Doubling and Halving:
Explore the essential concepts of doubling and halving, understand their applications, and practice with 50 carefully curated questions suitable for all grade levels.
Doubling and Halving Basics
Doubling and halving are fundamental arithmetic operations that involve increasing or decreasing a number by twofold or half, respectively. These operations are not only essential for basic math but also serve as building blocks for more complex mathematical concepts.
Doubling
Doubling a number means multiplying it by two. It is a quick way to add a number to itself.
Double of 7:
\[ 7 \times 2 = 14 \]
Here, 7 is doubled to become 14.
Halving
Halving a number means dividing it by two. It effectively reduces the number to half its original value.
Half of 14:
\[ 14 \div 2 = 7 \]
In this case, 14 is halved to become 7.
Methods and Strategies
Understanding various methods and strategies for doubling and halving enhances numerical fluency and aids in efficient problem-solving.
Doubling and Halving Machines
Visual tools like doubling and halving machines help students grasp the concept of these operations through interactive and engaging activities.
Use a doubling machine to find the double of 6:
\[ 6 \times 2 = 12 \]
Use a halving machine to find half of 12:
\[ 12 \div 2 = 6 \]
Doubling Using Multilink Cubes
Multilink cubes provide a hands-on approach to visualize doubling by physically manipulating the cubes to represent numbers.
To double 5 using multilink cubes:
Arrange 5 cubes and duplicate the arrangement:
\[ 5 \times 2 = 10 \]
Halving by Sharing
Halving can be understood as sharing a set of objects equally into two groups.
Divide 10 apples equally into two baskets:
\[ 10 \div 2 = 5 \]
Each basket receives 5 apples.
Number Line Techniques
Using a number line to perform doubling and halving operations helps visualize the process of multiplication and division by two.
Double 8 on a number line:
\[ 8 + 8 = 16 \]
Half of 16 on a number line:
\[ 16 \div 2 = 8 \]
Games and Interactive Activities
Engaging in games and interactive activities reinforces the concepts of doubling and halving in a fun and memorable way.
Play a doubles game where students take turns doubling numbers and halving them, enhancing their understanding through play.
For instance, if a student says "Double of 4 is 8," the next student says "Half of 8 is 4," and so on.
Practice Questions
Enhance your understanding of doubling and halving by practicing the following 50 questions. Each question is accompanied by a detailed solution to aid your learning.
Grade 1
Question 1: Double of 3 is?
Solution:
\[ 3 \times 2 = 6 \]
The double of 3 is 6.
Question 2: Half of 8 is?
Solution:
\[ 8 \div 2 = 4 \]
Half of 8 is 4.
Question 3: What is double of 5?
Solution:
\[ 5 \times 2 = 10 \]
The double of 5 is 10.
Question 4: What is half of 6?
Solution:
\[ 6 \div 2 = 3 \]
Half of 6 is 3.
Question 5: Double of 2 is?
Solution:
\[ 2 \times 2 = 4 \]
The double of 2 is 4.
Grade 2
Question 6: What is double of 7?
Solution:
\[ 7 \times 2 = 14 \]
The double of 7 is 14.
Question 7: Half of 10 is?
Solution:
\[ 10 \div 2 = 5 \]
Half of 10 is 5.
Question 8: Double of 4 is?
Solution:
\[ 4 \times 2 = 8 \]
The double of 4 is 8.
Question 9: Half of 12 is?
Solution:
\[ 12 \div 2 = 6 \]
Half of 12 is 6.
Question 10: What is double of 6?
Solution:
\[ 6 \times 2 = 12 \]
The double of 6 is 12.
Grade 3
Question 11: Double of 9 is?
Solution:
\[ 9 \times 2 = 18 \]
The double of 9 is 18.
Question 12: Half of 16 is?
Solution:
\[ 16 \div 2 = 8 \]
Half of 16 is 8.
Question 13: What is double of 11?
Solution:
\[ 11 \times 2 = 22 \]
The double of 11 is 22.
Question 14: Half of 20 is?
Solution:
\[ 20 \div 2 = 10 \]
Half of 20 is 10.
Question 15: Double of 5 is?
Solution:
\[ 5 \times 2 = 10 \]
The double of 5 is 10.
Grade 4
Question 16: What is double of 14?
Solution:
\[ 14 \times 2 = 28 \]
The double of 14 is 28.
Question 17: Half of 24 is?
Solution:
\[ 24 \div 2 = 12 \]
Half of 24 is 12.
Question 18: What is double of 18?
Solution:
\[ 18 \times 2 = 36 \]
The double of 18 is 36.
Question 19: Half of 30 is?
Solution:
\[ 30 \div 2 = 15 \]
Half of 30 is 15.
Question 20: Double of 7 is?
Solution:
\[ 7 \times 2 = 14 \]
The double of 7 is 14.
Grade 5
Question 21: What is double of 21?
Solution:
\[ 21 \times 2 = 42 \]
The double of 21 is 42.
Question 22: Half of 50 is?
Solution:
\[ 50 \div 2 = 25 \]
Half of 50 is 25.
Question 23: What is double of 13?
Solution:
\[ 13 \times 2 = 26 \]
The double of 13 is 26.
Question 24: Half of 44 is?
Solution:
\[ 44 \div 2 = 22 \]
Half of 44 is 22.
Question 25: Double of 10 is?
Solution:
\[ 10 \times 2 = 20 \]
The double of 10 is 20.
Grade 6
Question 26: What is double of 25?
Solution:
\[ 25 \times 2 = 50 \]
The double of 25 is 50.
Question 27: Half of 64 is?
