Decimals : Multiplication, Division and Changing Common Fractions with 10, 100, 1000 as Denominators to Decimals

SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS

SUBJECT: MATHEMATICS

CLASS: BASIC FOUR / / PRIMARY 4

WEEK 4

TOPIC : Decimals : Multiplication, Division and Changing Common Fractions with 10, 100, 1000 as Denominators to Decimals 

Learning Objectives

Pupils should be able to:

• calculate decimals by
  multiplying with 1-digit
  number
• calculate decimals by
  dividing with 1-digit nurnber.
  discover decimals by
  multiplying with 10, 100 and
  1000.
• divide decimals with 10.
  100, 1000
• use numbers greater than
  10 to multiply and divide
  decimals.

Learning Activities

• Pupils in a small group use cardboard to
  design twice the size of 0.25 which is half of a circle.
• Pupils in groups use different colours and sizes of cardboards to prepare flash cards on multiplication and division of numbers by multiples of 10, 100 and 1 000.
• Highlight boldly on shifting of the decimal point.

Embedded Core Skills 

• Critical thinking and problem solving
• Communication and Collaboration
• Leadership skills and Personal Development
• Creativity and Imagination

Audio Visual Resource

• Cardboards
• Marker
• Scissors
• Multiplication chart

Content

Decimals : Multiplication, Division and Changing Common Fractions with 10, 100, 1000 as Denominators to Decimals

Hello Grade 4 pupils! Today, we’re going to learn about decimals and how to do multiplication, division, and change common fractions to decimals using 10, 100, and 1000 as denominators.

Let’s start by defining decimals. Decimals are a way to write parts of a whole number. They are written using a decimal point and digits to the right of the decimal point. For example, the number 3.25 is a decimal because it shows three whole units and a quarter of a unit.

Now let’s talk about multiplication and division with decimals. When multiplying decimals, you need to line up the decimal points and then multiply like you would with whole numbers. For example, 2.5 multiplied by 3 is 7.5, because 2.5 times 3 equals 7.5.

When dividing decimals, you also need to line up the decimal points, and then divide like you would with whole numbers. For example, 1.5 divided by 0.5 is 3, because 1.5 divided by 0.5 equals 3.

Finally, let’s talk about changing common fractions to decimals using 10, 100, and 1000 as denominators. To do this, you need to divide the numerator (the top number) by the denominator (the bottom number). For example, let’s say you have the fraction 3/10. To change it to a decimal, you divide 3 by 10, which gives you 0.3. If you have the fraction 25/100, you divide 25 by 100, which gives you 0.25. And if you have the fraction 7/1000, you divide 7 by 1000, which gives you 0.007.

So that’s a brief introduction to decimals, multiplication, division, and changing fractions to decimals. I hope this helps you understand these concepts a little better.

Evaluation

1. What is the result of multiplying 4.6 by 2.3? a) 10.58 b) 8.99 c) 1.78 d) 6.12
2. What is the result of dividing 2.4 by 0.6? a) 4 b) 0.6 c) 2.4 d) 0.4
3. What is the decimal equivalent of the fraction 3/10? a) 0.1 b) 0.2 c) 0.3 d) 0.4
4. What is the decimal equivalent of the fraction 5/100? a) 0.5 b) 0.05 c) 0.005 d) 0.0005
5. What is the result of multiplying 0.08 by 25? a) 0.2 b) 2 c) 20 d) 200
6. What is the result of dividing 1.2 by 0.4? a) 3 b) 0.3 c) 1.6 d) 4.8
7. What is the decimal equivalent of the fraction 9/1000? a) 0.009 b) 0.09 c) 0.9 d) 9
8. What is the result of multiplying 0.03 by 200? a) 0.6 b) 6 c) 60 d) 600
9. What is the result of dividing 3.5 by 0.5? a) 7 b) 0.7 c) 3 d) 35
10. What is the decimal equivalent of the fraction 7/100? a) 0.07 b) 0.7 c) 0.007 d) 0.0007

Multiplication of Decimals by 1-digit number

When multiplying decimals by a 1-digit number, you can follow these steps:

Step 1: Line up the decimal points of the numbers you are multiplying.

Step 2: Multiply the numbers as you would with whole numbers, ignoring the decimal point for now.

