what is the relationship between multiplication and division

Students can visually see the actual size of each computation and learn how to interpret the partial products.. Write the multiplication fact for the following. Direct link to Austin Carrier's post how do you gets the enger, Posted 4 years ago. The number 5 represents the number of apples in each group. 2023 Smartick Intl. A double goal is achieved here: mastering the basic facts and grasping the relationship between multiplication and division. 252 lessons. This equation could also be written as 4 x 2 = Thus, division and multiplication are both describing the same relationship between two numbers: when you divide by two, you are, in effect, multiplying by two. The answer would be to divide the first number by the second number and then multiply the result by the third number. There isn't enough explanation in details. We hope you enjoy our Personal blog as much as we enjoy offering them to you. There are 6 groups and each group has 4 mangoes. Introduction (5 minutes) Draw a picture of 7 groups of 12 on the board and ask students to turn and share in pairs what they see and notice about the drawing. Here we will check the main differences between division and multiplication. So for example, if I were to tell you that 1/4 divided by, and I'm going to color-code What is Multiplication and Division in Maths? Unit Goals. A relation is its own sepparate value, but the wording of division does not distinguish between splitting and relating two values. The unknown factor problem is solved as above by using the reciprocal fraction of 32. The multiplication fact gives the total number of bananas. The answer to first part of the task. (Differentiated for two groups). To see the full exercise, follow. Read More The Relationship Between Quantity Supplied And Price IsContinue. It is also a creative method to learn the multiplication table, which explains you the exact . For example, if you have a multiplication equation of 6 x 5 = 30, the inverse operation or division can be used to solve the equation by dividing 30 by 5 to get 6 as the answer. try to think about it. So if 1/4 divided by six is equal to t, based on all of the 15 3 = 5 I don't understand this that much i just guess the answers can anybody explain because he makes no sense at all. The do's and don'ts of teaching problem solving in math, How to set up algebraic equations to match word problems, Seven reasons behind math anxiety and how to prevent it, Mental math "mathemagic" with Arthur Benjamin (video). The problem is solved by division 12 34 = , with the actual solution based on a model representing 12 as 24 and the division as 24 34 = 2 3 = 23. I don't understand which number I should use to divide. Both of them use equal sharing of objects between several groups while each interpretation addresses a different question. Maths KS1 / KS2: The relationship between multiplication and division BBC Teach > Primary resources > KS2 Maths > A World Without Maths Baz and Dave need to share out some kittens ready to go to. This is because when we multiply two numbers (which we call factors), we get a result that we call a product. Its an activity with a double goal. Multiplication and Division: What's the Connection? In conclusion, the relationship between division and multiplication is one of inverse operations. Listen for key terms such as "groups of," "multiplied," "divide," "repeated addition," etc. Unfortunately, This is very common in Khan Academy videos. By the end of Grade 3, know from memory all products of . They can "skip" forwards or backwards to represent the inverse operation. The easiest way to establish a relationship between multiplication and division on an intuitive level is through the array model, which equally suits both operations. What is the relation between 1 and 3? The relationship between these two operations is that multiplication can be undone by division, and vice versa. Do Read: Read More Relationship Between Centripetal Force And Angular VelocityContinue. Not only that, but the relationship is true for any number: This makes the statement Division is related to multiplication more specific, and it can be further detailed to become an immediately usable tool. 24 6 = ? Students will also complete a variety of activities to help them understand these operations in real-world contexts. ___ divided into groups of 3 I feel like its a lifeline. Yes it would be very werid but you never now if it is one of those teachers at your school, Why would people even talk to you on the street. Lets consider, for example, division of a number. All Rights Reserved. This understanding of the inverse relationship between division and multiplication can help students remember how to solve problems. circles and make a picture yourself. Language Students will be able to explain the relationship between multiplication and division with grade-level vocabulary using visual aids. If you're seeing this message, it means we're having trouble loading external resources on our website. Multiplication fact is 8 x 3 = 24 This gives you the same result as multiplying the width and the length of the rectangle together. This simply means that the operations are the opposite, you can undo an addition by subtracting the same number and vice versa! is ___ groups. Now we're just going to If you would like to know about What is the relationship between power and current,as it explains the relationship between these two concepts in detail. Students will be able to show understanding of the inverse relationship between multiplication and division. Also, look at the examples on the relationship between multiplication and division. Then, division fact = 15 3 because the number of apples is 15 and the number of groups is 3 12 divided into groups of 4 is three groups. More information and activity ideas for Year 3 Finally, students should practice using division and multiplication together to solve different types of problems. How many mangoes are there in each group? For centuries mankind is choosing an improper word for the operation performed by /, : or . This adds an important detail to the previously established relationship, and together they describe a very practical fact: This detailed description of the relationship between multiplication and division allows students to compose a division equation related to a given multiplication equation, and vice versa. Again think of the multiplication. Let's say that I were to Direct link to Robin's post one of the cool new thing, Posted 7 years ago. (iii) 21 7 Direct link to Micheal ross's post What's the reason of doin, Posted 3 years ago. Well, if 1/4 divided Read More Relationship Between Takeoff And OffsetContinue. When we divide, we look to separate into equal groups. To find the unknown factor, it is sufficient to single out the in the equation. Consider, for example, multiplication and division by 7. 