Page 67 - Start Up Mathematics_4

= 2,700 + 180 + 45 Step 3: Add the products
obtained.

= 2,925

So, 325 × 9 = 2,925.
Example 3: Multiply 7,415 by 8 using the expanded form.

Solution: 7,415 × 8 = (7,000 + 400 + 10 + 5) × 8

= (7,000 × 8) + (400 × 8) + (10 × 8) + (5 × 8)

= 56,000 + 3,200 + 80 + 40
= 59,320

Verification by actual multiplication:
3 1 4
7 4 1 5
× 8

5 9 3 2 0

EXERCISE 5.4

1. Find the product.
(a) 1,263 × 5 (b) 2,014 × 6 (c) 3,416 × 4 (d) 5,203 × 7

(e) 2,465 × 9 (f) 4,897 × 8 (g) 8,231 × 3 (h) 9,806 × 2
2. Multiply using the expanded form and verify the result by actual multiplication.

(a) 3,120 × 4 (b) 6,153 × 8 (c) 7,924 × 5 (d) 1,876 × 7

(e) 4,031 × 9 (f) 9,212 × 6 (g) 2,956 × 3 (h) 4,593 × 2

Multiplication by a 2-Digit Number

Example 4: Multiply (a) 134 by 45 (b) 2,069 by 57

Solution: (a) 134 × 45 (b) 2,069 × 57

1 1 ← Carry over of (134 × 40) 3 4 ← Carry over of (2,069 × 50)
1 2 ← Carry over of (134 × 5) 4 6 ← Carry over of (2,069 × 7)
1 3 4 2 0 6 9
× 4 5 × 5 7

1 1
6 7 0 ← (134 × 5) 1 4 4 8 3 ← (2,069 × 7)
1 ← (2,069 × 50)
+ 5 3 6 0 ← (134 × 40) + 1 0 3 4 5 0

6 0 3 0 1 1 7 9 3 3

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