Step 3: Count the total number of digits to the right of the decimal point in both numbers that you multiplied in Step 2.

Step 4: Place the decimal point in your answer so that the total number of digits to the right of the decimal point is equal to the number you counted in Step 3.

Let’s take an example to see how this works:

Example: What is 2.5 multiplied by 3?

Step 1: Line up the decimal points of 2.5 and 3, like this:

2.5

× 3

Step 2: Multiply the numbers as you would with whole numbers, ignoring the decimal point:

2.5

× 3

—–

7 5

Step 3: Count the total number of digits to the right of the decimal point in both numbers that you multiplied in Step 2. In this case, there is 1 digit to the right of the decimal point in 2.5, and 0 digits to the right of the decimal point in 3, for a total of 1 digit.

Step 4: Place the decimal point in your answer so that the total number of digits to the right of the decimal point is equal to the number you counted in Step 3. In this case, we have one digit to the right of the decimal point, so the answer is 7.5.

So the answer to the example problem is 7.5.

Evaluation

1. What is the product of 2.3 and 5? a) 10.3 b) 11.5 c) 12.3 d) 13.5
2. What is the result of multiplying 0.6 by 7? a) 4.2 b) 4.3 c) 4.6 d) 4.7
3. What is the product of 3.2 and 4? a) 10.8 b) 12.8 c) 13.2 d) 14.8
4. What is the result of multiplying 0.8 by 9? a) 7.2 b) 7.5 c) 7.6 d) 7.8
5. What is the product of 2.5 and 3? a) 5 b) 6 c) 7.5 d) 8.5
6. What is the result of multiplying 0.7 by 6? a) 4.2 b) 4.8 c) 4.9 d) 4.2
7. What is the product of 4.1 and 5? a) 20.1 b) 21.5 c) 22.5 d) 23.1
8. What is the result of multiplying 0.5 by 8? a) 3.5 b) 4 c) 4.5 d) 5
9. What is the product of 3.4 and 6? a) 20.4 b) 21 c) 21.4 d) 22.4
10. What is the result of multiplying 0.9 by 7? a) 6.1 b) 6.2 c) 6.3 d) 6.4

Division of Decimals by 1-digit number

When dividing decimals by a 1-digit number, you can follow these steps:

Step 1: Write the division problem like you would with whole numbers, ignoring the decimal point for now.

Step 2: Divide the numbers as you would with whole numbers.

Step 3: Place the decimal point in your answer directly above the decimal point in the original problem.

Let’s take an example to see how this works:

Example: What is 5.6 divided by 2?

Step 1: Write the division problem like you would with whole numbers, ignoring the decimal point for now:

56 ÷ 2

Step 2: Divide the numbers as you would with whole numbers. The first digit of the quotient is 2 because 2 times 2 is 4, which is the largest multiple of 2 that is less than 5. The remainder is 1. We bring down the next digit (the 6) and divide it by 2, which gives us a quotient of 3 with no remainder.

56
÷ 2
—–
2 8
—–

2 | 5 6
4
—–
1 6
1 6
—–

0

Step 3: Place the decimal point in your answer directly above the decimal point in the original problem. In this case, the original problem has one digit to the right of the decimal point, so we place the decimal point in our answer after the first digit:

5.6 ÷ 2 = 2.8

So the answer to the example problem is 2.8

Evaluation

1. What is the result of dividing 3.2 by 4? a) 0.8 b) 0.6 c) 0.4 d) 0.2
2. What is the result of dividing 6.4 by 8? a) 0.4 b) 0.6 c) 0.8 d) 1.2
3. What is the result of dividing 5.5 by 5? a) 0.5 b) 1 c) 1.5 d) 2
4. What is the result of dividing 2.7 by 3? a) 0.7 b) 0.9 c) 1.1 d) 1.3
5. What is the result of dividing 4.8 by 2? a) 2.2 b) 2.4 c) 2.6 d) 2.8
6. What is the result of dividing 6.3 by 7? a) 0.7 b) 0.9 c) 1.1 d) 1.3
7. What is the result of dividing 7.6 by 4? a) 1.4 b) 1.8 c) 2.1 d) 2.4
8. What is the result of dividing 3.9 by 5? a) 0.7 b) 0.78 c) 0.85 d) 0.9
9. What is the result of dividing 4.5 by 9? a) 0.5 b) 0.6 c) 0.7 d) 0.8
10. What is the result of dividing 5.4 by 6? a) 0.7 b) 0.8 c) 0.9 d) 1.0

Discover Decimals by Multiplying with 10, 100 and 1000

To discover decimals by multiplying with 10, 100, and 1000, you can follow these steps:

Step 1: Identify the number you want to multiply by 10, 100, or 1000.

