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E:\Working\Focus_Learning\Math_Genius_5_(05-10-2023)\Open_Files\CHAP_02
\\February 27, 2024 10:04 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

example 1: Multiply the following.
(a) 6172 by 435 (b) 4567 by 2315

Solution:
(a) Step 1: Expand the multiplier.
435 = 400 + 30 + 5 tL L tth th H t O

Step 2: Multiply by the ones. 6 1 7 2
6172 × 5 = 30860 × 4 3 5 400 + 30 + 5

Step 3: Multiply by the tens. 3 0 8 6 0 6172 × 5
6172 × 30 = 185160 + 2 1 8 5 1 6 0 6172 × 30
8
6
8
4
0
0
6172 × 400
Step 4: Multiply by the hundreds. 2 6 8 4 8 2 0
6172 × 400 = 2468800
Step 5: Add all the partial products.
30860 + 185160 + 2468800 = 2684820
Thus, 6172 × 435 = 2684820

(b) Step 1: Expand the multiplier.

2315 = 2000 + 300 + 10 + 5
Step 2: Multiply by the ones.
4567 × 5 = 22835 C tL L tth th H t O

Step 3: Multiply by the tens. 4 5 6 7 2000 + 300

4567 × 10 = 45670 × 2 2 3 1 5 + 10 + 5
2 8 3 5
4567 × 5
Step 4: Multiply by the hundreds. 4 5 6 7 0 4567 × 10
4567 × 300 = 1370100 1 3 7 0 1 0 0 4567 × 300

Step 5: Multiply by the thousands. + 9 1 3 4 0 0 0 4567 × 2000
4567 × 2000 = 9134000 1 0 5 7 2 6 0 5

Step 6: Add all the partial products.
22835 + 45670 + 1370100 + 9134000 = 10572605

Thus, 4567 × 2315 = 10572605

example 2: Factory produces 8754 LED bulbs in a day. How many LED bulbs will be
produced in a year by the factory?
Solution: Number of LED bulbs produced in a day = 8754 tL L tth th H t O

Number of LED bulbs will be produced in a year 8 7 5 4
= 8754 × 365 × 3 6 5

Thus, the factory will produce 3195210 LED bulbs in 5 4 3 7 7 0
2
5 2 4 0
a year. + 2 6 2 6 2 0 0
3 1 9 5 2 1 0

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