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MENTAL ARITHMETIC.

PRIMARY PROCESSES.

LESSON I.

Assuming that pupils who use this book are able to count and to perform the simple operations of Arithmetic, the following exercises on the fundamental processes have been prepared with a view to giving pupils greater facility in the use of numbers. The foundation for future progress is here to be laid, and the best judgment of the teacher and the earnest, persistent efforts of the pupil are requisite to a full measure of success.

The following are the forty-five simple combinations that can be formed from the nine digits :

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TO THE TEACHER. — Pupils should be drilled on these simple combinations until they can without hesitation name the sums. Vary the exercise by asking for the difference between the numbers. Point to the combinations, ask for the sum, and while the pupils have the sum in mind ask them to subtract each number from that sur. It is quite easy to lead a pupil to see that if 7 and 8 are 15, 7 from 15 will leave 8 and 8 from 15 will leave 7. Do not lightly esteem these simple exercises,

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LESSON II.

1. By the process of Addition, how may the following numbers be formed ?

4, 7, 6, 3, 2, 5, 9, 8, 10, 12, 11, 13, 15, 14, 18, 16, 17.

Model Answer.–4 may be made up of 1, 1, 1, and 1; of 2 and 2; or of 3 and 1.

2. How many must be taken from:

8 to leave 4 ? 7 to leave 2 ?
6 to leave 3 ? 5 to leave 2 ?
14 to leave 8 ? 11 to leave 4 ?
16 to leave 9 ? 18 to leave 7?
13 to leave 6? 15 to leave 8?

9 to leave 5 ?
10 to leave 6 ?
12 to leave 3 ?
17 to leave 9 ?
16 to leave 4 ?

Model Answer.-4 and 4 are 8; therefore, 4 must be taken from 8 to leave 4.

3. State promptly how many are: 3 and 2. 5 and 3.

6 less 4. 9 less 6. 10 less 5.

8 and 3. 8 and 7.

14 less 7. 6 and 7. 5 and 8.

13 less 5. 2 and 9. 9 less 2. 7 and 9.

15 less 6. 6 and 4. 9 less 7.

12 less 7. 18 less 9. 17 less 8.

9 and 8.

7 less 3.
5 and 6.
13 less 6.
16 less 9.
9 and 6.
9 and 9.
17 less 9.

4. How many are:

9 and 8 less 4 ?
7 and 9 less 6?
7 and 8 less 9?
6 and 6 less 5?
5 and 9 less 6?

5 and 4 and 3 less 5 ?
3 and 5 and 6 less 4?
4 and 6 and 3 less 9 ?
4 and 9 and 5 less 9 ?
2 and 7 and 7 less 8?

5. Taking 3 from each of the following, how many will be left : 9, 11, 8, 7, 12, 10, 5, 6?

6. How many must be added to 4 to make the following: 9, 5, 7, 8, 6?

7. How many must be taken from 12 to leave the following: 5, 8, 7, 3, 6, 4, 9?

LESSON III.

1. Jack paid 5 cents for a sandwich and 5 cents for sugar plums. How many cents did he pay for both ?

Solution.--He paid for the sandwich and sugar plums 5 cents and 5 cents, which are 10 cents.

2. Jane picked 5 white roses and 4 red ones. How many roses did she pick?

3. James paid 5 cents for his lunch and had 3 cents left. How many cents had he at first ?

4. Hannah is 6 years old ? How old will she be 4 years hence ?

5. A man earned 4 dollars on Monday and 4 dollars on Tuesday. How much did he earn in the two days ?

6. Virginia had 7 dollars and found a dollar. How many dollars had she then?

7. Victoria paid 5 dollars for shoes and had 6 dollars remaining How many dollars had she at first?

8. There are 6 letters in one name and 7 in another. How

many letters in both names ? 9. Bessie spent 7 weeks at the seashore and 5 weeks in the city. How many weeks did she spend at both places ?

10. Bruce rode 8 miles on his bicycle on Monday and 7 miles on Tuesday. How many miles did he ride in the two days ?

11. How many roses did Walter give away, if he gave Ruth 7 and May 9 ?

12. Two boys went out to gather berries. picked 8 quarts and the other 9 quarts, how many did both pick?

If one

LESSON IV.

Addition is the process of finding the sum of two or more numbers. The sign of Addition is the erect cross, +. It is used instead of and, and is read “plus."

1. A man earned 8 dollars and found 2 dollars. How many dollars had he then?

Solution.-He then had 8 dollars + 2 dollars, which are 10 dollars.

2. A boy paid 9 cents for a slate and 2 cents for a pencil. How many cents did both cost?

3. A hat cost 3 dollars and a coat 8 dollars. How much did both cost ?

4. A girl had 9 cents and her father gave her 8 cents. How many cents had she then?

5. I had 9 dollars and earned 9 dollars more. How many dollars had I then ?

6. A farmer sold 7 sheep to one man and 6 to another. How many sheep did he sell ?

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