Step 2: Move the decimal point to the right by one digit for every 10 you want to multiply by, two digits for every 100, and three digits for every 1000.

Step 3: Add zeros to the right of the number if necessary to maintain the same number of digits.

Let’s take an example to see how this works:

Example 1: Discover the decimal 0.35 by multiplying with 100.

Step 1: Identify the number you want to multiply by 100. In this case, it’s 0.35.

Step 2: Move the decimal point to the right by two digits, since we’re multiplying by 100. This gives us 35.

Step 3: Add a zero to the right of the number to maintain the same number of digits. This gives us 35.0.

So the answer to the example problem is 0.35 is equal to 35.0 when multiplied by 100.

Example 2: Discover the decimal 0.018 by multiplying with 1000.

Step 1: Identify the number you want to multiply by 1000. In this case, it’s 0.018.

Step 2: Move the decimal point to the right by three digits, since we’re multiplying by 1000. This gives us 18.

Step 3: Add two zeros to the right of the number to maintain the same number of digits. This gives us 18.000.

So the answer to the example problem is 0.018 is equal to 18.000 when multiplied by 1000

Evaluation

1. What is 0.2 when multiplied by 100? a) 20 b) 2 c) 0.002 d) 0.02
2. What is 0.7 when multiplied by 10? a) 7 b) 70 c) 0.07 d) 0.007
3. What is 0.5 when multiplied by 1000? a) 5 b) 500 c) 0.0005 d) 0.05
4. What is 0.03 when multiplied by 100? a) 0.03 b) 0.3 c) 3 d) 30
5. What is 0.06 when multiplied by 10? a) 0.006 b) 0.06 c) 0.6 d) 6
6. What is 0.002 when multiplied by 1000? a) 0.002 b) 0.02 c) 0.2 d) 2
7. What is 0.25 when multiplied by 10? a) 0.025 b) 0.25 c) 2.5 d) 25
8. What is 0.008 when multiplied by 100? a) 0.08 b) 0.8 c) 8 d) 80
9. What is 0.6 when multiplied by 1000? a) 6 b) 60 c) 600 d) 0.0006
10. What is 0.07 when multiplied by 10? a) 0.007 b) 0.07 c) 0.7 d) 7

Discover Decimals by Dividing by 10, 100 and 1000

To discover decimals by dividing by 10, 100, and 1000, you can follow these steps:

Step 1: Identify the number you want to divide by 10, 100, or 1000.

Step 2: Move the decimal point to the left by one digit for every 10 you want to divide by, two digits for every 100, and three digits for every 1000.

Step 3: Add zeros to the left of the number if necessary to maintain the same number of digits.

Let’s take an example to see how this works:

Example 1: Discover the decimal 2.5 by dividing by 10.

Step 1: Identify the number you want to divide by 10. In this case, it’s 2.5.

Step 2: Move the decimal point to the left by one digit, since we’re dividing by 10. This gives us 0.25.

Step 3: Add a zero to the left of the number to maintain the same number of digits. This gives us 0.025.

So the answer to the example problem is 2.5 is equal to 0.025 when divided by 10.

Example 2: Discover the decimal 0.0036 by dividing by 1000.

Step 1: Identify the number you want to divide by 1000. In this case, it’s 0.0036.

Step 2: Move the decimal point to the left by three digits, since we’re dividing by 1000. This gives us 0.0000036.

Step 3: Add three zeros to the left of the number to maintain the same number of digits. This gives us 0.00000036.

