LESSON XXXVIII. 1. How many oranges are 5 times 3 oranges? 2. There are two ways of solving this example. FIRST. Write the figure 3 five times in a column, and draw a short line under it. Then count, or add, thus: 3, 6, 9, 12, 15, and write the result below the line. SECOND.-Write the figure 3 but once, and write the figure 5 under it, to show how many times 3 is to be FIRST. taken, and draw a short line. Then By Multiplication. say 5 times 3 are 15, and write the result below the line. The result is 15 in both cases, but in the first case it is obtained by addition and is called 3 5 15 Product. the Sum; in the second case, it is obtained by multiplication and is called the Product. Hence, 3. Multiplication is also a short method of adding equal EXERCISES FOR THE SLATE AND BOARD. Find the result by Addition and by Multiplication 4. Of 2 times 5 cents. 5. Of 4 times 3 figs. 6. Of 3 times 5 marbles. 7. Of 5 times 4 hats. LESSON XXXIX. 1. How many peaches are there on 3 plates, if there are 5 peaches on each plate? SOLUTION. Since there are 5 peaches on one plate, on 3 plates there are 3 times 5 peaches, which are 15 peaches. Hence, there are 15 peaches on 3 plates. 2. If a yard of ribbon cost 4 cents, how much will 3 yards cost? 3. If 1 orange cost 5 cents, what will 2 oranges cost? 4. How much will 4 pencils cost, if 1 pencil cost 5 cents? 5. How many eggs in 3 nests, if there are 3 eggs in each nest? 6. How many marbles have 4 boys, if each boy has 5 marbles? 7. How many fishes did 3 boys catch, if each boy caught 5 fishes? 8. Mary gave 5 cents a yard for 5 yards of ribbon. How many cents did she give for the whole? 9. Which is greater, 4 times 5, or 5 times 4? 10. How much greater is 4 times 3 than 2 times 5? 11. What is the difference in the cost of 3 oranges at 5 cents a piece, and 5 lemons at 3 cents a piece? 1. I had 12 marbles and gave 4 to James; how many had I left? 2. I gave 4 more to Louis; then, how many had I left? 3. I gave 4 more to Asa; then, how many had I left? 4. How many times 4 marbles did I give away? 5. How many are 12 less 4? S less 4? 4 less 4? 6. How many times can 4 marbles be taken from 12 marbles? How many 4's in 12? 7. Instead of saying that 4 can be taken from 12, 3 times, or that there are 3 fours in 12, say, 4 is contained in 12, 3 times. 8. Make a short horizontal line on your slate; thus, 9. Make two dots, one above, and one below the line; thus,÷ 10. This sign,, is used in place of the words divided by; thus, instead of writing 12 divided by 4, write 124. 11. Express by figures and the proper signs: Two is contained in twelve, six times. Four is contained in twenty, five times. Five is contained in twenty-five, five times. 1. How many oranges, at five cents each, can you buy for 15 cents? 2. How many times can 5 cents be taken from 15 cents? 3. How many times 5 cents in 15 cents? 5 is contained in 15 how many times? 15 ÷ 5 4. Finding how many times one number is contained in another is called Division. = :? 5. The sign,, is called the Sign of Division. It is read, divided by; thus, 155 is read, 15 divided by 5. 6. The number obtained by dividing one number by another is called the Quotient. LESSON XLII. 1. Among how many boys can 15 cents be divided and each boy receive 5 cents? FIRST. By Subtraction. 15 cents. 5 10 cents. 5 2. There are two ways of solving this example: FIRST-Taking 5 cents from 15 cents, 10 cents are left; again, taking 5 cents from 10 cents, 5 cents are left; again, taking 5 cents from 5 cents, no cents are left. Since 5 cents have been subtracted or taken from 15 cents 3 times, I gave the 15 cents to 3 boys. SECOND.-Since we wish to find how many times 5 cents are contained in 15 cents, write the expression thus, 15÷5=3, and read it, 15 divided by 5 equals 3. Or, write 15, and on the left write 5, with a short curved line between them, and a short line under the 15. Then say, 5 is contained in 15, 3 times, and write the result below the line. 5 cents. 5 0 cents. SECOND. By Division. 5)15 3. The result is 3 in both cases, but in the first case it is obtained by Subtraction, in the second case by Division. Hence, Division is also a short method of performing several subtractions of the same number. 4. Find the result, both by Subtraction and by Division of each of the following: How many 7. 4's in 20 ? 9. 5's in 20? 10. 5's in 25 ? |