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 written correctly:

Is the position of the decimal point correct in each number?

6.31+216.222

Video Solution

Step-by-Step Solution

First let's fill the zeros in the empty space as follows:

006.310+216.222  006.310\\+216.222\\\

Here We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

Answer

Yes

Exercise #2

Determine whether the exercise is correctly written or not.

True or false:

The positions of the decimal points correspond.

21.52+3.4

Video Solution

Step-by-Step Solution

First let's fill in the zeros in the empty spaces as follows:

21.52+03.40 21.52\\+03.40\\ Note that the decimal points are written one below the other.

Therefore, the positions of the decimal points correspond and thus 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

Choose the correct answer to the following exercise:

5.4+3.22

Video Solution

Step-by-Step Solution

To avoid confusion, 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 then 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

Finally, simply solve the addition as follows:

5.40+3.228.62 5.40\\+3.22\\8.62

Answer

8.62

Exercise #6

Choose the correct answer to the following exercise:

1.02+6.4

Video Solution

Step-by-Step Solution

To avoid confusion, 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 start by adding the hundredths after the decimal point:

2+0=2 2+0=2

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

0+4=4 0+4=4

Finally, we will add the units before the decimal point:

1+6=7 1+6=7

Finally, calculate as follows:

1.02+6.407.42 1.02\\+6.40\\7.42

Answer

7.42

Exercise #7

Solve 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 obtain the following:

6.550+3.4129.962 6.550\\+3.412\\9.962

Answer

9.962

Exercise #8

Choose the correct answer:

111.25+112.3

Video Solution

Step-by-Step Solution

To avoid confusion when 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\\

First we'll combine the hundredths after the decimal point:

5+0=5 5+0=5

Next 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

This gives us:

111.25+112.30223.55 111.25\\+112.30\\223.55

Answer

223.55

Exercise #9

Solve 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 obtain the following:

2.1012+3.21205.3132 2.1012\\+3.2120\\5.3132

Answer

5.3132

Exercise #10

Solve 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 obtain the following:

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:

22.1-12.0

Video Solution

Step-by-Step Solution

Let's solve the exercise in order.

First, we'll subtract the tenths after the decimal point:

10=1 1-0=1

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

22=0 2-2=0

21=1 2-1=1

We obtain:

22.112.010.1 22.1\\-12.0\\10.1

Answer

10.1

Exercise #15

Solve the following exercise:

33.10-11.10

Video Solution

Step-by-Step Solution

Let's solve the exercise in order:

We'll first subtract the hundreds after the decimal point:

00=0 0-0=0

Next, 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

Therefore:

33.1011.1022.00 33.10\\-11.10\\22.00

Answer

22