Question 33

We need to find the missing values in the table by performing division.

Step 1 — Find the base division Let us look at the first filled cell. Here, the value of b is 37. The value of a is 1517. The cell value is 41. This means that a ÷ b = 41. Let us check this division.

$1517 \div 37$

We perform the division.

$= 41$

$\boxed{41}$

This confirms our base division.

Step 2 — Understand decimal shifts in division We know that 1517 ÷ 37 = 41. Let us see how decimal points affect the result. If we divide a by 10, the result also divides by 10. For example, 151.7 ÷ 37 = (1517 ÷ 10) ÷ 37 = 41 ÷ 10 = 4.1. If we divide b by 10, the result multiplies by 10. For example, 1517 ÷ 3.7 = 1517 ÷ (37 ÷ 10) = 41 × 10 = 410. We will use this rule to fill the table.

Step 3 — Calculate missing cells in Row 1 (b = 37) For this row, b is 37. The base result is 41.

(i) For a = 151.7: We divide a by 10 compared to 1517. So, we divide the base result by 10.

$151.7 \div 37$

$= (1517 \div 10) \div 37$

$= (1517 \div 37) \div 10$

$= 41 \div 10$

$\boxed{4.1}$

(ii) For a = 15.17: We divide a by 100 compared to 1517. So, we divide the base result by 100.

$15.17 \div 37$

$= (1517 \div 100) \div 37$

$= (1517 \div 37) \div 100$

$= 41 \div 100$

$\boxed{0.41}$

(iii) For a = 1.517: We divide a by 1000 compared to 1517. So, we divide the base result by 1000.

$1.517 \div 37$

$= (1517 \div 1000) \div 37$

$= (1517 \div 37) \div 1000$

$= 41 \div 1000$

$\boxed{0.041}$

(iv) For a = 15170: We multiply a by 10 compared to 1517. So, we multiply the base result by 10.

$15170 \div 37$

$= (1517 \times 10) \div 37$

$= (1517 \div 37) \times 10$

$= 41 \times 10$

$\boxed{410}$

Step 4 — Calculate missing cells in Row 2 (b = 3.7) For this row, b is 3.7. This is 37 ÷ 10. Dividing by 3.7 is like multiplying the result by 10.

(v) For a = 1517: We divide 1517 by 3.7.

$1517 \div 3.7$

$= 1517 \div (37 \div 10)$

$= (1517 \div 37) \times 10$

$= 41 \times 10$

$\boxed{410}$

(vi) For a = 151.7: We divide 151.7 by 3.7. a is 1517 ÷ 10. b is 37 ÷ 10.

$151.7 \div 3.7$

$= (1517 \div 10) \div (37 \div 10)$

$= (1517 \div 37) \times (10 \div 10)$

$= 41 \times 1$

$\boxed{41}$

(vii) For a = 1.517: We divide 1.517 by 3.7. a is 1517 ÷ 1000. b is 37 ÷ 10.

$1.517 \div 3.7$

$= (1517 \div 1000) \div (37 \div 10)$

$= (1517 \div 37) \times (10 \div 1000)$

$= 41 \div 100$

$\boxed{0.41}$

(viii) For a = 15170: We divide 15170 by 3.7. a is 1517 × 10. b is 37 ÷ 10.

$15170 \div 3.7$

$= (1517 \times 10) \div (37 \div 10)$

$= (1517 \div 37) \times (10 \times 10)$

$= 41 \times 100$

$\boxed{4100}$

Step 5 — Calculate missing cells in Row 3 (b = 0.37) For this row, b is 0.37. This is 37 ÷ 100. Dividing by 0.37 is like multiplying the result by 100.

(ix) For a = 1517: We divide 1517 by 0.37.

$1517 \div 0.37$

$= 1517 \div (37 \div 100)$

$= (1517 \div 37) \times 100$

$= 41 \times 100$

$\boxed{4100}$

(x) For a = 151.7: We divide 151.7 by 0.37. a is 1517 ÷ 10. b is 37 ÷ 100.

$151.7 \div 0.37$

$= (1517 \div 10) \div (37 \div 100)$

$= (1517 \div 37) \times (100 \div 10)$

$= 41 \times 10$

$\boxed{410}$

(xi) For a = 15.17: We divide 15.17 by 0.37. a is 1517 ÷ 100. b is 37 ÷ 100.

$15.17 \div 0.37$

$= (1517 \div 100) \div (37 \div 100)$

$= (1517 \div 37) \times (100 \div 100)$

$= 41 \times 1$

$\boxed{41}$

(xii) For a = 1.517: We divide 1.517 by 0.37. a is 1517 ÷ 1000. b is 37 ÷ 100.

$1.517 \div 0.37$

$= (1517 \div 1000) \div (37 \div 100)$

$= (1517 \div 37) \times (100 \div 1000)$

$= 41 \div 10$

$\boxed{4.1}$

(xiii) For a = 15170: We divide 15170 by 0.37. a is 1517 × 10. b is 37 ÷ 100.

