Simple Operations with Decimal Numbers

We will solve addition and subtraction operations of decimal numbers in vertical form, always keeping in mind the following rules:
• All the rules that are applicable to the addition and subtraction of whole numbers also apply to decimal numbers.
• The decimal points must always be aligned one under the other.
• Numbers must be written in an orderly manner - both to the right of the decimal point and to its left (tenths under tenths, hundredths under hundredths, and so on)

Suggested Topics to Practice in Advance

  1. Converting a Decimal Fraction to a Mixed Number
  2. What is a Decimal Number?
  3. Decimal Fractions
  4. Reducing and Expanding Decimal Numbers

Practice Addition and Subtraction of Decimal Fractions

Examples with solutions for Addition and Subtraction of Decimal Fractions

Exercise #1

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds..

6.31+216.222

Video Solution

Step-by-Step Solution

Let's fill in the zeros in the empty space as follows:

006.310+216.222  006.310\\+216.222\\\ We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

Answer

True

Exercise #2

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

21.52+3.4

Video Solution

Step-by-Step Solution

Let's fill in the zeros in the empty space as follows:

21.52+03.40 21.52\\+03.40\\

Note that the decimal points are written one below the other

Therefore, the exercise is written in the correct form

Answer

True

Exercise #3

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

La posición del punto decimal coincide.

3.05+213.22

Video Solution

Step-by-Step Solution

Note that the decimal points are not written one below the other.

Therefore, the exercise is not written correctly.

Answer

Not true

Exercise #4

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

3.05+53.2

Video Solution

Step-by-Step Solution

Note that the decimal points are not written one below the other.

Therefore, the exercise is not written correctly.

Answer

Not true

Exercise #5

Solve the following exercise and circle the appropriate answer:

22.1-12.0

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the tenths after the decimal point:

10=1 1-0=1

Finally, we'll subtract the whole numbers before the decimal point accordingly:

22=0 2-2=0

21=1 2-1=1

And we get:

22.112.010.1 22.1\\-12.0\\10.1

Answer

10.1

Exercise #6

8.5+5.2+8.4= 8.5+5.2+8.4=

Video Solution

Step-by-Step Solution

We will break down each of the factors in the exercise into a whole number and its remainder.

We get:

8+0.5+5+0.2+8+0.4= 8+0.5+5+0.2+8+0.4=

Now we'll combine only the whole numbers:

8+5+8=13+8=21 8+5+8=13+8=21

Now we'll calculate the remainder:

0.5+0.2+0.4=0.7+0.4=1.1 0.5+0.2+0.4=0.7+0.4=1.1

And now we'll get the exercise:

21+1.1=22.1 21+1.1=22.1

Answer

22.1

Exercise #7

10.1x+5.2x+2.4x= 10.1x+5.2x+2.4x=

Video Solution

Step-by-Step Solution

We will factor each of the terms in the exercise into a whole number and its remainder.

We get:

10x+0.1x+5x+0.2x+2x+0.4x= 10x+0.1x+5x+0.2x+2x+0.4x=

Now we'll combine only the whole numbers:

10x+5x+2x=15x+2x=17x 10x+5x+2x=15x+2x=17x

Now we'll calculate the remainder:

0.1x+0.2x+0.4x=0.3x+0.4x=0.7x 0.1x+0.2x+0.4x=0.3x+0.4x=0.7x

And now we'll get the exercise:

17x+0.7x=17.7x 17x+0.7x=17.7x

Answer

17.7X

Exercise #8

0.75+0.35= 0.75+0.35=

Video Solution

Answer

1.1

Exercise #9

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

312.54+1203.22

Video Solution

Answer

Not true

Exercise #10

Circle the correct answer to the following exercise:

5.4+3.22

Video Solution

Answer

8.62

Exercise #11

Circle the correct answer to the following exercise:

1.02+6.4

Video Solution

Answer

7.42

Exercise #12

Circle the correct answer to the following exercise:

6.55+3.412

Video Solution

Answer

9.962

Exercise #13

Circle the correct answer to the following exercise:

111.25+112.3

Video Solution

Answer

223.55

Exercise #14

Circle the correct answer to the following exercise:

2.1012+3.212

Video Solution

Answer

5.3132

Exercise #15

Circle the correct answer to the following exercise:

115.32+115.102

Video Solution

Answer

230.422

Topics learned in later sections

  1. Comparison of Decimal Numbers
  2. Converting Decimals to Fractions