Exercises

I. Answer the following questions on the text:

1. What is the process of addition?

2. What is the sign that shows addition?

3. On what is the modern method based?

4. How is addition performed best?

5. Do we sum the figures up from below when adding?

6. Will the same result be found if we begin to sum up from the top downwards?

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

decimal system, the hundreds column, to make it easy to read, modern method of counting, to sum the figures up, from below, from the top downwards, is best performed.

Lesson 3

SUBTRACTION

Subtraction is a process in simple arithmetic which is closely connected with addition. The putting together of numbers to make a larger number is addition, but subtraction is the taking away of a number from a larger number to see how many are left. For example, 5 and 3 make 8 (addition), but 3 from 8 leaves 5 (subtraction).

The number which is subtracted is called the subtrahend, the other is called the minuend, and their difference, the number which remains after subtraction, is called the remainder or difference.

In order to find the remainder, the subtrahend is written under the minuend as in addition. Beginning at the right each figure in the subtrahend is subtracted from the figure above it and the individual remainder written below in the same column. When the process is completed the third complete number, below the subtrahend, is the desired remainder.

As an example, it is required to subtract 42356 from 98577. The separate operations are 7–6=1, 7–5=2, 5–3=2, 8–2=6, 9–4=5, giving 56221 as the remainder. The operation is written out in full as follows:

_98577 (minuend)

_42356 (subtrahend)

56221 (remainder)

As a check the remainder and the subtrahend should be added. If the subtraction is correct the sum of this addition will be equal to the minuend.

If any figure in the subtrahend is a number greater than the one above it in the minuend, it cannot be subtracted directly and the following method is used. A single unit (1) is “borrowed” from the next figure to the left in the minuend and written (or imagined to be written) before the figure which is too small. The figure of the subtrahend is then subtracted from the number so formed and the remainder figure written down in the usual way.

The minuend figure from which the 1 was borrowed is now considered as a new figure, 1 less than the original, and its corresponding subtrahend figure subtracted in the usual way. If the minuend figure is again too small, the process just described is repeated. For example:

_49825 (minuend)

_26543 (subtrahend)

23282 (remainder)

Subtraction can be used to solve the three following types of problems:

1) To find the remainder, or how much is left.

A newspaper boy had 60 papers and sold 28. How many were left?

2) To compare one number with another.

On Monday a motorist travelled 55 miles and on Tuesday 38 miles. How much less did he travel on Tuesday than on Monday?

This question can be put in two other ways:

a) How many more miles did he travel on Monday than on Tuesday?

b) What is the difference between the lengths of his journeys on the two days?

3) To find how much is needed to make a larger number.

A motorist had travelled 53 miles out of a total journey of 87 miles. How many more miles had he to travel to complete his journey?