$15170 \div 0.37$

$= (1517 \times 10) \div (37 \div 100)$

$= (1517 \div 37) \times (10 \times 100)$

$= 41 \times 1000$

$\boxed{41000}$

Step 6 — Calculate missing cells in Row 4 (b = 0.037) For this row, b is 0.037. This is 37 ÷ 1000. Dividing by 0.037 is like multiplying the result by 1000.

(xiv) For a = 1517: We divide 1517 by 0.037.

$1517 \div 0.037$

$= 1517 \div (37 \div 1000)$

$= (1517 \div 37) \times 1000$

$= 41 \times 1000$

$\boxed{41000}$

(xv) For a = 15.17: We divide 15.17 by 0.037. a is 1517 ÷ 100. b is 37 ÷ 1000.

$15.17 \div 0.037$

$= (1517 \div 100) \div (37 \div 1000)$

$= (1517 \div 37) \times (1000 \div 100)$

$= 41 \times 10$

$\boxed{410}$

(xvi) For a = 1.517: We divide 1.517 by 0.037. a is 1517 ÷ 1000. b is 37 ÷ 1000.

$1.517 \div 0.037$

$= (1517 \div 1000) \div (37 \div 1000)$

$= (1517 \div 37) \times (1000 \div 1000)$

$= 41 \times 1$

$\boxed{41}$

(xvii) For a = 15170: We divide 15170 by 0.037. a is 1517 × 10. b is 37 ÷ 1000.

$15170 \div 0.037$

$= (1517 \times 10) \div (37 \div 1000)$

$= (1517 \div 37) \times (10 \times 1000)$

$= 41 \times 10000$

$\boxed{410000}$

Step 7 — Calculate missing cells in Row 5 (b = 370) For this row, b is 370. This is 37 × 10. Dividing by 370 is like dividing the result by 10.

(xviii) For a = 1517: We divide 1517 by 370.

$1517 \div 370$

$= 1517 \div (37 \times 10)$

$= (1517 \div 37) \div 10$

$= 41 \div 10$

$\boxed{4.1}$

(xix) For a = 151.7: We divide 151.7 by 370. a is 1517 ÷ 10. b is 37 × 10.

$151.7 \div 370$

$= (1517 \div 10) \div (37 \times 10)$

$= (1517 \div 37) \div (10 \times 10)$

$= 41 \div 100$

$\boxed{0.41}$

(xx) For a = 15.17: We divide 15.17 by 370. a is 1517 ÷ 100. b is 37 × 10.

$15.17 \div 370$

$= (1517 \div 100) \div (37 \times 10)$

$= (1517 \div 37) \div (100 \times 10)$

$= 41 \div 1000$

$\boxed{0.041}$

(xxi) For a = 1.517: We divide 1.517 by 370. a is 1517 ÷ 1000. b is 37 × 10.

$1.517 \div 370$

$= (1517 \div 1000) \div (37 \times 10)$

$= (1517 \div 37) \div (1000 \times 10)$

$= 41 \div 10000$

$\boxed{0.0041}$

(xxii) For a = 15170: We divide 15170 by 370. a is 1517 × 10. b is 37 × 10.

$15170 \div 370$

$= (1517 \times 10) \div (37 \times 10)$

$= (1517 \div 37) \times (10 \div 10)$

$= 41 \times 1$

$\boxed{41}$

Answer

(i) The cell for b=37, a=151.7 is 4.1. (ii) The cell for b=37, a=15.17 is 0.41. (iii) The cell for b=37, a=1.517 is 0.041. (iv) The cell for b=37, a=15170 is 410. (v) The cell for b=3.7, a=1517 is 410. (vi) The cell for b=3.7, a=151.7 is 41. (vii) The cell for b=3.7, a=1.517 is 0.41. (viii) The cell for b=3.7, a=15170 is 4100. (ix) The cell for b=0.37, a=1517 is 4100. (x) The cell for b=0.37, a=151.7 is 410. (xi) The cell for b=0.37, a=15.17 is 41. (xii) The cell for b=0.37, a=1.517 is 4.1. (xiii) The cell for b=0.37, a=15170 is 41000. (xiv) The cell for b=0.037, a=1517 is 41000. (xv) The cell for b=0.037, a=15.17 is 410. (xvi) The cell for b=0.037, a=1.517 is 41. (xvii) The cell for b=0.037, a=15170 is 410000. (xviii) The cell for b=370, a=1517 is 4.1. (xix) The cell for b=370, a=151.7 is 0.41. (xx) The cell for b=370, a=15.17 is 0.041. (xxi) The cell for b=370, a=1.517 is 0.0041. (xxii) The cell for b=370, a=15170 is 41.