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.

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:

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 #8

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 #9

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 #10

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 #11

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 #12

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

Exercise #13

Circle the correct answer to the following exercise:33.23-30.1

Video Solution

Step-by-Step Solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 30.1 as follows:

33.2330.10 33.23\\-30.10\\

Now let's solve the exercise in order:

We'll subtract the hundredths after the decimal point:

30=3 3-0=3

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:

30=3 3-0=3

33=0 3-3=0

And we get:

33.2330.1003.13 33.23\\-30.10\\03.13

Answer

3.13

Exercise #14

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 #15

0.85+7.61+2.3= 0.85+7.61+2.3=

Video Solution

Step-by-Step Solution

According to the order of operations, we will solve the exercise from left to right.

We will first calculate the addition exercise in the vertical column, since it contains two numbers after the decimal point:

0.85+7.61=8.46 0.85+7.61=8.46

Now we will get the exercise:

8.46+2.3= 8.46+2.3=

Let's remember that:

2.3=2.30 2.3=2.30

We will calculate in the vertical column and get:

10.76 10.76

Answer

10.76

Topics learned in later sections

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