Find the products:
(i) `{:(" 458"),(ul(xx67)):}`
(ii) `{:(3709),(ul(xx89)):}`
(iii)`{:(" 4617"),(ul(xx234)):}`
(iv ) `{:(15208),(ul(xx542)):}`

Answer

To find the products of the given pairs of numbers, we will perform multiplication step by step for each part.

### Solution:

**(i) Find the product of 458 and 67:**

1. **Multiply 458 by 7 (the unit digit of 67):**
- \( 458 \times 7 = 3206 \)

2. **Multiply 458 by 6 (the tens digit of 67) and shift one position to the left:**
- \( 458 \times 6 = 2748 \) (shifted left becomes 27480)

3. **Add the two results:**
- \( 3206 + 27480 = 30626 \)

**Product of 458 and 67 is 30626.**

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**(ii) Find the product of 3709 and 89:**

1. **Multiply 3709 by 9 (the unit digit of 89):**
- \( 3709 \times 9 = 33381 \)

2. **Multiply 3709 by 8 (the tens digit of 89) and shift one position to the left:**
- \( 3709 \times 8 = 29672 \) (shifted left becomes 296720)

3. **Add the two results:**
- \( 33381 + 296720 = 330001 \)

**Product of 3709 and 89 is 330001.**

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**(iii) Find the product of 4617 and 234:**

1. **Multiply 4617 by 4 (the unit digit of 234):**
- \( 4617 \times 4 = 18468 \)

2. **Multiply 4617 by 3 (the tens digit of 234) and shift one position to the left:**
- \( 4617 \times 3 = 13851 \) (shifted left becomes 138510)

3. **Multiply 4617 by 2 (the hundreds digit of 234) and shift two positions to the left:**
- \( 4617 \times 2 = 9234 \) (shifted left becomes 923400)

4. **Add the three results:**
- \( 18468 + 138510 + 923400 = 1080378 \)

**Product of 4617 and 234 is 1080378.**

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**(iv) Find the product of 15208 and 542:**

1. **Multiply 15208 by 2 (the unit digit of 542):**
- \( 15208 \times 2 = 30416 \)

2. **Multiply 15208 by 4 (the tens digit of 542) and shift one position to the left:**
- \( 15208 \times 4 = 60832 \) (shifted left becomes 608320)

3. **Multiply 15208 by 5 (the hundreds digit of 542) and shift two positions to the left:**
- \( 15208 \times 5 = 76040 \) (shifted left becomes 7604000)

4. **Add the three results:**
- \( 30416 + 608320 + 7604000 = 8242736 \)

**Product of 15208 and 542 is 8242736.**

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### Summary of Products:
- (i) 458 x 67 = 30626
- (ii) 3709 x 89 = 330001
- (iii) 4617 x 234 = 1080378
- (iv) 15208 x 542 = 8242736