Question 3 - Page 144 - Fast Multiplications Using the Distributive Property - Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)

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Question 3(i) - Page 144 Use this to find (i) 89 × 101We do these steps Step 1: The Right End. Copy the last two digits down. The last two digits are 89. Write 89. (Current Answer: _ _ 89) Step 2: Add Neighbors two places to right (moving left). We get to 9, there is no neighbor with a gap of 2. Write down 9. (Current Answer: _ 989) Step 3: Left end. We get to fist digit 8. There’s no carry. Write down 8. (Current Answer: 8989) So, the answer is 8989 Question 3(ii) - Page 144 Use this to find (ii) 949 × 101We do these steps Step 1: The Right End. Copy the last two digits down. The last two digits are 49. Write 49. (Current Answer: _ _ _ 49) Step 2: Add Neighbors two places to right (moving left). Add the last digit (9) to neighbor with a gap of 1 (9). 9 + 9 = 18. Write down 8 and carry over the 1. (Current Answer: _ _ 849) Step 3: Add Neighbors two places to right (moving left). We get to 4, there is no neighbor with a gap of 1. Add carry (1) = 4 + 1 = 5. Write down 5. (Current Answer: _ 5849) Step 3: Left end. We get to fist digit 9. There’s no carry. Write down 9. (Current Answer: 95849) So, the answer is 95849 Question 3(iii) - Page 144 Use this to find (iii) 265831 × 1001 We do these steps Step 1: The Right End. Copy the last three digits down. The last three digits are 831. Write 831. (Current Answer: _ _ _ _ _ _ 831) Step 2: Add Neighbors three places to right (moving left). Add the last digit (1) to neighbor with a gap of 2 (5). 1 + 5 = 6. Write down 6. (Current Answer: _ _ _ _ _ 6831) Step 3: Keep Moving Left. Add next digit (3) to neighbor with a gap of 2 (6). 3 + 6 = 9. Write down 9. (Current Answer: _ _ _ _ 96831) Step 4: Keep Moving Left. Add next digit (8) to neighbor with a gap of 2 (2). 8 + 2 = 10. Write down 0. Carry over 1 (Current Answer: _ _ _ 096831) Step 5: Keep Moving Left. Then, we get to 5, there is no neighbor with a gap of 2. Add carry = 5 + 1 = 6. Write down 6 (Current Answer: _ _ 6096831) Step 6: Keep Moving Left. Then, we get to 6, there is no neighbor with a gap of 2. Write down 6 (Current Answer: _ 66096831) Step 7: First digit. Then, we get to 2, there is no neighbor with a gap of 2. Write down 2 (Current Answer: 266096831) So, the answer is 266096831 Question 3(iv) - Page 144 Use this to find (iv) 1111 × 1001We do these steps Step 1: The Right End. Copy the last three digits down. The last three digits are 111. Write 111. (Current Answer: _ _ _ _ 111) Step 2: Add Neighbors three places to right (moving left). Add the last digit (1) to neighbor with a gap of 2 (1). 1 + 1 = 2. Write down 2. (Current Answer: _ _ _ 2111) Step 3: Keep Moving Left. Then, we get to 1, there is no neighbor with a gap of 2. Write down 1. (Current Answer: _ _ 12111) Step 4: Keep Moving Left. Next is 1, there is no neighbor with a gap of 2. Write down 1. (Current Answer: _ 112111) Step 5: First digit. First digit is 1, there is no neighbor with a gap of 2. Write down 1. (Current Answer: 1 112111) So, the answer is 1112111 Question 3(v) - Page 144 Use this to find (v) 9734 × 99To do this, we make 99 = 100 – 1 Now, 9734 × 99 = 9734 × (100 – 1) = 973400 – 9734 Putting 9734000 and 9734 below each other to subtract Question 3(vi) - Page 144 Use this to find (vi) 23478 × 999To do this, we make 999 = 1000 – 1 Now, 23478 × 999 = 23478 × (100 – 1) = 23478000 – 23478 Putting 23478000 and 23478 below each other to subtract