﻿ Remainders or Subtraction — Matemáticas18

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# Subtraction

Content

## What is remainders or subtraction?

Subtraction (also known as remainders) is one of the four basic operations of arithmetic that consists of the difference between a certain amount and another. The word remainders derives from the Latin "restis" and means "agrees".

### Symbol or sign of the subtraction

The sign of the subtraction is represented by means of a “-” intermediate line or hyphen that is known as “minus” or “negative”.

Note: In the subtraction only 2 numbers can be subtracted at a time, it is considered a term with positive sign (+) and the other term with negative sign (-).

## Parts of the subtraction

When performing a subtraction operation there are three elements:

• Minuend: The number to be subtracted an amount indicated on the subtrahend.
• Subtrahend: The number that is subtracted.
• Difference: The result of the operation by subtracting one number from the other.
-
5 ← Minuend 2 ← Subtrahend / 3 ← Difference

Another way to represent the previous subtraction would be: 5 - 2 = 3 (5 is a minuend, 2 is a subtrahend and 3 is the difference or the result of the subtraction).

Note: In some cases they may call the "difference" as "subtraction", depending on the author.

## Subtraction Properties

The properties of the subtraction are very different from the properties of the addition, due to the operation performed there may be some special cases of change of sign where the result is negative.

• Subtracting: This property indicates that by increasing the value of the subtracting the result (difference) decreases, therefore, when decreasing the value of the subtracting the result(difference) increases. For example:
6 - 4 = 2
6 - 3 = 3
6 - 5 = 1
The first value of the subtrahend is 4 and the result is 2, when decreasing the subtrahend to 3 the result is 3 and when increasing the subtrahend to 5 the result is 1.
• Uniformity: To vary proportionally the minuend and the subtrahend the difference will be maintained. For example:
8 - 3 = 5
(8 + 2) - (3 + 2) = 10 - 5 = 5

## How do we subtract?

To begin learning to add, it is advisable to use familiar objects and a simple math game. For example: You have 3 balls bouncing where 2 are blue and one is red, then the red ball stopped bouncing. How many balls are still bouncing after the red one stood still? In total there are 3 balls and one ball stops bouncing, therefore, 3 – 1 = 2, there are 2 balls that continue to bounce.

There are different learning methods for performing subtractions, among these methods we can find especially two, which are used for numbers of small quantities and the other method for numbers of large quantities.

• Subtract arranged in a line: It is used when small quantities are going to be extracted to the minuendo, as experience is obtained it will increase the facility of this method for larger numbers. Keep in mind that when starting in the world of mathematics a 4-2 operation can be confusing, but the purpose is to gradually raise the difficulty and on this website you can find exercises of greater difficulty. This method helps the learning of mental calculation.

Examples:

5 - 3 = 2
7 - 2 = 5
5 - 2 = 3
8 - 4 = 4

Exercise:

A) 8 - 4 = ?
B) 3 - 2 = ?
C) 9 - 4 = ?
D) 8 - 7 = ?
• Subtraction in column: This is a method for the subtraction of large addends. the minuend is on the subtrahend, it is important to put the numbers in columns so that they are with their corresponding. The place value structure of each number must be considered; aligning ones with one units,tens with tens, hundreds with hundreds and so on. Suppose the number 415, first we have to start from right to left, this means that we have 5 ones, 1 ten and 4 hundreds, which is equivalent to 5 + 10 + 400 = 415.

Examples:

-
28 15 / 13
-
56 44 / 12
-
346 243 / 103
-
563 321 / 242

Exercise:

A) -
18 16 / ?
B) -
68 45 / ?
C) -
55 54 / ?
D) -
97 05 / ?

In some remainders we will have the case of a carried number, and this can complicate the the subtraction of larger subtractions. It is recommended to have an order to facilitate subtraction the columns of remainders and obtain the correct result. What is a carried number? Assuming we have 32 - 8 = 24, since in the column of ones units the number 8 is greater than the number 2 then you should ask for help to the next column that corresponds to 3 tens units, when asking for help to 3 tens units you subtract 1 from that column , since we are actually extracting 10 units or its equivalent 1 tenth so that the number 2 is now 12, therefore we could already do the subtraction in the column of ones units 12-8 = 4 (we have 4 ones units as a result), now we pass the column of tens where the number 30 or 3 tens units is subtracted from the 10 units or 1 tens unit that were borrowed, therefore, 30 - 10 = 20 units or 3-1 = 2 tens units. We group the units and the tens, resulting in 20 + 4 = 24 or the equivalent as 2 tens units + 4 ones units = 24.

Examples:

-
2 34 25 / 09
-
4 53 19 / 34
-
5 163 154 / 009
-
25 364 187 / 177

The red number represents the new value of the minuend since the number on the right asked for help.

Exercise:

A) -
21 12 / ?
B) -
63 45 / ?
C) -
124 118 / ?
D) -
308 258 / ?

## Subtract with decimals

When subtracting numbers with decimals, it is important to align the numbers according to the quantity they represent by aligning the decimal points, and then each number according to its place value by these quantities: the ones, tens, hundreds and thousands units are aligned to the left of the point; to the right of the point the tenths, hundredths and thousandths must line up.

Examples:

-
4 5.2 4.6 / 0.6
-
5 6.3 4.4 / 1.9
-
63.7 53.7 / 10.0
-
23   5 342.67 187.38 / 155.29

The red number represents the new value of the minuend since the number on the right asked for help.

Exercise:

A) -
8.2 1.6 / ?
B) -
15.42 13.68 / ?
C) -
111.82    8.63 / ?
D) -
842.86 652.96 / ?

## Subtraction Tricks

Here are some techniques that may be useful to facilitate the operations to be performed.

• Convert subtraction to sum:

This method consists in thinking about what should be added to one number to get the other, for example: 9 - 6 =? Can we interpret it as 6 +? = 9, where do we identify that? = 3

## Identify the amount it represents

Ones units (A), tens (B), hundreds (C) and thousand units (D) are aligned to the left of the point; to the right of the point the tenths (E), hundredths (F) and thousandths (G) are aligned.

-
DCBA . EFG 5 4 2 8 . 2 3 4 3 3 5 4 . 5 6 3 / 2 0 7 3 . 6 7 1

We have as a result: 2 thousand units, 0 hundreds, 7 tens and 3 ones to the left of the point; to the right of the point we have: 6 tenths, 7 hundredth and 1 thousandths.

## Checking the subtraction

The subtraction can be checked with its inverse mathematical operation, which is addition. To check the subtraction, the subtrahend is added to the result and from this sum the minuend must be obtained, indicating that the subtraction was correct.

Examples:

-
18 15 / 03
+
03 15 / 18

Taking the result of the subtraction (03) and adding the subtrahend (15) we will obtain the minuend (18).

## Subtraction of Fractions

In order to perform subtraction with fractions, the same denominator must be obtained. When fractions do not have the same denominator, it is possible to subtracting them together by following a slightly different procedure.

Ejemplo:

9 / 3
-
5 / 3
=
9 - 5 /
3
=
4 /
3