Division of Fractions and Decimals Mathematics Primary 5 First Term Lesson Notes Week 11

Division of Decimals by Whole Numbers

Dividing Decimals by Whole Numbers:

• When dividing a decimal by a whole number, divide as you would with whole numbers, then place the decimal point directly above its position in the dividend.

Applying the Rule of Shifting Decimal Points:

• If necessary, you can shift the decimal point in both the dividend and divisor to make the division easier. For example, to divide 3.5 by 5, you can perform the division directly without moving the decimal.

Examples:

1. 7.2 ÷ 3 = 2.4
2. 9.75 ÷ 5 = 1.95
3. 5.6 ÷ 2 = 2.8
4. 12.48 ÷ 4 = 3.12
5. 16.5 ÷ 3 = 5.5

Class Work:

1. 8.4 ÷ 4 = ?
2. 13.6 ÷ 2 = ?
3. 25.5 ÷ 5 = ?
4. 9.9 ÷ 3 = ?
5. 18.2 ÷ 2 = ?

Division of Fractions

Dividing One Fraction by Another:

• To divide one fraction by another, invert (flip) the second fraction (the divisor) and multiply it by the first fraction (the dividend).

Inverting the Second Fraction and Multiplying:

• For example, to divide 2/3 by 4/5, you flip 4/5 to become 5/4 and then multiply: 2/3 × 5/4.

Examples:

1. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12, which simplifies to 5/6
2. 3/7 ÷ 2/9 = 3/7 × 9/2 = 27/14
3. 5/8 ÷ 3/4 = 5/8 × 4/3 = 20/24, which simplifies to 5/6
4. 7/10 ÷ 1/2 = 7/10 × 2/1 = 14/10, which simplifies to 7/5 or 1 2/5
5. 4/9 ÷ 5/6 = 4/9 × 6/5 = 24/45, which simplifies to 8/15

Class Work:

1. 1/2 ÷ 3/5 = ?
2. 3/4 ÷ 2/7 = ?
3. 7/8 ÷ 1/3 = ?
4. 5/6 ÷ 4/9 = ?
5. 2/5 ÷ 5/6 = ?

Real-Life Problems on Division of Decimals and Fractions

Applying Division of Decimals and Fractions to Solve Real-Life Problems:

• Division of decimals and fractions is used in various real-life situations such as dividing money, ingredients, or items among people.

Examples:

1. If you have $15.75 and want to split it equally among 3 friends, how much does each friend get?
   • Solution: $15.75 ÷ 3 = $5.25 per friend
2. You have 3/4 of a pizza and want to share it equally between 3 people. How much pizza does each person get?
   • Solution: 3/4 ÷ 3 = 1/4
3. A recipe calls for 1.5 cups of sugar, but you want to make only half of the recipe. How much sugar should you use?
   • Solution: 1.5 ÷ 2 = 0.75 cups
4. You have 5.4 meters of fabric and want to cut it into 6 equal pieces. How long is each piece?
   • Solution: 5.4 ÷ 6 = 0.9 meters per piece
5. A car drives 9.5 miles using 2 gallons of fuel. How many miles does it drive per gallon?
   • Solution: 9.5 ÷ 2 = 4.75 miles per gallon

Class Work:

1. You have $18.90 and want to share it equally among 3 people. How much does each person get?
2. If you have 2/3 of a cake and want to share it equally between 2 people, how much does each person get?
3. A recipe requires 2.5 cups of flour, but you want to make half the amount. How much flour should you use?
4. You have 7.2 meters of ribbon and want to cut it into 4 equal pieces. How long is each piece?
5. A car drives 12.6 miles using 3 gallons of fuel. How many miles does it drive per gallon?

Quantitative Reasoning

Solving Quantitative Aptitude Problems Involving the Division of Decimals and Fractions:

Examples:

1. A tank holds 25.2 liters of water. If you divide it into 6 equal parts, how much water is in each part?
   • Solution: 25.2 ÷ 6 = 4.2 liters
2. You have 4/5 of a liter of juice and want to divide it equally among 4 cups. How much juice does each cup get?
   • Solution: 4/5 ÷ 4 = 1/5 liter
3. A car travels 45.6 miles on 4 gallons of fuel. How many miles does it travel per gallon?
   • Solution: 45.6 ÷ 4 = 11.4 miles
4. If you have 7/8 of a pound of butter and need to divide it into 4 equal portions, how much butter is in each portion?
   • Solution: 7/8 ÷ 4 = 7/32 pounds
5. A rope is 18.4 meters long. If it is cut into 8 equal pieces, how long is each piece?
   • Solution: 18.4 ÷ 8 = 2.3 meters

Class Work:

1. A container holds 19.5 liters of water. If you divide it into 5 equal parts, how much water is in each part?
2. You have 3/4 of a kilogram of flour and want to divide it equally among 3 people. How much flour does each person get?
3. A car travels 52.8 miles on 4 gallons of fuel. How many miles does it travel per gallon?
4. If you have 6/7 of a cake and need to divide it into 3 equal portions, how much does each portion get?
5. A wire is 22.5 meters long. If it is cut into 5 equal pieces, how long is each piece?

