Vocabulary Notes

a kind of adding – összeadás fajta

by either method – bármilyen módszerrel

successive – következő

how much they make up – mennyit tesznek ki

in turn – felváltva, sorjában

multiplicand – szorzandó

multiplier – szorzó

product – szorzat

factor – szorzótényező

partial product – részleges szorzat

Exercises

I. Answer the following questions on the text:

1. What kind of process is multiplication?

2. In what cases do we use addition and in what cases multiplication?

3. What is the multiplication sign?

4. What is the number which is multiplied called?

5. What is the number by which it is multiplied called?

6. Do you know the Multiplication Tab1e?

II. Give the Hungarian equivalents for the following words and word combinations. Use them in sentences of your own:

the multiplication sign, by either method, quantity, multiplicand, multiplier, product.

III. Multiply the following numbers orally:

7 by 9; 8 by 7; 5 by 6; 9 by 3; 6 by 7; 7 by 7; 8 by 9; 3 by 8.

Lesson 5 division

Just as multiplication is a short way of adding equal numbers, so division can be thought of as a short way of doing subtraction. The process of finding how many times one number is contained in a second number is called division. In division there are special terms or names for the number divided, the number by which it is divided and the answer.

The number divided is called the dividend.

The number by which it is divided is called the divisor.

The answer, or the number of times the divisor is contained in the dividend, is called the quotient. If the dividend is not an exact number of times the divisor there will also be a remainder.

Here is a very simple example to illustrate division.

John has 28 cards. How many groups of 7 can he make?

To find the answer to this problem actually using cards John would first count out 7 cards in one group. From the 21 remaining cards he would count out a second group of 7 cards. The 14 remaining cards would give him a further two groups of 7 cards. In other words John counts out one group of 7 cards after another until all the cards are used.

From the 28 cards exactly four groups of 7 can be made. The answer to the problem then is 4 groups. To divide 28 by 7 is 4 because 4 times 7 are 28. The operation is indicated by writing 28 ÷ 7 = 4. Here, 28 is the dividend, 7 is the divisor and 4 the quotient.

As one more illustration let us divide 129,636 by 3. As 3 is not contained in 1 a whole number of times the first two figures, 12, are taken as a partial dividend. Then 12 ÷ 3 = 4, 6 ÷ 3 = 2, 3 ÷ 3 = 1, 6 ÷ 3 = 2 and the complete quotient is 43,212. That is, 129,636 ÷ 3 = 43,212. This operation is usually written out in the following form: and the separate quotients are written below the corresponding separate dividends.

If any of the separate dividends (figures of the complete dividend) are smaller than the divisor, or do not contain the divisor exactly a whole number of times, a slightly different procedure is followed, as illustrated by the following example: divide 189,576 by 9. We get 18 ÷ 9 = 2 and 9 ÷ 9 = 1, but 9 is not contained in 5, so a cipher is written for the next individual dividend is then taken as 57 instead of 7, and 57 ÷ 9 = 6 with a remainder of 3 (since 6 × 9 = 54). This 3 is written (or imagined written) before the next figure, 6 giving 36, and this 36 is used as the next dividend. The final figure of the quotient is then 36 ÷ 9 = 4, the successive figures of the complete quotient are 2, 1, 0, 6 and 4. The result is, therefore, 189576 ÷ 9 = 21064. The complete operation is written as follows: ÷ 9

Sometimes there can be an exact answer to a division sum, as in 28 divided by 7; and sometimes there will be a remainder, as in 30 divided by 7, the answer to this sum being 4, the remainder 2.

There are three division signs: ÷, :, /.