154 METHODS IN TEACHING 



ond line that is marked off with a brace is three times the 

 length of the first one. They write the two fractions, J, f , 

 realizing that to obtain the latter they have multiplied the 

 first by 3, and that only the numerator has changed. Many 

 drills follow, that, in spite of their simplicity, fix the fact 

 that to multiply the numerator of a fraction by an integer 

 multiplies the value of the fraction. 



To multiply a fraction by an integer by dividing the 

 denominator is also illustrated by lines and circles. Many 

 illustrations, continued at intervals for several days, fix the 

 fact that the smaller the denominator the fewer and larger 

 are the parts into which an object is divided; hence, divid- 

 ing the denominator by any number multiplies the size of 

 the part by that number. 



Division of fractions reverses the illustrations for multi- 

 plication of fractions ; consequently, because of the resultant 

 confusion in the minds of pupils, special care must be ob- 

 served in making the illustrations, which 

 ivision should be frequent and numerous. The steps 



taken are : I . To divide a fraction by an 

 integer by dividing the numerator. 2. To divide a fraction 

 by an integer by multiplying the denominator. 3. To divide 

 a mixed number by an integer. 4. To divide an integer by 

 a fraction whose numerator is I. 5. To divide an integer 

 by a fraction when the integer is exactly divisible. 6. To 

 divide an integer by a fraction when the integer is not 

 exactly divisible. 7. To divide a fraction by a fraction 

 when the numerator of the dividend is exactly divisible. 

 8. To divide a fraction by a fraction when the numera- 

 tor is not exactly divisible. 9. To divide a mixed number 