Fill-in-the-Blank Questions (Assessment):

1. Divide 1/2 by 1/4. The result is __________.
   a) 1/2
   b) 2
   c) 1/4
   d) 4
2. 0.8 divided by 4 is __________.
   a) 0.2
   b) 0.4
   c) 0.1
   d) 0.5
3. Divide 3/5 by 2/5. The result is __________.
   a) 1/5
   b) 3/10
   c) 3/2
   d) 3/5
4. 0.75 divided by 5 is __________.
   a) 0.15
   b) 0.5
   c) 0.25
   d) 1.5
5. Divide 7/8 by 3/4. The result is __________.
   a) 7/12
   b) 7/6
   c) 7/4
   d) 7/3
6. 0.4 divided by 2 is __________.
   a) 0.8
   b) 0.4
   c) 0.2
   d) 1.2
7. Divide 5/6 by 2/3. The result is __________.
   a) 5/9
   b) 10/9
   c) 1/3
   d) 1
8. 0.9 divided by 3 is __________.
   a) 0.6
   b) 0.3
   c) 1
   d) 0.9
9. Divide 9/10 by 1/5. The result is __________.
   a) 1/2
   b) 9/50
   c) 9/5
   d) 45/50
10. 0.5 divided by 2 is __________.
    a) 0.1
    b) 1
    c) 0.25
    d) 0.5
11. Divide 4/9 by 2/3. The result is __________.
    a) 4/27
    b) 4/3
    c) 6/3
    d) 2/3
12. 0.45 divided by 5 is __________.
    a) 0.09
    b) 0.5
    c) 0.1
    d) 0.18
13. Divide 7/10 by 1/2. The result is __________.
    a) 7/20
    b) 14/10
    c) 7/5
    d) 7/4
14. 0.6 divided by 3 is __________.
    a) 1
    b) 0.2
    c) 0.5
    d) 0.3
15. Divide 2/7 by 1/14. The result is __________.
    a) 4/7
    b) 1/2
    c) 1/14
    d) 4/2

15 Frequently Asked Questions (FAQs) with Answers:

1. Q: How do you divide one fraction by another?
   A: Invert (flip) the second fraction and multiply it by the first fraction.
2. Q: What happens when you divide a decimal by a whole number?
   A: The decimal point shifts to the left according to the number of places in the divisor.
3. Q: How do you solve real-life problems involving division of fractions?
   A: Translate the problem into a mathematical expression and then divide the fractions.
4. Q: What is the rule for dividing decimals by 10, 100, or 1000?
   A: Shift the decimal point to the left by 1, 2, or 3 places, respectively.
5. Q: Why is it important to understand how to divide fractions and decimals?
   A: It helps in solving problems related to measurements, sharing, and understanding numbers.
6. Q: What should you do if the fraction cannot be simplified after division?
   A: Leave the fraction as it is or express it as a mixed number if possible.
7. Q: How can division of decimals be applied in daily life?
   A: It is used in situations like calculating prices, measurements, and distributing items.
8. Q: How can you check your answer after dividing fractions?
   A: Multiply the quotient by the divisor; it should equal the dividend.
9. Q: What is the purpose of shifting the decimal point during division?
   A: It helps in maintaining the correct place value in the answer.
10. Q: How is quantitative reasoning related to division of fractions and decimals?
    A: It involves using logical thinking to solve complex division problems.
11. Q: What is the first step in dividing a mixed number by a fraction?
    A: Convert the mixed number into an improper fraction.
12. Q: Why is it important to understand division of fractions in academics?
    A: It builds a foundation for more advanced mathematical concepts and applications.
13. Q: How do you solve real-life problems involving division of decimals?
    A: Convert the problem into a division equation and then solve it by shifting the decimal point if necessary.
14. Q: How does dividing by a fraction differ from dividing by a whole number?
    A: Dividing by a fraction involves multiplying by its reciprocal, while dividing by a whole number simply reduces the size of the dividend.
15. Q: What is a division story involving fractions?
    A: A scenario where fractions are divided to solve a problem, such as dividing a pizza among friends.

Presentation:

Step 1: Review the concept of multiplication of fractions and decimals.
Step 2: Explain and demonstrate the division of fractions and decimals by whole numbers.
Step 3: Solve real-life problems involving division of fractions and decimals.

Teacher’s Activities:

• Demonstrate the process of dividing fractions and decimals.
• Provide examples and guide pupils in solving practice problems.
• Encourage pupils to create their own division stories and solve them.

Learners’ Activities:

• Participate in solving division problems.
• Complete worksheets with fraction and decimal division problems.
• Practice quantitative reasoning problems.

Assessment:

1. Divide fractions and decimals by whole numbers.
2. Solve real-life problems involving the division of fractions.
3. Apply the rule of shifting decimal points in division.
4. Solve quantitative aptitude problems related to division.

10 Evaluation Questions:

1. What is the result of dividing 3/7 by 2/7?
2. How do you shift the decimal point when dividing by 10?
3. Solve: 0.56 divided by 4.
4. Divide 5/8 by 1/4.
5. What is the rule for dividing fractions?
6. Solve a real-life problem involving division of decimals.
7. What is the importance of understanding division of fractions?
8. Solve: 0.9 divided by 3.
9. Divide 6/11 by 3/11.
10. How can you apply division of fractions in everyday life?

Conclusion:

The teacher will review the lesson, address any difficulties pupils may have, and ensure that they understand the process of dividing fractions and decimals. Pupils will discuss how these skills are used in real-life situations, such as in measuring and sharing.

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