Division division Dividend ÷ Divisor = Quotient Quotient × Divisor = Dividend Example. Using the division box, write 1 ÷ 5. (There is nothing to calculate.) Answer. 5 is the divisor. It goes outside the box. division Before going on to short division, the student should be clear about division with remainder, and how to name the remainder. See Example 11 of that Lesson.
2. How do we do short division? division
From the left of the dividend (252), take as many digits as necessary to form a number (25) that will contain the divisor (7) at least once but less than ten times. Divide that partial dividend by the divisor, and obtain the first digit of the quotient (3). Write it over the last digit (5) of the partial dividend -- and write the remainder beside the next digit of the dividend. Continue the operation, until there are no more digits in the dividend.
Speakdivision division "7 goes into 25 three (3) times (21) with 4 left over." Write the remainder 4 beside the 2. Continue: "7 goes into 42 six (6) times exactly." Compare the simplicity of that with long division: division In long division, we bring down the 2 and write it next to the remainder 4. In short division, we simply write the remainder next to 2. Long division, moreover, de-emphasizes the spoken nature of arithmetic. It gives the false impression that, like algebra, arithmetic is a written skill. Long division now properly belongs to the history of mathematics. For no other reason than tradition, long division is still taught. Since both long and short division are nothing but methods, neither one requires a true understanding of division. That comes only with decomposing the dividend -- which in any case is the principle on which all methods are based.
division Begin, "5 goes into 17 three (3) times (15) with 2 left over." division Write 3 over the 7 (not over the 1), and write the remainder 2 next to the 9. Continue: "5 goes into 29 five (5) times (25) with 4 left over. division Write 5 over the 9, and write the remainder 4 next to the 8. Finally, "5 goes into 48 nine (9) times (45) with 3 left over." division Write 9 over the 8. The final remainder is 3. division This problem will illustrate the following point: Upon placing the first digit in the quotient, then, over every digit in the dividend we must write a digit in the quotient. We proceed one digit at a time. division We will write a digit over the 1, then over the 6, then over the 0, and so on, until finally we write a digit over the 3. Begin, "4 goes into 21 five (5) times (20) with remainder 1 ." division Next, "4 goes into 16 four (4) times exactly." division Next, "4 goes into 0 zero (0)." division Whenever the partial dividend is less than the divisor -- 0 is less than 4 -- write 0 in the quotient. Next, we must write a digit over the 2: "4 goes into 2 zero (0)." division Now the 2 remains. It is the remainder. Whenever the quotient is 0, that digit beneath it in the dividend is the remainder. "4 goes into 24 six (6) times exactly." division Finally, "4 goes into 3 zero (0)." division 3 is the final remainder. Again, whenever the quotient is 0, the digit beneath it in the dividend is the remainder. division "3 goes into 15 five (5) times. 3 goes into 2 zero (0)." 2 is the remainder. That is, 152 = 50 × 3 + 2.
We use short division whenever it is easy to multiply the divisor. Example 4. Harold has a debt of $3,164. He is able to pay $25 a week. How many weeks will it take him to pay the debt? Solution. How many 25's will equal 3,164. To find out, we must divide: division "25 goes into 31 one (1) time (25) with 6 left over." division "25 goes into 66 two (2) times (50) with 16 left over." division "25 goes into 164 six (6) times (150) with 14 left over." division At the end of 126 weeks, then, the debt will be almost paid. $14 will remain. Therefore, it will take Harold 127 weeks. Problem. The multiples of 8 that are less than 100, are what percent of all the numbers less than 100? To see the answer, pass your mouse over the colored area. To cover the answer again, click "Refresh" ("Reload"). Do the problem yourself first!
The multiples of 8 are the numbers 8, 16, 24, 32, and so on. How many multiples of 8 are contained in 100 -- that is, what number is 100 ÷ 8? 100 ÷ 8 = 12 R 4. That means, there are 12 eights less than 100. (12 × 8 = 96.) So the question is: 12 is what percent of 100? The student should know immediately that the answer is 12% -- because that should be the first lesson in percent! Lesson 4. * We will now consider the case in which the dividend is a decimal. The divisor, we have seen (Lesson 11), must always be a whole number. (In Lesson 13 we will consider the case in which the divisor is a decimal.)
3. How do we proceed when the dividend is a decimal?
Well 3 divided by 100 is 3 hundredths. 3/100=.03 that would be an example. another is 30000 divided by 100. that would be 300. you just take away 2 zeros for that one.
