Fractions and Decimals
Lesson 8 Mathematical Operations on Decimals
Welcome Friends!! You must have come across the situations when your mom asks you, John, tell me you have $ 2.50 in your account in cafeteria at school , You need to add some more money so that your account reaches to $ 7.00 How much money will you deposit to your account then?
Such transactions involve the subtraction operation on decimals.
In this lesson we will learn about Mathematical operations (addition, Subtraction, Multiplication and Division) on Decimals
Objectives: To learn Addition, Subtraction, Multiplication and Division on Decimals.
Mathematical Operations on Decimals
Addition and Subtraction:
Step1: The numbers should be placed one below the other, i.e. Ones under Ones, Tens under Tens.Etc.
Step 2: The numbers are added or subtracted in the same way as whole numbers
Step3: The Decimal point is put under the column of decimal point.
E.g. Add 134.453 and 17.357
134.453
+ 17.357
-__________________________
151.810
Example of Subtraction:
Subtract 354.72 – 104.875
354.720
- 104.875
________________________
249.845
Multiplication:
· Multiplication of Decimal by an Integer
o When you multiply a decimal number by an integer other than 10,100, 1000……., then just multiply the decimal point
o Once multiplication is done, put the decimal point in the product counting from right as many places as were in the decimal before multiplication.
o e. g 15.07 * 3 = 45.21
o When you multiply a decimal number by an integer 10,100, 1000……., then
o We just move the decimal point to the right as many places as the number of zeros in 10, 100, 1000….etc.
o e.g. 15.07 * 100 = 1507
· Multiplication of Decimal by Decimal
o When multiply decimal by another decimal, first ignore the decimal points.
o Multiply them as multiplication of whole numbers.
o Once multiplication is done, put the decimal point in the product counting from the right as many places as were together in the multiplicand and multiplier.
o e.g. 0.45 * 3.15
§ Multiply 45 * 315 = 14175
§ There were 4 decimal places together in the multiplier and multiplicand, so put the decimal point four places counting from right.
§ So the answer is 1.4175
Division:
· Division of Decimal by Integer
o When we divide a decimal number by an integer other than 10, 100, 1000……
o Divide the decimal number by the integer ignoring he decimal point.
o When division is over, put the decimal point in the quotient counting as many. places from right as there were in the dividend.
E.g. Divide 0.54 by 3
§ Ignore decimal point and divide 54 /3 = 18
§ Put the decimal point 2 places from right.
§ So the answer is 0.18
o When we divide a decimal number by an integer 10, 100, 1000……
o Move the decimal point to the left as many places as the number of zeros in the divisor, i.e. 10, 100, 1000…..
o E.g. Divide 15.053 by 100
§ Shift the decimal point towards left as many places as the number of zeros in the divisor.
§ Divisor is 100, has two zeros,
§ So the answer is 0.15053
· Division of Decimal by Decimal
· When divisor (A number by which you divide) is decimal. Move the decimal point to right to make it a whole number (Integer)
· For dividend move the decimal point to the right by same number of places. (add zeros if necessary)
· Perform the division as if it is a division of decimal by whole number.
e.g.
o Do the division 0.345 / 0.03
o After we make divisor the whole number we get 34.5 / 3
o Now we proceed as this is a division of decimal by an integer as explained above.
o 345/3 = 115
o Insert the decimal point one place from the right as there is only one decimal point in the dividend.
o So the answer is 11.5
Such transactions involve the subtraction operation on decimals.
In this lesson we will learn about Mathematical operations (addition, Subtraction, Multiplication and Division) on Decimals
Objectives: To learn Addition, Subtraction, Multiplication and Division on Decimals.
Mathematical Operations on Decimals
Addition and Subtraction:
Step1: The numbers should be placed one below the other, i.e. Ones under Ones, Tens under Tens.Etc.
Step 2: The numbers are added or subtracted in the same way as whole numbers
Step3: The Decimal point is put under the column of decimal point.
