Ray's New Higher Arithmetic · Art. 78, Long Division · Unit 6: Division
17. Long division
Goal: Your student does long division with large divisors, places the quotient figures correctly, and proves the work by multiplying.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The worked example $4225 ÷ 13, the rule for long division with notes on choosing quotient figures, the proof, and 24 examples with printed answers, including practical problems.
The lesson, step by step
Warm-up
Mental: 4200 ÷ 7; 390 ÷ 13; 65 ÷ 13.
Work the book's example
Divide $4225 equally among 13 men. 13 doesn't go into 4, so take 42 hundreds: 3 hundreds, remainder 3. Bring down 2: 32 tens, 2 tens, remainder 6. Bring down 5: 65 units, 5. Each man gets $325.
The rule and notes
Read the step that most often goes wrong:
Find how often the divisor is contained in the left-hand figure, or figures, of the dividend
Then the note on checking each step:
The remainder after each subtraction must be less than the divisor;
If it isn't, the quotient figure was too small.
Proof
Read:
Multiply the Divisor by the Quotient, and to this product add the Remainder, if any;
the sum is equal to the Dividend when the work is correct.
Guided practice
Together:
2. 5484888 ÷ 67
17. If 25 acres produce 1825 bushels of wheat, how much is that per acre?
(81864; 73 bushels.)
Independent practice
Your student works Examples 1 to 24 over one or two sittings. Numbers 10 to 16 square two numbers A and B and divide; numbers 17 to 24 are word problems, such as:
How many sacks, each containing 55 pounds, can be filled with 2035 pounds of flour?
Check
The book prints all answers. Prove at least three by multiplying back.
Wrap-up
Ask: Where do you put a cipher in the quotient? (When the next partial dividend is too small to hold the divisor.)
Afterwards
Split the 24 examples over two days.