So the answer to the example problem is 0.0036 is equal to 0.00000036 when divided by 1000

Evaluation

1. If Adeboye has 0.25 of a cake, what is this quantity when divided by 10? a) 0.0025 b) 0.025 c) 0.25 d) 2.5
2. If Joshua has 3.8 liters of water, what is this quantity when divided by 100? a) 0.038 b) 0.38 c) 3.8 d) 38
3. If Chris has 12.6 pencils, what is this quantity when divided by 10? a) 1.26 b) 12.6 c) 126 d) 0.126
4. If Enouch has 0.0045 kg of rice, what is this quantity when divided by 1000? a) 0.0045 b) 0.00045 c) 0.0000045 d) 0.00000045
5. If Babatope has 0.09 meters of fabric, what is this quantity when divided by 10? a) 0.009 b) 0.09 c) 0.9 d) 9
6. If Olukoya has 4.25 liters of petrol, what is this quantity when divided by 1000? a) 0.0425 b) 0.425 c) 4.25 d) 42.5
7. If Gabriel has 0.0023 kg of sugar, what is this quantity when divided by 1000? a) 0.023 b) 0.0023 c) 0.00023 d) 0.000023
8. If Olufunmi has 8.7 cm of ribbon, what is this quantity when divided by 10? a) 0.87 b) 8.7 c) 87 d) 870
9. If Adeboye has 1.25 liters of milk, what is this quantity when divided by 100? a) 0.0125 b) 0.125 c) 1.25 d) 12.5
10. If Joshua has 0.0072 kg of salt, what is this quantity when divided by 1000? a) 0.00072 b) 0.0072 c) 0.072 d) 0.72

Using Numbers Greater Than 10 to Multiply and Divide Decimals

When we use numbers greater than 10 to multiply or divide decimals, it can be good or bad depending on the situation.

If we need to multiply a decimal by a number greater than 10, it can be nice because it allows us to quickly find the answer without having to do lots of repeated addition. For example, if we need to find 0.5 multiplied by 20, we can simply move the decimal point one place to the right and get the answer of 10. So in this case, using a number greater than 10 to multiply decimals is nice because it makes the calculation easy and quick.

On the other hand, if we need to divide a decimal by a number greater than 10, it can be bad because it can result in a very long, difficult calculation. For example, if we need to find 0.8 divided by 15, we have to do long division to find the answer of 0.0533 recurring. In this case, using a number greater than 10 to divide decimals can be bad because it makes the calculation long and difficult.

Let’s take another example to see how this works:

Example: Find the value of 0.4 multiplied by 25.

Solution: To multiply 0.4 by 25, we can simply move the decimal point one place to the right, since 25 is 10 times 2.5. This gives us 10. So the answer is 0.4 multiplied by 25 is equal to 10.

This is a nice example of using a number greater than 10 to multiply decimals because it makes the calculation easy and quick

Evaluation

1. If Adeboye has 2.5 kg of sugar, what is this quantity when multiplied by 15? a) 0.375 kg b) 25 kg c) 37.5 kg d) 150 kg
2. If Joshua has 3.6 liters of petrol, what is this quantity when multiplied by 12? a) 43.2 liters b) 36 liters c) 0.36 liters d) 0.432 liters
3. If Chris has 0.4 meters of fabric, what is this quantity when multiplied by 20? a) 0.08 meters b) 8 meters c) 40 meters d) 400 meters
4. If Enouch has 0.007 kg of salt, what is this quantity when multiplied by 100? a) 0.7 kg b) 0.007 kg c) 0.7 grams d) 0.07 grams
5. If Babatope has 2.5 liters of water, what is this quantity when multiplied by 25? a) 6.25 liters b) 25 liters c) 62.5 liters d) 625 liters
6. If Olukoya has 0.6 meters of ribbon, what is this quantity when multiplied by 10? a) 60 meters b) 6 meters c) 0.6 meters d) 0.06 meters
7. If Gabriel has 1.2 kg of rice, what is this quantity when divided by 20? a) 0.06 kg b) 0.12 kg c) 6 kg d) 12 kg
8. If Olufunmi has 5.4 liters of juice, what is this quantity when divided by 15? a) 0.36 liters b) 0.54 liters c) 36 liters d) 54 liters
9. If Adeboye has 0.4 meters of cloth, what is this quantity when multiplied by 30? a) 0.012 meters b) 0.12 meters c) 12 meters d) 120 meters
10. If Joshua has 0.08 kg of flour, what is this quantity when multiplied by 50? a) 0.04 kg b) 0.4 kg c) 4 kg d) 40 KG

Lesson Presentation

Introduction (10 minutes):

• Ask the students what they know about decimals.
• Define decimals as numbers that represent parts of a whole or a fraction of a number.
• Explain that decimals are written with a dot called a decimal point.
• Write examples of decimals on the board, such as 0.5, 0.25, and 0.75.

