Lesson 16<br />WHAT IS DIVISION?<br />Objectives<br />After this lesson, the students are expected to:<br />define division;<br />identify the parts of division;<br />discuss the division operation.<br />In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication. Division can be described as repeated subtraction whereas multiplication is repeated addition. Division is defined as this reverse of multiplication. In high school, the process is also the same.<br />Example<br /> since<br />64÷8=8since8 X 8=64<br /> <br /> .<br />1213945216228<br />In the above expression, a is called the dividend, b the divisor and c the quotient.<br />Example: Suppose that we have twelve students in the class and we want to divide the class into three equal groups. How many should be in each group?Solution: We can ask the alternative question, "
Three times what number equals twelve?"
The answer to this question is four.<br /> quotient divisor dividend or dividend ÷ divisor = quotientWe write 4 3 12 or 12 ÷ 3 = 4we call the number 12 the dividend, the number 3 the divisor, and the number 4 the quotient. <br />
Division by Oneself414961624678
<br />Example Suppose that you had $100 and had to distribute all the money to 100 people so that each person received the same amount of money. How much would each person get? Solution If you gave each person $1 you would achieve your goal. This comes directly from the identity property of one. Since the the questions asks what number times 100 equals 100. In general we conclude, <br /> Any number divided by itself equals 1<br />4240530795655Examples100 ÷ 100 = 1 38 ÷ 38 = 1 15 ÷ 15 = 1<br />B. Division by 1 <br />Example Now let’s suppose that you have twelve pieces of paper and need to give them to exactly one person. How many pieces of paper does that person receive?<br />Solution Since the only person to collect the paper is the receiver, that person gets all twelve pieces. This also comes directly from the identity property of one, since one times twelve equals one. <br />In general we conclude, <br />Any number divided by 1 equals itself<br />Examples12 ÷ 1 = 12 42 ÷ 1 = 42 33 ÷ 1 = 33<br />4764471123759When Zero is the Dividend <br /> Example<br />Now lets suppose that you have zero pieces of pizza and need to distribute your pizza to four friends so that each person receives the same number of pieces. How many pieces of pizza does that person receive?<br />Solution Since you have no pizza to give, you give zero slices of pizza to each person. This comes directly from the multiplicative property of zero, since zero times four equals zero.<br />In general we conclude, <br />Zero divided by any nonzero number equals zero<br />4354195984885Examples0 ÷ 4 = 0 0 ÷ 1 = 0 0 ÷ 24 = 0<br />The Problem with Dividing by Zero <br />
Example Finally lets suppose that you have five bags of garbage and you have to get rid of all the garbage, but have no places to put the garbage. How can you distribute your garbage to no places and still get rid of it all?
SolutionYou can't! This is an impossible problem. There is no way to divide by zero.<br />In general we conclude, <br />Dividing by zero is impossible<br />Examples5 ÷ 0 = undefined 0 ÷ 0 = undefined 1 ÷ 0 = undefined<br />-420414-440121WORKSHEET NO. 16<br />NAME: ___________________________________DATE: _____________ <br />YEAR & SECTION: ________________________RATING: ___________<br />Give the name of the following unknown parts of division. <br /> <br />___________ 56÷8=7_________<br />_______________<br />-406717582550As far as you remember, try to divide the following. <br />56÷7=<br />54÷6=<br />4133850264795900÷100=<br />64÷16=<br />56÷8=<br />122÷11=<br />3623310255905144÷12=<br />256÷16=<br />180÷9=<br />360÷4=<br />