MENTAL ARITHMETIC.

PART FIRST.

SECTION I.

MULTIPLICATION OF TENS AND UNITS.

1. A man drove six oxen to market, and sold three of them for 50 dollars apiece. What did they come to?

Three times 50 are 150. Ans. 150 dollars.

He sold the remaining three for 52 dollars apiece. What did they come to?

Three times 50 are 150, and three times 2 are 6, which added to 150 makes 156. Ans. 156 dollars.

What did they all come to?

Twice 100 is 200, and twice 50 is 100, which added to 200 makes 300, and 6 added to 300 makes 306. Ans. 306 dollars. 2. A merchant bought 45 barrels of flour for 6 dollars a barrel. What did it come to?

6 times 40 are 240, and 6 times 5 are 30; 30 added to 240 makes 270. Ans. 270 dollars.

He bought 75 barrels more at 5 dollars a barrel. What did it come to?

5 times 70 are 350; 5 times 5 are 25, which added to 350 makes 375. Ans. 375 dollars.

What did all the flour come to?

300 and 200 are 500, 70 and 70 are 140, which added to 500 makes 640, and 5 are 645. Ans. 645 dollars.

3. What will 87 barrels of flour come to at 6 dollars a barrel?

6 times 80 are 480, and 6 times 7 are 42, which added to 480 makes 522. Ans. 522 dollars.

4. What are 7 times 68? What are 9 times 84?

What are 8 times 72 ?
What are 4 times 96?

8 times 64? 5 times 72? 7 times 83? 5 times 79?
4 times 98? 3 times 81? 6 times 73? 6 times 86?

The preceding examples will show the importance of being able readily to multiply tens by units. This becomes easy, after acquiring the Multiplication Table. It may be connected with a review of the Multiplication Table in the following manner.

3 times 1? 3 times 10? 3 times 3? 3 times 30? 3 times 5? 3 times 50? 3 times 7? 3 times 70? 3 times 9? 3 times 90? 4 times 1? 4 times 10? 4 times 3? 4 times 30? 4 times 5? 4 times 50? 4 times 7? 4 times 70? 4 times 9? 4 times 90? 5 times 1? 5 times 10? 5 times 3? 5 times 30? 5 times 5? 5 times 50? 5 times 7? 5 times 70? 5 times 9? 5 times 90? 6 times 1? 6 times 10? 6 times 3? 6 times 30? 6 times 5? 6 times 50? 6 times 7? 6 times 70? 6 times 9? 6 times 90? 7 times 1? 7 times 10? 7 times 3? 7 times 30? 7 times 5? 7 times 50? 7 times 7? 7 times 70? 7 times 9? 7 times 90?

A number which contains another number a certain number

of times, is a multiple of that number.

Thus 6 is a multiple of 2; 15 of 3; 28 of 7.*

Name all the multiples of 2, from 2 to 60.
Name the multiples of 20, from 20 to 600.

What are the multiples of 3 up to 75? of 30 up to 750? What are the multiples of 4 up to 80? of 40 up to 800? What are the multiples of 5 up to 100? of 50 up to 1000? of 6 to 72? of 60 to 720? of 7 to 84? of 70 to 840? of 8 to 96? of 80 to 960? of 9 to 108? of 90 to 1080? of 10 to 120? of 100 to 1200?

* See Note 1, at the end of Part First.

SECTION II.

MULTIPLICATION OF TENS AND UNITS.—COMPLEMENT.

1. What will 17 tons of hay come to at 8 dollars a ton? Ans. 8 times 10 are 80, and 8 times 7 are 56; 56 added to 80 makes 136. 136 dollars.

2. What will 37 pounds of sugar come to at 9 cents a pound? 3. A man drove 87 sheep to market, and sold them for 6 dollars apiece. What did they come to?

4. A man travelled on foot 8 days; he travelled 29 miles each day. How many miles did he travel in all?

In each of the above examples the second product when added to the first makes a sum exceeding the next even hundred: thus, in the 1st ex. 80+56; in the 2d, 270+63; in the 3d, 480+42; in the 4th, 160+72.

In order to perform such examples with ease, quickness, and without mistake, each step in the process should be made the subject of distinct practice. To illustrate these steps by the first example, 80+56, the first thing to be done is to think of the number which must be added to 80 to make 100, namely, 20; the next is to take this 20 from the 56, and what remains, — 36,—will belong to the next hundred.

The number which in such cases must be added to a given number to make up an even hundred may be called the Complement of that number. Thus the complement of 80 is 20; of 60, 40; of 90, 10; of 56, 44. What is the complement of 10? 30? 50? 70?

19? 29? 39?

99?

49 ? 59? 69? 79? 89?

How many are 40+76? 80+34? 70+91? 90+17? 25+83? 36+71? 45+82? 56+73? 43+82? 9536? 37+84? 45+76? 88+37? 94+17? 76+87 ?

* See Note 2.

To multiply any number less than 10 by 11, repeat the figure expressing the number: as 3 times 11 is 33, 4×11=44. To multiply by 11 any number of two figures. Think of the first figure, then of the sum of the two figures, then of the last figure. These three figures will express the answer.

*Note 3.