Body (30 minutes):

• Explain how to change common fractions with 10, 100, 1000 as denominators to decimals by dividing the numerator by the denominator.
• Demonstrate with examples on the board, such as 3/10, 5/100, and 7/1000.
• Use decimal blocks to show how to multiply and divide decimals by 1-digit numbers, such as 0.5 x 3 and 0.6 ÷ 5.
• Give the students worksheets with practice problems for multiplying and dividing decimals by 1-digit numbers.
• Explain how to discover decimals by multiplying with 10, 100, and 1000 by moving the decimal point to the right.
• Use examples on the board, such as 0.3 x 100 and 0.05 x 10.
• Give the students worksheets with practice problems for discovering decimals by multiplying with 10, 100, and 1000.

Conclusion (10 minutes):

• Recap the lesson by asking the students what they learned about decimals.
• Have the students share any questions they have or areas where they may need additional practice.
• Provide feedback on student performance and encourage them to continue practicing and using decimals in everyday situations.

Assessment:

• The worksheets provided will be collected and graded.
• The teacher will also assess student understanding through observation and class participation during the lesson.

Weekly Assessment /Test 

1. To change a fraction with a denominator of 10 to a decimal, divide the __________ by 10.
2. When multiplying a decimal by a 1-digit number, move the decimal point to the ___________.
3. To change a fraction with a denominator of 100 to a decimal, divide the __________ by 100.
4. When dividing a decimal by a 1-digit number, move the decimal point to the __________.
5. To change a fraction with a denominator of 1000 to a decimal, divide the __________ by 1000.
6. When multiplying a decimal by 10, move the decimal point to the __________.
7. When dividing a decimal by 10, move the decimal point to the __________.
8. When multiplying a decimal by 100, move the decimal point to the __________.
9. When dividing a decimal by 100, move the decimal point to the __________.
10. When multiplying a decimal by 1000, move the decimal point to the __________.

Answers

1. Numerator
2. Right
3. Numerator
4. Left
5. Numerator
6. Right
7. Left
8. Two places to the right
9. Two places to the left
10. Three places to the right

Explanation

1. When changing a fraction with a denominator of 10 to a decimal, we divide the numerator by 10 because 10 is the same as 10/1 or 1 followed by one zero. For example, to change 3/10 to a decimal, we divide 3 by 10 and get 0.3.
2. When multiplying a decimal by a 1-digit number, we move the decimal point to the right by the same number of places as there are zeros in the factor. For example, to multiply 0.5 by 3, we move the decimal point one place to the right and get 1.5.
3. When changing a fraction with a denominator of 100 to a decimal, we divide the numerator by 100 because 100 is the same as 100/1 or 1 followed by two zeros. For example, to change 5/100 to a decimal, we divide 5 by 100 and get 0.05.
4. When dividing a decimal by a 1-digit number, we move the decimal point to the left by the same number of places as there are zeros in the divisor. For example, to divide 0.6 by 5, we move the decimal point one place to the left and get 0.12.
5. When changing a fraction with a denominator of 1000 to a decimal, we divide the numerator by 1000 because 1000 is the same as 1000/1 or 1 followed by three zeros. For example, to change 7/1000 to a decimal, we divide 7 by 1000 and get 0.007.
6. When multiplying a decimal by 10, we move the decimal point one place to the right. For example, to multiply 0.3 by 10, we move the decimal point one place to the right and get 3.
7. When dividing a decimal by 10, we move the decimal point one place to the left. For example, to divide 1.2 by 10, we move the decimal point one place to the left and get 0.12.
8. When multiplying a decimal by 100, we move the decimal point two places to the right. For example, to multiply 0.25 by 100, we move the decimal point two places to the right and get 25.
9. When dividing a decimal by 100, we move the decimal point two places to the left. For example, to divide 7.5 by 100, we move the decimal point two places to the left and get 0.075.
10. When multiplying a decimal by 1000, we move the decimal point three places to the right. For example, to multiply 0.02 by 1000, we move the decimal point three places to the right and get 20.