132. A Fraction is one or more of the equal parts of a unit. 133. Common Fractions are written in figures as follows, 134. The Terms of a fraction are the two numbers used to express it. 135. The Denominator is the term that names the parts and shows their size by telling into how many equal parts the unit is divided. It is written below the line. Thus, 4 is the denominator of 3. 136. The Numerator is the term that shows how many of the equal parts of the unit are expressed by the fraction. It is written above the line. Thus, 4 is the numerator of §. 137. A Proper Fraction is a fraction whose numerator is less than its denominator. As §, 3, 10 9 138. An Improper Fraction is a fraction whose numerator is not less than its denominator. As , 10, 16. 139. An Integer may be expressed in a fractional form by writing 1 under it for a denominator. Thus, 2 may be written, read 2 ones. 140. A Mixed Number is an integer and a fraction. united. As 4ğ, read four and five eighths. 141. A Fraction may be regarded as an indicated division (Art. 97), the numerator being the dividend, and the denominator the divisor. Hence 142. The Value of a Fraction is the quotient of the numerator divided by the denominator. Thus, $ is of $1, or of $3. Each equals 75 cents. 9 16,,, 61, 10, 15, 1, 71, 11. 11. Which denominator shows the largest equal part? The smallest ? 12. Name a fraction which represents seven of the eight equal parts of a dollar. 13. Tell what is shown by each term of the fraction REDUCTION OF FRACTIONS. 143. Reduction of Fractions is changing their form without changing their value. 144. To change Integers and Mixed Numbers to Fractions. 3. Into how many thirds can an apple be divided? How many thirds in 1 apples? In 13 apples? In 3 apples? 4. Into how many fourths can an apple be divided? How many fourths in 2 apples? In 21? In 3? 1. (a) In 4 how many fourths? (b) In 63? (c) In 292 ? Solution. (a) In 1 there are 4 fourths; in 4 there are 4 times 4 fourths, or 16 fourths. (b) In 1 there are ; in 6 there are 6 times, or 2; 24 and 4 are 27. Hence 68 = 27. 293 4 116 3 119 Ans. (c) In 1 there are ; in 29 there are 29 times, or 11; 146 plus are 12. Hence 293 = 112. To change an integer or a mixed number to an improper. fraction, Multiply the integer by the denominator; if there is a fractional part, add its numerator to the product, and under the result place the denominator. Change the following to improper fractions. 146. To change Improper Fractions to Integers or Mixed Numbers. ORAL AND WRITTEN EXERCISES. 1. How many apples in 2 halves of an apple? In 3 thirds? In 4 fourths? In 6 thirds? In 8 fourths ? 2. (a) In 19 fourths how many fourths? (b) In 495 fourths ? Solution. (a) As 4 fourths are one, 19 fourths are as many ones as there are 4's in 19, or 44. 4) 495 123, Ans. (b) As are one, 495 are as many ones as there are 4's in 495. 495 ÷ 4 = 1233, Ans. To change an improper fraction to an integer or mixed number, Divide the numerator by the denominator. Change the following improper fractions to integers |