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

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.

3.05+213.22

Video Solution

Step-by-Step Solution

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

Therefore, the exercise is not written correctly.

Answer

Not true

Exercise #4

Determine whether the exercise is correctly written or not.

3.05+53.2

Video Solution

Step-by-Step Solution

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

Therefore, the exercise is not written correctly.

Answer

Not true

Exercise #5

Circle the correct answer to the following exercise:

5.4+3.22

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 5.4 as follows:

5.40+3.22 5.40\\+3.22\\

Now let's solve the exercise in order:

We'll add the hundredths after the decimal point:

0+2=2 0+2=2

We'll add the tenths after the decimal point:

4+2=6 4+2=6

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

5+3=8 5+3=8

And we get:

5.40+3.228.62 5.40\\+3.22\\8.62

Answer

8.62

Exercise #6

Circle the correct answer to the following exercise:

1.02+6.4

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 6.4 as follows:

1.02+6.40 1.02\\+6.40\\

Now let's solve the exercise in order:

We'll add the hundredths after the decimal point:

2+0=2 2+0=2

We'll add the tenths after the decimal point:

0+4=4 0+4=4

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

1+6=7 1+6=7

And we get:

1.02+6.407.42 1.02\\+6.40\\7.42

Answer

7.42

Exercise #7

Circle the correct answer to the following exercise:

6.55+3.412

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 6.55 as follows:

6.550+3.412 6.550\\+3.412\\

Now let's solve the exercise in order:

Let's add the thousandths after the decimal point:

0+2=2 0+2=2

Let's add the hundredths after the decimal point:

5+1=6 5+1=6

Let's add the tenths after the decimal point:

5+4=9 5+4=9

Finally, let's add the whole numbers before the decimal point:

6+3=9 6+3=9

And we get:

6.550+3.4129.962 6.550\\+3.412\\9.962

Answer

9.962

Exercise #8

Circle the correct answer to the following exercise:

111.25+112.3

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 112.3 as follows:

111.25+112.30 111.25\\+112.30\\

Now let's solve the exercise in order:

We'll combine the hundredths after the decimal point:

5+0=5 5+0=5

We'll combine the tenths after the decimal point:

2+3=5 2+3=5

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

1+2=3 1+2=3

1+1=2 1+1=2

1+1=2 1+1=2

And we get:

111.25+112.30223.55 111.25\\+112.30\\223.55

Answer

223.55

Exercise #9

Circle the correct answer to the following exercise:

2.1012+3.212

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we'll first add the digit 0 to the number 3.212 in the following way:

2.1012+3.2120 2.1012\\+3.2120\\

Now let's solve the exercise in order:

Let's multiply the ten-thousandths after the decimal point:

2+0=2 2+0=2

Let's multiply the thousandths after the decimal point:

1+2=3 1+2=3

Let's multiply the hundredths after the decimal point:

0+1=1 0+1=1

Let's multiply the tenths after the decimal point:

1+2=3 1+2=3

Finally, let's multiply the whole numbers before the decimal point:

2+3=5 2+3=5

And we get:

2.1012+3.21205.3132 2.1012\\+3.2120\\5.3132

Answer

5.3132

Exercise #10

Circle the correct answer to the following exercise:

115.32+115.102

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 115.32 as follows:

115.320+115.102 115.320\\+115.102\\

Now let's solve the exercise in order:

Let's multiply the thousandths after the decimal point:

0+2=2 0+2=2

Let's multiply the hundredths after the decimal point:

2+0=2 2+0=2

Let's multiply the tenths after the decimal point:

3+1=4 3+1=4

Finally, let's multiply the whole numbers before the decimal point accordingly:

5+5=10 5+5=10

We'll add the tens to the tens digit and get:

1+1+1=3 1+1+1=3 1+1=2 1+1=2

And we get:

115.320+115.102230.422 115.320\\+115.102\\230.422

Answer

230.422

Exercise #11

Solve the following exercise and circle the appropriate answer:

3.512+4.313

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll add up the thousandths after the decimal point:

2+3=5 2+3=5

We'll add up the hundredths after the decimal point:

1+1=2 1+1=2

We'll add up the tenths after the decimal point:

5+3=8 5+3=8

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

3+4=7 3+4=7

And we get:

3.512+4.3137.825 3.512\\+4.313\\7.825

Answer

7.825

Exercise #12

Solve the following exercise and circle the appropriate answer:

21.38+13.41

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll add up the hundredths after the decimal point:

8+1=9 8+1=9

We'll add up the tenths after the decimal point:

3+4=7 3+4=7

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

1+3=4 1+3=4

2+1=3 2+1=3

And we get:

21.38+13.4134.79 21.38\\+13.41\\34.79

Answer

34.79

Exercise #13

Solve the following exercise and circle the appropriate answer:

13.29-12.13

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the hundredths after the decimal point:

93=6 9-3=6

We'll subtract the tenths after the decimal point:

21=1 2-1=1

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

32=1 3-2=1

11=0 1-1=0

And we'll get:

13.2912.1301.16 13.29\\-12.13\\01.16

Answer

1.16

Exercise #14

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 #15

Solve the following exercise and circle the appropriate answer:

33.10-11.10

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll subtract the hundreds after the decimal point:

00=0 0-0=0

We'll subtract the tenths after the decimal point:

11=0 1-1=0

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

31=2 3-1=2

31=2 3-1=2

And we get:

33.1011.1022.00 33.10\\-11.10\\22.00

Since there are only zeros after the decimal point, we can ignore them and we actually got the number: 22

Answer

22

Topics learned in later sections

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