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E:\Working\Focus_Learning\Math_Genius_4_(25-10-2023)\Open_Files\Chap-03
\\December 6, 2023 1:25 PM Bharat Arora P-6 Reader _________________________ Date: ___________________74

2. Match the following multiplication sum with their properties.
Column A Column B

(a) 3 × (4 × 6) = (3 × 4) × 6 (i) Distributive property of multiplication

(b) 3 × 6 = 18 = 6 × 3 (ii) Multiplicative property of 1

(c) 4 × (50 + 3) = 4 × 50 + 4 × 3 (iii) Order property of multiplication
(d) 16 × 0 = 0 (iv) Grouping property of multiplication

(e) 24 × 1 = 24 or 1 × 24 = 24 (v) Multiplicative property of 0
teacher’s Discuss with students that, like the distributive property of multiplication over addition, we can also use the
tip distributive property of subtraction, like: (200 – 3) × 43 = 200 × 43 − 3 × 43 = 8600 – 129 = 8471 which is

same as the product of 197 (= 200 – 3) and 43.
estiMating tHe proDuct

We have already learned about rounding off numbers and finding the estimated sum and
difference of numbers. The same concept can be used to find the estimated product.
To estimate a product, we round off the multiplier and the multiplicand to the

nearest ten, hundred or thousand, whichever is required. Then, multiply the rounded
numbers to get the estimated product.

example 1: Estimate the product 38 × 44.
Solution: th H t O th H t O

3 8 4 0 Rounded up to the nearest ten

× 4 4 × 4 0 Rounded down to the nearest ten
1 6 0 0 Estimated product
Actual product = 38 × 44 = 1672

example 2: Estimate the product 516 × 393 to the nearest (a) tens (b) hundreds.
Solution: (a) th H t O L tth th H t O

5 1 6 5 2 0 Rounded up to the nearest ten
× 3 9 3 × 3 9 0 Rounded down to the nearest ten
2 0 2 8 0 0 Estimated product
(b)
th H t O L tth th H t O

5 1 6 5 0 0 Rounded down to the nearest hundred
× 3 9 3 × 4 0 0 Rounded up to the nearest hundred
2 0 0 0 0 0 Estimated product
Actual product = 516 × 393 = 202788

From the above results, we see that rounding off to the nearest ten produces a
closer approximation of the exact product than rounding off to the nearest hundred.
However, 520 × 390 involves more calculations than 500 × 400.

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