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EXERCISE 11

1. The sum of two numbers is 2872 and the lesser is 929. What is the greater number?

2. The greater of two numbers is 17,214 and their difference is 2685. What is the lesser number?

3. If the minuend is 15,293 and the subtrahend 12,525, what is the remainder ?

4. If the subtrahend is 32,658 and the minuend 61,229, what is the remainder ?

5. If the minuend is 21,712 and the remainder 2564, what is the subtrahend ?

6. If the subtrahend is 16,567 and the remainder 7543, what is the minuend ?

7. A merchant sold some goods for $2962.50, and gained $548.75. What did they cost him ?

8. What must be added to the sum of $175.50 and $62.75 to make $300 ?

9. What must be added to the sum of $62.30, $41.75, and $25, to make $500 ?

10. How much greater is the sum of $75.30 and $21.75, than the difference between these amounts ?

11. What is the difference between $725.25 and the sum of $15.50, $17.92, $25.36, $48.75, $19.36, and $42.75?

12. What must be subtracted from $1000 to make the remainder equal to the sum of $175 and $42.50 ?

13. A man borrowed $1250 and paid back $125 at one time and $960 at another. How much did he still owe ?

14. A man having $375.50 in the bank deposited at different times $175, $320, and $15.40. He then drew out $645. How much had he left in the bank ?

CHAPTER IV

MULTIPLICATION OF INTEGERS

34. Multiplication. The process of taking a number as many times as there are units in another number is called multiplication.

This means multiplication by an integer. Multiplication by a fraction is considered later.

35. Terms. The number that is multiplied is called the multiplicand; the number that shows how many times the multiplicand is taken is 4 multiplicand called the multiplier; the result of the

3 multiplier

12 product multiplication is called the product.

36. Multiple. The product of two or more integers is called a multiple of each.

For example, 15 is a multiple of 3 and 5, and 40 is a multiple of 2, 4, 5 and also of 8, 10, 20.

37. Factors. Integral numbers whose product is a given number are called factors of that number; the multiplicand and the multiplier, for example, are factors of the product.

38. Symbol. The symbol of multiplication is an oblique cross, X. It is read times or multiplied by.

Thus 3 x 4 12 is read "3 times 4 equals 12.”

The multiplier may be written either before or after the multiplicand, but the tendency in this country is to write the multiplier first, as we naturally read it. For example, 3 x $4 is read "3 times $4," and $4 x 3 is read "$4 multiplied by 3."

39. The Multiplication Table. The following table, already learned, must be reviewed so that you can tell instantly any product when the teacher tells you the factors :

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40. Multiplying by a One-Figure Multiplier. Required the product of 587 by 6.

We may multiply each part of 587 by 6 and add the results, as shown in the upper solution. This method is long, so we use it only

for explanation, and write the work 587 multiplicand

as in the lower solution. Beginning 6 multiplier

at the right, we have 6 x 7 = 42; we 42 6 x

write the 2 in the units' place and 7 48 6x 8 (tens)

reserve the 4 tens to add to the prod

uct of the tens. Then 6 X 8 tens 48 30 6 x 5 hundreds

tens, which, with the 4 tens reserved, 3522 6 x 587 product

makes 52 tens, or 5 hundreds and 2

tens. We therefore write the 2 tens in the tens' place, and reserve the 5 hundreds to add to the product of

the hundreds. Then 6 x 5 hundreds = 30 hundreds, which, 587

with the 5 hundreds reserved, makes 35 hundreds, or 3 thou6

sands and 5 hundreds, which we write in the thousands' and 3522

hundreds' places. The product is therefore 3522.

41. Order of the Factors. The product is the same whatever the order of the factors.

That is, 3 x 4 = 4 x 3. If we read these dots by rows, we have 3 x 4 dots; if we read by columns, we have 4 x 3 dots. But the dots do not change, so 3 x 4=4 x 3.

This is true for any number of rows and columns. For this reason we may always use the smaller factor as the multiplier, thus making the work easier.

Thus, instead of multiplying 3 by 478, we would multiply 478 by 3. In the same way, if we wished to find the product of 478 x $3, we would take the product of 3 x $478, the answer being the same.

42. Nature of the Factors. Since the multiplier shows how many times the multiplicand is taken, we have the following:

The multiplier is always an abstract number.

The multiplicand may be either abstract or concrete, and it and the product will always be like numbers.

In 3 x $4 = $12, 3 is abstract and $4 and $12 are like numbers.

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