a59ade68...
bc1c9548...
e540b8b8...
98b74122...
5a8afbdd...
1e9ccd6c...
The student finds each quotient digit by estimating against a two-digit divisor and adjusting, rather than reciting a table that does not exist.
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The same four moves, but now you have to work out each quotient digit.
When moving to a two-digit divisor, the basic framework of division stays exactly the same. You still start from the extreme left of the dividend, follow the same four moves (divide, multiply, subtract, bring down), and make sure each quotient digit goes precisely above its own place value.
Round the divisor, estimate the digit, then multiply to test it.
To avoid blindly guessing numbers for a two-digit divisor, try this three-move strategy:
The book's own example, with each guess shown and tested.
Problem. Find the quotient and remainder when 9,856 is divided by 23.
Worksheet 3 question 1(a), with every estimate blanked.
To divide 7,982 by 11, we first round the divisor 11 down to . We look at 79 hundreds and estimate how many times this rounded number fits, giving a first quotient digit of 7. We test this by multiplying , which leaves 2 hundreds left over. Bring down the 8 to make 28 tens, and estimate again to try the digit 2. Multiplying leaves 6 tens. Bring down the 2 to make 62 ones, and try the digit . Since , we have 7 left over. We check our final answer using the relation: .
Three divisions from Worksheet 3 question 1.
Problems: (b) (d) (e)
Hint for (e): Watch out for trailing zeroes. The quotient is 30, not 3. Your check step is what proves it!
Enter the final values for all three problems.
Briefly describe how you guessed the digits and write out the relation check.
Three items from Worksheet 3 question 2, each with its check.
Problems: (a) (b) (d)
Note: Problem (b) has a zero in the ones place of the quotient. Problem (d) has a remainder of 41—remember to confirm that this remainder is smaller than your divisor!
Provide the quotient and remainder for each item.
Verify your math using: Divisor × Quotient + Remainder = Dividend
Explain why 41 is a valid remainder here.