Subtraction of natural numbers. Reduced, Subtracted, Difference
The concept of subtraction is best understood with an example. You decide to drink tea with sweets. There were 10 candies in the vase. You ate 3 candies. How many candies are left in the vase? If we subtract 3 from 10, then 7 sweets will remain in the vase. Let's write the problem mathematically:
Let's take a closer look at the entry:
10 is the number from which we subtract or which we reduce, therefore it is called reduced.
3 is the number we are subtracting. Therefore it is called deductible.
7 is the result of subtraction or is also called difference. The difference shows how much the first number (10) is greater than the second number (3) or how much the second number (3) is less than the first number (10).
If you are in doubt whether you have found the difference correctly, you need to do verification. Add the second number to the difference: 7+3=10
When subtracting l, the minuend cannot be less than the subtrahend.
We draw a conclusion from what has been said. Subtraction- this is an action with the help of which the second term is found by the sum and one of the terms.
In literal form, this expression will look like this:
a -b=c
a - reduced,
b - subtracted,
c is the difference.
Properties of subtracting a sum from a number.
13 — (3 + 4)=13 — 7=6
13 — 3 — 4 = 10 — 4=6
The example can be solved in two ways. The first way is to find the sum of numbers (3 + 4), and then subtract from total number(13). The second way is to subtract the first term (3) from the total number (13), and then subtract the second term (4) from the resulting difference.
In literal form, the property for subtracting the sum from a number will look like this:
a - (b + c) = a - b - c
The property of subtracting a number from a sum.
(7 + 3) — 2 = 10 — 2 = 8
7 + (3 — 2) = 7 + 1 = 8
(7 — 2) + 3 = 5 + 3 = 8
To subtract a number from the sum, you can subtract this number from one term, and then add the second term to the result of the difference. Under the condition, the term will be greater than the subtracted number.
In literal form, the property for subtracting a number from a sum will look like this:
(7 + 3) — 2 = 7 + (3 — 2)
(a +b) —c=a + (b - c), provided b > c
(7 + 3) — 2=(7 — 2) + 3
(a + b) - c \u003d (a - c) + b, provided a > c
Subtraction property with zero.
10 — 0 = 10
a - 0 = a
If you subtract zero from the number then it will be the same number.
10 — 10 = 0
a -a = 0
If you subtract the same number from a number then it will be zero.
Related questions:
In the example 35 - 22 = 13, name the minuend, the subtrahend and the difference.
Answer: 35 - reduced, 22 - subtracted, 13 - difference.
If the numbers are the same, what is their difference?
Answer: zero.
Do a subtraction check 24 - 16 = 8?
Answer: 16 + 8 = 24
Subtraction table for natural numbers from 1 to 10.
Examples for tasks on the topic "Subtraction of natural numbers."
Example #1:
Insert the missing number: a) 20 - ... = 20 b) 14 - ... + 5 = 14
Answer: a) 0 b) 5
Example #2:
Is it possible to subtract: a) 0 - 3 b) 56 - 12 c) 3 - 0 d) 576 - 576 e) 8732 - 8734
Answer: a) no b) 56 - 12 = 44 c) 3 - 0 = 3 d) 576 - 576 = 0 e) no
Example #3:
Read the expression: 20 - 8
Answer: “Subtract eight from twenty” or “Subtract eight from twenty.” Pronounce words correctly
Subtraction- This arithmetic operation the reverse of addition, by means of which as many units are subtracted (subtracted) from one number as there are in another number.
The number to be subtracted from is called reduced, the number that specifies how many units to subtract from the first number, is called deductible. The number resulting from subtraction is called difference(or remainder).
Let's take subtraction as an example. There are 9 sweets on the table, if you eat 5 sweets, then there will be 4 of them. The number 9 is reduced, 5 is subtracted, and 4 is the remainder (difference):
The - (minus) sign is used to write subtraction. It is placed between the minuend and the subtrahend, while the minuend is written to the left of the minus sign, and the subtrahend is written to the right. For example, the entry 9 - 5 means that the number 5 is subtracted from the number 9. To the right of the subtraction entry, put the sign = (equal), after which the result of the subtraction is written. Thus, the complete subtraction entry looks like this:
This entry reads as follows: the difference between nine and five is four, or nine minus five is four.
In order to get a natural number or 0 as a result of subtraction, the minuend must be greater than or equal to the subtrahend.
Consider how, using the natural series, you can perform subtraction and find the difference of two natural numbers. For example, we need to calculate the difference between the numbers 9 and 6, we note in natural series number 9 and count from it to the left 6 numbers. We get the number 3:
Subtraction can also be used to compare two numbers. Wanting to compare two numbers with each other, we ask ourselves how many units one number is more or less than the other. To find out, you need to more subtract less. For example, to find out how much 10 is less than 25 (or how much 25 is more than 10), you need to subtract 10 from 25. Then we find that 10 is less than 25 (or 25 is more than 10) by 15 units.
Subtraction check
Consider the expression
where 15 is the minuend, 7 is the subtrahend, and 8 is the difference. To find out if the subtraction was performed correctly, you can:
- add the subtrahend with the difference, if it turns out to be reduced, then the subtraction was performed correctly:
