Exact versus inexact division. Since those are the multiples of 3, we say that 3 is their divisor. In other words, we say that one number is a divisor of a second if the second is its multiple. Example 9. A bottle holds 35 ounces. A glass holds 8 ounces. How many glasses can you fill from that bottle? Now, 8 goes into 32 exactly, but 8 does not go into 35 exactly:. Therefore you could fill 4 glasses, and 3 ounces will remain in the bottle. Say there are a large number of people, and we want to divide them into groups of 5.
But say we discover that there is not an exact number of 5's. Then how many people might we not be able to group? How many people might remain? Answer: Either 1, or 2, or 3, or 4. Because if more than 4 remained, we could make another group of 5. Example Say the whole number quotient and the remainder. Do not write the division box. How would you know that you have to add 5? The horizontal line separating 16 and 8 is called the division bar.
The division bar is also used to signify a fraction, because a fraction sometimes requires division of the numerator by the denominator. Lessons 20 and We also use the division bar to indicate the ratio of two numbers.
Lesson Ignore the 0. Therefore 7 goes into forty 40 times. Lesson 9, Question 2. In other words, since 28 is divisible by 7, then so is '28' followed by any number of 0's. Please "turn" the page and do some Problems. Mental calculation: Decomposing the dividend. Introduction Home Table of Contents. E-mail: teacher themathpage. In this Lesson, we will address the following: What is the problem of "division"?
If we divide a number into equal parts, how can we know how many there are in each part? The result is called the quotient. It is a division word. The quotient is the result you get when you divide a number dividend by another number divisor. Divide the larger number by the smaller. If the result has no remainder no decimal then the smaller number is a factor of the larger. It is called division. A fraction is a shorthand display of the operation, and the end result of it is a quotient.
Binary result. When you add the values 3, 5, 8, 12 and 20 and then divide by the number of values, the result is 9. Yes, if you divide a positive number by a negative number the result will be a negative number. You divide the dividend by the divisor. The result is the quotient. Same as for other numbers. You sum them together and divide the result by the number of fractions.
A quotient is the result of dividing two numbers. If we divide one number into another number, the result is the quotient. It might be argued that the quotient is the ratio of two numbers, but what has been stated applies. The two numbers that are being added are each called addends, and the result is called a sum. Log in. Math and Arithmetic.
Study now. See Answer. Best Answer. But no matter the grade, remind students that there are many ways to think about division, just like there are many ways to think about multiplication, and this algorithm is one tool to help solve math problems. Materials: Base-ten blocks that all students can see for example, with an overhead projector ; base-ten blocks that students can use.
Preparation: Be sure to provide at least one set of base-ten blocks for each pair of students. Prerequisite Skills and Concepts: Students should know their basic division facts and have used or seen the use of base ten blocks. Introduce students to the vocabulary dividend, divisor, and quotient prior to the lesson. After using manipulatives to introduce the division algorithm for multi-digit numbers, it's time to develop the concept more fully.
Do not rush the development of this concept. Many students struggle with division of multi-digit numbers, and it is important to allow students plenty of time to master it.
Students need a great deal of practice when learning to divide multi-digit numbers. Do not be in a rush for students to put away their manipulatives when learning this difficult concept. This can be a trying time in many students' mathematical development! As a teacher, do not be discouraged by slow progress. Remember, this may be the first time many of your students have ever encountered the concept.
Your task is to take the needed time and effort to encourage students to learn this process. As much as possible, try to relate different division problems to your students. If they're interested in basketball, for example, have them divide groups of players or basketballs.
Additionally, connect division to other topics, such as multiplication, fractions, and equations, when they appear to reinforce the concept many times. Continual assessment when teaching division is necessary and can take the form of warm-up problems, digital practice for example with our own digital math practice solution, Waggle , or exit tickets, in addition to more formal assessment such as quizzes and tests. Return to the concept throughout the year to ensure retention and build mastery.
Need more ideas to teach what is a divisor in math? Looking for more free lessons and activities for elementary and middle school? Be sure to explore our Free Teaching Resources hub! Give a lesson on the significance of National Pearl Harbor Remembrance Day with these Pearl Harbor activities for elementary and middle school students.
Teach your students about the different ways to describe data, including the concepts of mean average , median, and mode. Sign In. Cart 0. My Account. Tweet Tweet Share. Comparing Division and Multiplication In order to teach division, it usually helps to start with multiplication. Dividend vs.
The Standard Algorithm for Division As students master their basic division facts, the need will arise for students to learn how to divide larger dividends. Lesson 1: Introducing the Concept of Division As with addition, subtraction, and multiplication, students practice strategies and algorithms that allow them to perform operations beyond basic facts. Materials: Base-ten blocks that all students can see for example, with an overhead projector ; base-ten blocks that students can use Preparation: Be sure to provide at least one set of base-ten blocks for each pair of students.
The 54 represents the total number of items you begin with. The Fundamental Fact of Fractions. If you multiply or divide the top and bottom of a fraction by the same thing, you get a different name for the same number. Reducing or Simplifying Fractions. Factor the top and bottom until you get factors that cannot be factored further. If you find the same factor on both the top and bottom, you can cancel them.
If after factoring the top and bottom as much as possible, if there are no common factors in the top and bottom, the fraction is reduced to lowest terms. Adding Subtracting Fractions. If you have common denominators, add subtract the numerators. If not, find common denominators. To find common denominators, factor all the denominators and fill in the missing factors. You can multiply the bottom by whatever you want so long as you multiply the top by the same thing.
Multiply the tops and multiply the bottoms. You can cancel either before or after you multiply. Invert the divisor and multiply.
You can make any change you want on one side of an equation so long as you make the same change on the other side. One of the most common techniques is to get rid of a term on one side by subtracting it from both sides.
When you get rid of a term on one side, it pops up on the other side with its sign changed. Moving a term from one side to the other and changing its sign is called transposing the term. If you move a factor from one side to the other, move it across the fraction bar. Steps in solving first degree equations. Clear Denominators: Multiply both sides by a common denominator.
Simplify: Remove parentheses and combine like terms. Transpose known terms to one side and unknown terms to the other. Divide both sides by the coefficient of the unknown. Steps in solving quadratic equations by factoring. Steps in solving quadratic equations by completing the square. Steps in solving quadratic equations using the quadratic formula. Clear denominators: Multiply both sides by a common denominator.
Transpose all terms to one side leaving a 0 on the other. Substitute the coefficients into the quadratic formula.
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