In this lesson, we will apply the halving and doubling technique to find the product of two numbers.
The halving and doubling technique involves adjusting two numbers being multiplied, that is:
\(*\) Halve one of the numbers and
\(*\) Double the other number.
This adjustment simplifies calculations without changing the final product because multiplication is commutative and associative.
Example 1
Use the halving and doubling method to find the product of 4 and 7
Solution
Product of 4 and 7
\(\Rightarrow\) 4 \(\times\) 7
Halving 4 and doubling 7
\(\Rightarrow\) \((\frac{1}{2} \times 4)\) \(\times\) \((2 \times7) \)
\(\Rightarrow\) \(2 \times 14\)
\(\Rightarrow\) \(28\)
Multiplication is based on the principle that the product of two numbers remains constant if one number is halved and the other is doubled.
Steps for Halving and Doubling
1. Identify the two numbers to be multiplied.
2. Choose one number to halve (preferably the even number).
3. Double the other number.
4. Multiply the adjusted numbers to get the product.
Example 2
Apply the halving and doubling technique to find the product of 28 and 5.
Solution
Example 3
Apply the halving and doubling technique to find the product of 125 and 4.
Solution
Example 4
Use the doubling and halving technique to find the product of 25 and 7.
Solution
Example 5
Use the doubling and halving technique to find the product of 9 and 21.
Solution
Use the doubling and halving technique to find the product of the following pairs of numbers.
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17 and 18
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29 and 12
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16 and 7
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15 and 11
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9 and 16
Test yourself on what you have learnt so far. Click on the link below when you are ready.
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