Useful Tips

Decimal Addition and Subtraction

Put decimal fractions in a column as natural numbers, not paying attention to commas.

In the answer, put a comma under the commas in the original fractions.

If the initial decimal fractions have a different number of decimal places (digits), then the fraction with less decimal places must be assigned the required number of zeros in order to equalize the number of decimal places in the fractions.

Let's look at an example. Find the sum of decimal fractions.

Equal the number of decimal places in decimal fractions. Add two zeros to the right to the decimal fraction 13.7.

If decimal addition Since you have already learned well, then the missing zeros can be attributed mentally.

So, again briefly the basic rules of addition:

  • equalize the number of decimal places,
  • write decimal fractions under each other so that the commas are under each other,
  • we perform the addition of decimal fractions, not paying attention to commas, according to the rules of addition in a column of natural numbers,
  • we put in response a comma under the commas.

Decimal

To learn how to correctly add the decimal fractions, it is enough to learn the rule, consisting of only three words.

Three words are: Comma under the Comma. This is the most important thing to remember when adding decimal fractions. Adding the decimal fractions, we write them so that the commas in the terms are strictly one under the other. If there are fewer digits after the decimal point in one term than in the other, you can add the missing digits with zeros (or you can not do this). The rest of the addition of decimal fractions is practically no different from the addition of natural numbers - a topic that took place in elementary school.

Let's look at examples of how the addition of decimal fractions occurs.

To add 5.7 and 6.8, write their comma under the comma. Then we add the numbers according to the digits and in the received answer we demolish the comma all according to the same rule - the comma under the comma.

When adding 2.256 and 0.74 numbers, we write so that the comma is under the comma. Since there are two digits after the comma in the second number, and three in the first, we supplement the missing one sign at the end of the second number with zero (but you can omit it). After that, add up the numbers, not paying attention to the comma (that is, we add 740 to 2256). As a result, we demolish the comma (exactly under the comma of the terms).

4,98+52,462=?

As usual, we begin the addition of decimal fractions by writing them so that the comma is exactly under the comma. The first is more convenient to write down a number with more digits after the decimal point. To equalize the number of decimal places in both terms, we write zero in the second third digit after the decimal point. Add 52462 and 4980, not paying attention to the comma. In the answer, we demolish the comma under the comma.

To add decimal fractions, we write them “comma under the comma”. Add 4821 and 3179, not paying attention to the comma. After that, we demolish the comma under the comma. Since zeros are not written in the decimal place after the decimal point, the final answer is 8.

In order to add a decimal fraction to a natural number, you can add a comma and as many zeros as necessary in the natural number record at the end (in this example, three). Then add 35000 and 3146 and demolish the comma.

We begin the addition by writing decimal fractions according to the rule “comma under comma”. Then we add the missing decimal place of 8.3 to zero. Add 374 and 830. In response, we demolish the comma under the comma.

Decimal Addition and Subtraction Rule

The rule
1. Sign one fraction under another so that the comma
one decimal was under another, i.e. what would the numbers
discharges of the same name were exactly under each other,

2. Add (or subtract) fractions bitwise, starting with the least significant bit,

3. As a result, put a comma under the commas of both fractions.

Example
+ 12, 733 11, 255 23, 988 - 27, 957 12, 126 15, 831


+ 21, 277 13, 112 34, 289 - 37, 993 23, 441 14, 582


+ 37, 216 11, 323 48, 539 - 77, 292 53, 130 24, 162

Subtraction rule

The rule
! When subtracting, the rule applies. occupy unit at the senior level (example 1).

! When subtracting, the number of digits in the fractional part is preliminarily equalized with zeros (example 2).

Example
- 122, 43 • 41, 22 81, 21 - 46, 300 • • • 14, 457 31, 843


- 153, 64 • 82, 13 71, 51 - 67, 400 • • • 25, 679 41, 721


- 204, 75 • 72, 61 132, 12 - 93, 700 • • • 71, 923 21, 777