24.-1. Write in figures three hundred sixteen thousand four hundred five.

316,405

SOLUTION.-Writing 316 for the hundreds, tens and ones of thousands, and 405 for the hundreds, tens and ones of units, gives 316,405, the required expression.

Write in figures—

2. Three hundred seventy-three. Four hundred. 3. Seven hundred sixty-one. Three hundred one. 4. Eight hundred eighty-five. Seventy-nine. 5. One thousand one hundred forty-nine. 6. Nine thousand three hundred thirty-three. 7. Twenty-five thousand three hundred sixty-five. 25. Rule for Numeration.-Beginning with the lowest order of units, separate the figures of the given number into periods of three figures each.

In reading, begin with the highest period; read the hundreds, tens and ones of each period; and give the name of each period, except units, after

its ones.

26. Rule for Notation.- Write the figures expressing the hundreds, tens and ones of each period in their order.

PROBLEMS.

27. Write and read

1.

711. 5. 11,224. 9. 100,000. | 13.

2.

3,163,000.

309. 6. 12,560. 10. 525,125. 14. 4,725,555. 3. 1,624. 7. 50,000. 11. 500,025. 15. 65,008,721. 4. 3,052. 8. 60,606. 12. 751,157. 16. 364,230,000. 28. Express by figures—

1. Five hundred. Five thousand. Five hundred five. 2. Five thousand five. Eight hundred nine. 3. One thousand one hundred nineteen.

4. Two thousands five hundreds ninety.

5. Eight hundreds seventy-seven.

6. Twenty-five thousands eight hundred eight. 7. Fifty-nine thousands nine hundreds.

8. One hundred sixty-three thousands.

29. TEST QUESTIONS.-1. What is a unit? A number? What is a figure?

2. Name the first nine numbers. What numbers are expressed by a single figure? When a number is expressed by two figures, side by side, what does the figure on the right express? The figure on the left?

3. What is numeration? Notation? What does a figure written alone, or at the left of the decimal point, express?

4. How are orders of units expressed? What does the first figure at the left of the decimal point express? The second? The third? Recite the orders of the Numeration Table.

5. What is used to separate figures into classes or periods? What is used to mark the order of primary units?

6. What is a solution? A problem? A proof? A rule? A principle?

7. What is a principle of notation?

SECTION III.

ADDITION.

30.-1. Jane has 5 books, and her sister has 6. How many have both?

2. Albert has 7 white roses and 8 red ones. How many roses has he in all?

3. How many are 5 and 6? How many ones are 8 and 7?

4. How many cents are 8 cents and 4 cents? How many cents are 4 cents and 8 cents?

5. In a garden there are 10 pear trees and 7 peach trees. How many trees are there of the two kinds?

6. A man bought a plow for 10 dollars, and sold it for 2 dollars more than he gave for it. How many dollars did he get for it?

7. A boy rode 8 miles, and walked 7. How far did he travel?

8. In a certain class there are 9 boys and 8 girls. How many pupils are there in the class?

9. How many ones are 10 and 2? 10 and 7? 9 and 8? 10 and 8?

10. How many ones are 9 and 1? 10 and 2? 7 and 4? 9 and 7? 10 and 6?

11. What number is formed by uniting the ones in 6 and 5? 10 and 9?

12. What number is formed by uniting the ones in 7 and 3? 10 and 3?

31. The Sum of two or more numbers is a number containing as many units or ones as those numbers.

32. Addition is the process of uniting two or more numbers to find their sum.

33. The Sign of Addition is an upright cross, +, and is called plus.

34. The Sign of Equality is =, and is read equals or equal. Thus, 9 +5 14, is read nine plus five equals fourteen, and means that 5 added to 9 equals 14.

=

MENTAL EXERCISES.

35.-1. If Henry has 9 dollars and his brother has 7, how many dollars have both?

SOLUTION.-If Henry has 9 dollars and his brother has 7, both have as many dollars as the sum of 9 and 7, which is 16, the answer required.

2. If you gather 7 quarts of berries and your brother 6 quarts, how many do both of you gather?

3. A boy caught 7 fishes, and another boy caught 5. How many did both catch?

4. Harry had 8 cents, and had 5 more given him. How many had he then?

5. How many are 11 and 3? 5 and 8? 10 and 5? 6. John has 6 cents, George 5 and Victor 2. How many cents have they in all?

7. If I give to one boy 5 peaches, to another 7, and keep 4, how many peaches had I at first?

8. How many are 5, 7 and 4? and 7? 7, 4 and 5? 4, 5 and 7?

9. How many are 9 and 4? and 4?

7, 5 and 4? 5, 4

4, 7 and 6?

6, 3 and 2? 3, 6

10. How many are 13 and 2? 15 and 2? 15 and 4? 11. What does 11 + 7 mean?

8+3=11?

12. A boy paid 5 cents for an orange, 7 cents for a melon and 6 cents for a pencil.

he pay for them all?

How many cents did

13. How many are 16 and 2? 16 and 4? 17 and 2? 17 and 3? 18 and 2?