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The student names the four parts of a division and uses the relation between them to check an answer or find a missing number.
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The four names, taken from the figure on page 40.
When we divide numbers, each part has a specific job. Let's look at a real example: .
This division gives us with left over. Here are the four parts as we label them:
A check that catches almost every wrong answer in this chapter.
There is a hidden rule in every division problem: the remainder is always smaller than the divisor.
Why? Because if your remainder was as big as your divisor, you could have taken out one more full group!
Looking at our examples:
Five blanks from the recall questions on page 40.
Dividing a number by 1 leaves the number unchanged, so 17 divided by 1 equals . Similarly, if 9 divided by an unknown number equals 9, that number must be . When you divide a non-zero number by itself, the result is always 1, which means 32 divided by equals 1. Zero divided by any non-zero number is always . Because of this rule, 0 divided by 8 is 0, and if an unknown number divided by 6 equals 0, that starting number must be .
Divisor times quotient plus remainder gives the dividend back.
Let us solve . The quotient is and the remainder is .
What happens if we work backwards?
First, find the divisor times the quotient: .
Next, add the remainder to it: . We get , which is the exact dividend we started with!
The rule, the four names, and how to run it backwards.
To find a missing remainder, take the divisor times quotient away from the dividend.
If Divisor = 8, Quotient = 7, and Dividend = 56:
Worksheet 1 question 1(d), worked and then verified.
Problem. Divide by and check your answer.
Given:
Three items from Worksheet 1 question 1, each with its check.
When we divide 98 by 8, we get a quotient of and a remainder of 2. We check this by multiplying 8 by 12 to get 96, and then adding to get back to 98. For 87 divided by 9, the quotient is 9 and the remainder is . The check is 9 times 9 equals 81, plus 6 equals . Finally, when we divide 132 by 6, the quotient is with a remainder of 0. We check this perfectly because 6 times 22 equals exactly .