E.g. Add 134.453 and 17.357
134.453
+ 17.357
-__________________________
151.810
Example of Subtraction:
Subtract 354.72 – 104.875
354.720
- 104.875
________________________
249.845
Multiplication:
· Multiplication of Decimal by an Integer
o When you multiply a decimal number by an integer other than 10,100, 1000……., then just multiply the decimal point
o Once multiplication is done, put the decimal point in the product counting from right as many places as were in the decimal before multiplication.
o e. g 15.07 * 3 = 45.21
o When you multiply a decimal number by an integer 10,100, 1000……., then
o We just move the decimal point to the right as many places as the number of zeros in 10, 100, 1000….etc.
o e.g. 15.07 * 100 = 1507
· Multiplication of Decimal by Decimal
o When multiply decimal by another decimal, first ignore the decimal points.
o Multiply them as multiplication of whole numbers.
o Once multiplication is done, put the decimal point in the product counting from the right as many places as were together in the multiplicand and multiplier.
o e.g. 0.45 * 3.15
§ Multiply 45 * 315 = 14175
§ There were 4 decimal places together in the multiplier and multiplicand, so put the decimal point four places counting from right.
§ So the answer is 1.4175
Division:
· Division of Decimal by Integer
o When we divide a decimal number by an integer other than 10, 100, 1000……
o Divide the decimal number by the integer ignoring he decimal point.
o When division is over, put the decimal point in the quotient counting as many. places from right as there were in the dividend.
E.g. Divide 0.54 by 3
§ Ignore decimal point and divide 54 /3 = 18
§ Put the decimal point 2 places from right.
§ So the answer is 0.18
o When we divide a decimal number by an integer 10, 100, 1000……
o Move the decimal point to the left as many places as the number of zeros in the divisor, i.e. 10, 100, 1000…..
o E.g. Divide 15.053 by 100
§ Shift the decimal point towards left as many places as the number of zeros in the divisor.
§ Divisor is 100, has two zeros,
§ So the answer is 0.15053
· Division of Decimal by Decimal
· When divisor (A number by which you divide) is decimal. Move the decimal point to right to make it a whole number (Integer)
· For dividend move the decimal point to the right by same number of places. (add zeros if necessary)
· Perform the division as if it is a division of decimal by whole number.
e.g.
o Do the division 0.345 / 0.03
o After we make divisor the whole number we get 34.5 / 3
o Now we proceed as this is a division of decimal by an integer as explained above.
o 345/3 = 115
o Insert the decimal point one place from the right as there is only one decimal point in the dividend.
o So the answer is 11.5
Practice Problems
Remember you will simply solve these problems on your own; It is not needed to email the answers to the instructor.
Solve the following:
1. 11.0+ 1.23+ 0.008
2. 5.65 – 4.53
3. 15.05 + 20.50
4. 23* 12.5
5. 12.8 / 3.2
Solve the following:
1. 11.0+ 1.23+ 0.008
2. 5.65 – 4.53
3. 15.05 + 20.50
4. 23* 12.5
5. 12.8 / 3.2
Assignment 8
Please email the answers to this Assignment 8 to the email address provided at the bottom of the page. Please do not forget to write the Assignment number.
Solve the following:
1. 28.5 + 280.05+2.8050
2. 3.45 – 1.22
3. 23. 13 * 22.1
Solve the following:
1. 28.5 + 280.05+2.8050
2. 3.45 – 1.22
3. 23. 13 * 22.1
Assessment 8
Please email the answers to this Assessment 8 to the email address provided at the bottom of the page. Do not forget to write the Assessment number.
Addition:
1. 0.2 + 1.3
2. 2.5 + 3.5
3. 4.7 + 5.8
4. 23.45 + 12. 23
5. 34.032 + 10. 304
Subtraction
1. 0.45 – 0.12
2. 1.12 – 1.10
3. 3.12 – 1.02
4. 23.35 – 12. 05
5. 11.12 – 8. 04
Multiplication
1. 0.2 * 1.5
2. 1.2 * 2.4
3. 2.3 *5.78
4. 23.44 * 12.06
5. 10.01 * 12.21
Division
1. 0.2/0.2
2. 1.2/0.6
3. 3.4/1.7
4. 24.2/0.2
5. 14.4/2.4
Addition:
1. 0.2 + 1.3
2. 2.5 + 3.5
3. 4.7 + 5.8
4. 23.45 + 12. 23
5. 34.032 + 10. 304
Subtraction
1. 0.45 – 0.12
2. 1.12 – 1.10
3. 3.12 – 1.02
4. 23.35 – 12. 05
5. 11.12 – 8. 04
Multiplication
1. 0.2 * 1.5
2. 1.2 * 2.4
3. 2.3 *5.78
4. 23.44 * 12.06
5. 10.01 * 12.21
Division
1. 0.2/0.2
2. 1.2/0.6
3. 3.4/1.7
4. 24.2/0.2
5. 14.4/2.4
Objectives of next lesson
Brief Objective of next Lesson: In the next lesson we will study Real World Problems involving Decimals.
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