Subtracted by 7 and reduced by 5 more. Subtracting numbers

Subtraction is an arithmetic operation inverse to addition, by means of which as many units are subtracted (subtracted) from one number as are contained in another number.

The number from which it is subtracted is called reducible, the number that indicates how many units will be subtracted from the first number is called deductible. The number resulting from subtraction is called difference(or the remainder).

Let's look at subtraction using an example. There are 9 candies on the table, if you eat 5 candies, then there will be 4 left. The number 9 is the minuend, 5 is the subtrahend, and 4 is the remainder (difference):

To write a subtraction, use the - (minus) sign. It is placed between the minuend and the subtrahend, with the minuend written to the left of the minus sign, and the subtrahend 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 an = (equal) sign, after which the result of the subtraction is written. So the complete subtraction notation looks like this:

This entry reads like this: the difference between nine and five equals four or nine minus five equals four.

In order to obtain a natural number or 0 as a result of subtraction, the minuend must be greater than or equal to the subtrahend.

Let's 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, mark the number 9 in the natural series and count 6 numbers from it to the left. We get the number 3:

Subtraction can also be used to compare two numbers. Wanting to compare two numbers, we ask ourselves how many units one number is greater or less than the other. To find out, you need to subtract the smaller number from the larger number. 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 whether the subtraction was performed correctly, you can:

1. add the subtrahend with the difference, if you get the minuend, then the subtraction was performed correctly:

The concept of subtraction is best understood with an example. You decide to drink tea with sweets. There were 10 sweets in the vase. You ate 3 candies. How many candies are left in the vase? If we subtract 3 from 10, there will be 7 sweets left in the vase. Let's write the problem mathematically:

Let's look at the entry in detail:
10 is the number from which we subtract or decrease, which is why it is called reducible.
3 is the number we are subtracting. That's why they call him 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 doubt whether you found the difference correctly, you need to do check. 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 by which the second term is found from the sum and one of the terms.

In literal form, this expression will look like this:

a—b =c

a – minuend,
b – subtrahend,
c – 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 the numbers (3+4), and then subtract from the 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 of subtracting a 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 a sum, you can subtract this number from one term, and then add the second term to the resulting difference. The condition is that the summand will be greater than the number being subtracted.

In literal form, the property of 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=(a - c) + b, provided a > c

Subtraction property with zero.

10 — 0 = 10
a - 0 = a

If you subtract zero from a 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.

Questions on the topic:
In example 35 - 22 = 13, name the minuend, subtrahend and difference.
Answer: 35 – minuend, 22 – subtrahend, 13 – difference.

If the numbers are the same, what is their difference?
Answer: zero.

Do the subtraction test 24 - 16 = 8?
Answer: 16 + 8 = 24

Subtraction table for natural numbers from 1 to 10.

Examples for problems 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