and in the 4 apples. Fractions having different denomin changed to equivalent ones so that all will b denominator. 34. If the sum of two fractions is and o 3, what is the other fraction? 81 35. What fraction added to 3 gives 11? 36. What fraction subtracted from 37. gives In smoothing off a brass cylinder for was reduced from a diameter of in. to 33 in. smaller is the second diameter ? 38. Mixed Numbers.-A whole number and a fracti taken together are called a mixed number. Mixed numbe are written with the fraction following right after the who number; 6, 5, etc. 39. Proper and Improper Fractions. In proper fractio the numerator is less than the denominator; . In improp fractions the numerator is not less than the denominato or . 40. Reducing Mixed Numbers to Improper Fractions. The whole number in a mixed number can be reduced to fraction and added to the fraction of the mixed number. 14 + 4 = 18. Thus, 24 = 41. Reducing Improper Fractions to Mixed Numbers. An improper fraction can be reduced to a mixed numbe Reduce all final results to those in which the fractio are proper fractions in their lowest terms. EXERCISES Use pencil and paper only when absolutely necessary. 1. Simplify: 2, 18, 18, 30, 32, 15, 14. 2. Change to improper fractions: 2, 3, 6, 7, 61, 8 7, 9, 6, 4. 3. How many dollars and quarters are there in 8 qua ters? in 10 quarters? in 6 quarters? in 15 quarters? 4. Express the above in dollars and fractions of a dolla as 7 quarters equal 12 dollars. 5. Express as feet and fractions of a foot: 15 in.; 18 i 24 in.; 32 in.; 42 in.; 48 in.; 52 in. 1421 8/3/ 23 15 200 22 26/1/ 18 um ui AVALADU TUCAN. Change fractions to equivalent f same denominator and place th Add fractions. Reduce to a mix sum is an improper fraction. Ad bers and any ones found in the sun 7248 38 = 118 Annex the remaining fraction to t EXERCISES 1. 457392 Read and add the following: 3. 6784093 5. 845673 43. Subtraction of Mixed Numbers.-In th of mixed numbers, consider the fractions fir The fraction in the subtrahend may be larg in the minuend. |