Find 2615 divided 4 using short division. Explain how to use the algorithm. Find

Question

Find 2615 divided 4 using short division. Explain how to use the algorithm. Find 2268 divided 7 using repeated subtraction. Then find it using standard long division and explain how the idea of repeated subtraction leads to standard long division. Cathy found her own algorithm for subtraction. Explain how and why method works. 97 -1 +70 =69 Alexander is a particularly bright 2nd grade student who rarely makes mistakes. However, you overheard him telling Olivia that either A is a subset of B or B is a subset of A. What incorrect assumption is Alexander making? How would you address it?

Explanation / Answer

Solution:

2615/4

Algorithm used:

Short division is a shorter method of dividing two numbers. The technique can be used only when dividing by a single-digit number and requires us to multiply, divide and subtract mentally without writing the long equations out. In lieu of writing each individual multiplication product underneath the dividend, subtracting and bringing down the next numeral, the remainders are inserted between the digits in the dividend.

Step 1

Write the large number to be divided (the dividend) on a piece of paper. Draw a division sign (a short vertical line to the left of the number and a longer horizontal line over the number). Write the single-digit number (divisor) to the left of the division sign.

Step 2

Divide the divisor into the first digit of the dividend. Given in the question, if the dividend is 2615 and the divisor is 4, you would first divide 2 by 4, only to find that it is impossible. Use that 6 at the tens place with 2 and divide 4 by five, which yields 6.

Step 3

Write the number of times the divisor goes into the first number over the horizontal line and the ones place of that numerical section of the dividend. Using the question asked, the number 6 is written over the 2 in the dividend. Subtract the product of the number written over the dividend and the divisor, equaling 24, from the numerals that were used to divide (26).

Step 4

Write the remainder from the first simple division to the left of the next number to act as the tens place with the following number. Using the question, the remaining 2 from dividing 4 into 26 is placed between the 2 in the 26 and the 1, making the next number to be divided into 21. Divide 21 by 4, resulting in a 5 being written over the 1 in the dividend. Subtract the product of 4 times 5 from the 21 to get the remainder of 1.

Step 5

Write the remainder, 1, between the 1 and 5 in the dividend to create the last mental division problem of dividing15 by 4. The answer is 3, which is written over the final number in the divided. The answer, thus, is 653.

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