Solution:
\[ 64 \div 2 = 32 \]
Half of 64 is 32.
Question 28: What is double of 19?
Solution:
\[ 19 \times 2 = 38 \]
The double of 19 is 38.
Question 29: Half of 90 is?
Solution:
\[ 90 \div 2 = 45 \]
Half of 90 is 45.
Question 30: Double of 16 is?
Solution:
\[ 16 \times 2 = 32 \]
The double of 16 is 32.
Grade 7
Question 31: What is double of 33?
Solution:
\[ 33 \times 2 = 66 \]
The double of 33 is 66.
Question 32: Half of 100 is?
Solution:
\[ 100 \div 2 = 50 \]
Half of 100 is 50.
Question 33: What is double of 21?
Solution:
\[ 21 \times 2 = 42 \]
The double of 21 is 42.
Question 34: Half of 56 is?
Solution:
\[ 56 \div 2 = 28 \]
Half of 56 is 28.
Question 35: Double of 17 is?
Solution:
\[ 17 \times 2 = 34 \]
The double of 17 is 34.
Grade 8
Question 36: What is double of 40?
Solution:
\[ 40 \times 2 = 80 \]
The double of 40 is 80.
Question 37: Half of 150 is?
Solution:
\[ 150 \div 2 = 75 \]
Half of 150 is 75.
Question 38: What is double of 29?
Solution:
\[ 29 \times 2 = 58 \]
The double of 29 is 58.
Question 39: Half of 84 is?
Solution:
\[ 84 \div 2 = 42 \]
Half of 84 is 42.
Question 40: Double of 25 is?
Solution:
\[ 25 \times 2 = 50 \]
The double of 25 is 50.
Mixed Grades
Question 41: What is double of 12?
Solution:
\[ 12 \times 2 = 24 \]
The double of 12 is 24.
Question 42: Half of 68 is?
Solution:
\[ 68 \div 2 = 34 \]
Half of 68 is 34.
Question 43: What number is missing: $20 + \_ = 40$?
Solution:
\[ \_ = 40 - 20 = 20 \]
The missing number is 20.
Question 44: What is double of 19?
Solution:
\[ 19 \times 2 = 38 \]
The double of 19 is 38.
Question 45: Half of 46 is?
Solution:
\[ 46 \div 2 = 23 \]
Half of 46 is 23.
Question 46: What is double of 23?
Solution:
\[ 23 \times 2 = 46 \]
The double of 23 is 46.
Question 47: Half of 100 is?
Solution:
\[ 100 \div 2 = 50 \]
Half of 100 is 50.
Question 48: What is double of 17?
Solution:
\[ 17 \times 2 = 34 \]
The double of 17 is 34.
Question 49: Half of 88 is?
Solution:
\[ 88 \div 2 = 44 \]
Half of 88 is 44.
Question 50: What is double of 29?
Solution:
\[ 29 \times 2 = 58 \]
The double of 29 is 58.
Word Problems Involving Doubling & Halving
Problem 1: Scaling Ingredients
A recipe requires 4 cups of sugar. If you want to make double the amount of the recipe, how many cups of sugar do you need?
To double the recipe, multiply the amount of sugar by 2:
\[ 4 \times 2 = 8 \text{ cups} \]
You need 8 cups of sugar.
Problem 2: Sharing Equally
There are 24 candies to be shared equally among 4 friends. How many candies does each friend receive?
To find out how many candies each friend gets, divide the total number by the number of friends:
\[ 24 \div 4 = 6 \]
Each friend receives 6 candies.
Problem 3: Doubling the Quantity
Mark has 15 marbles. He finds another set of marbles equal to what he already has. How many marbles does Mark have now?
Doubling the number of marbles:
\[ 15 \times 2 = 30 \]
Mark now has 30 marbles.
Problem 4: Halving the Distance
The distance from home to school is 10 kilometers. If you decide to walk half the distance, how many kilometers will you walk?
Halving the distance:
\[ 10 \div 2 = 5 \text{ kilometers} \]
You will walk 5 kilometers.
Problem 5: Doubling the Speed
If a car is traveling at 60 km/h, what will be its speed after doubling?
Doubling the speed:
\[ 60 \times 2 = 120 \text{ km/h} \]
The car's speed will be 120 km/h.
Problem 6: Halving the Quantity
Jane has 48 pages to read for her assignment. She decides to read half of them today. How many pages does she read today?
Halving the number of pages:
\[ 48 \div 2 = 24 \text{ pages} \]
Jane reads 24 pages today.
Problem 7: Doubling the Investment
Alex invests \$200 in a savings account. After one year, his investment doubles. How much money does Alex have after one year?
Doubling the investment:
\[ 200 \times 2 = 400 \text{ dollars} \]
Alex has \$400 after one year.
Problem 8: Halving the Recipe
A cake recipe calls for 8 eggs. If you want to make half of the recipe, how many eggs do you need?
Halving the recipe:
\[ 8 \div 2 = 4 \text{ eggs} \]
You need 4 eggs.
Problem 9: Doubling the Hours
Sara spends 5 hours studying for her exam. If she doubles her study time, how many hours will she study?
Doubling the study time:
\[ 5 \times 2 = 10 \text{ hours} \]
Sara will study for 10 hours.
Problem 10: Halving the Quantity of Food
There are 36 cookies to be packed equally into 6 boxes. How many cookies will each box contain?
Halving the quantity (since 36 divided by 6 is halving into 6 equal groups):
\[ 36 \div 6 = 6 \text{ cookies per box} \]
Each box will contain 6 cookies.
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