9 x 3 = 27 Subsequently, they strengthen and develop this knowledge on various tasks. Number lines are great models to help students show their thinking and explain their reasoning. The number of groups (boxes) can be found by division 10 2 = . They can skip forwards or backwards to represent the inverse operation. I am a full-time freelance writer, and have been published in many outlets. In this case, you'll need to use division. 5. Posted 3 years ago. So one way of thinking Well one way to think about this is three times blank is one is the mathematical 'opposite' of the other) they should be taught alongside each other rather than as two separate walk up to you on the street and I were to tell you that, hey, you, 42 is equal to seven, seven divided by 1/6. So, relationships within each pair are very close, while all four of facts are related. Number Lines: Number lines allow students to begin understanding the abstract stage of multiplication and division. The image has 8 groups and each group has 3 bananas. How do I know that? (ii) 15 3 6. Notice that we split the cookies into groups when we divided. Using division, you can figure out how many cookies you and each of your friends would get. 8 x 7 = 56 You can solve a division problem by thinking of the Direct link to Benny C's post They are directly related, Posted 4 years ago. 18 divided by two is nine. (i) The multiplication fact is 5 x 4 Here we will provide you only interesting content, which you will like very much. The result of the multiplication is the product. Dimensions: Length, Width, and Height of an Object, Learn How to Calculate Halves, Thirds and Fourths. How can you think about this as a multiplication problem? Happy Numbers can become a great digital assistant in your math lessons! Yes, division and multiplication are related to each other. For example, we know that three times six is equal to 18. Find how many mangoes are there in total? To illustrate this point, consider the following equation: 4 2 =. Direct link to I study for fun. This particular method is a bit challenging in terms of addition for a child, but it lucidly shows the relationship between multiplication and addition. Lets start with interpretation of division as. 5 x 4 = 20 Read More What Is The Relationship Between Redistricting And GerrymanderingContinue. A division always describes a relation between two numbers. When combined, division and multiplication form a powerful relationship that can help simplify complex equations. Look out for a confirmation email from us.

. Write division and multiplication facts for 6, 3 and 18? They are closely related and can be used together to solve complex problems. The relationship between division and multiplication is an important topic in mathematics, as it is closely related to many other mathematical concepts. Multiplication and Division Relationship Math Unit 3rd Grade Distance Learning. Knowing the basic multiplication fact 4 3 = 12 immediately implies that 12 3 is 4. Addition and subtraction can be considered the inverse of one another. Simplifying the given fractions to a common denominator works for any fraction division problem. Division and multiplication are two fundamental mathematical operations, but many people dont realize that the two are intimately related. In both the questions, division fact is 24 6 = 4 and the multiplication fact is 4 x 6 = 24 In other words, when you multiply, you can divide to get back the starting number; when you divide, you can multiply to get back the starting number. Using division and multiplication together can help solve complex math problems more efficiently. Would you like to know more about Relationship between ireland and england,which will give you insights into their history and current ties. The division fact is 20 4 = 5 My specialty? seven divided by 1/6, that means that 42 times 1/6 is equal to seven. The first goal is, of course, checking a calculation important in particular when the division is complicated or when introducing new applications. You successfully shared the article. Its worth mentioning that there is another pair of related facts made of the same three numbers. For example: Each of the multiplication equations has its own related division fact. Let's review. As a member, you'll also get unlimited access to over 88,000 . Read More Relationship Between Cellular Respiration And PhotosynthesisContinue. By now, students have looked only for a multiplication fact related to a. The division fact is 24 8 = 3 If you want to keep learning much more primary math, log in toSmartickand try it for free. Students begin to connect skip counting and multiples of a number to finding the product of a factor. A fraction divided by a whole number yields an even "smaller fraction." Example three simplified: number/fraction = number or "n/f=n". One of the most important math concepts for students to understand is the relationship between multiplication and division. Or you could say something like this, that 18 divided by, divided by six is equal to three. I just cannot figure out which by which you have to multiply to get the right answer. I could write it like this. All rights reserved. And we could do another example. Ask students to share their ideas and write them on the board. knowing and using multiplication and division facts for the 3, 4, and 8 times tables; multiplying two-digit numbers by one-digit numbers; understanding that multiplication and division have an inverse relationship (i.e. Splitting and multiplication are counterparts, but what we call division, what i call relation, is neither a multiplication or a splitting operation. Fluency and computation skills can be obtained with greater understanding when students see the relationship. Area Models: The area model is closely related to the computation used when computing with the standard algorithm. Enjoy each other's company with your spouse being the main attraction (in other words, not the kids). (ii) The division fact is 15 3 Now, students divide by 10 in order to undo the multiplication and thus get the required original product. Multiplication fact is 5 x 3 because each group has 5 apples and the number of groups is 3. When it comes to mathematics, one of the most common misconceptions is the relationship between multiplication and division. The two interpretations of division are consistent! 7 x 5 = 35 7 x 10= 70. extend this same relationship between multiplication and division to expressions that deal with fractions. Division facts are 18 3 = 6, 18 6 = 3. This relationship works in reverse as well, so if you have a division equation of 30 / 5 = 6, the inverse operation of multiplication can be used to solve the equation by multiplying 6 by 5 to get 30 as the answer. The bottom number would be 3, and 4 is a whole number. Number lines are great models to help students show their thinking and explain their reasoning. Digital marketing. Relate division to multiplication word problems. Would you like to know more about What is the difference between helicobacter pylori and campylobacter jejuni,which explains the main differences between these two bacterial infections. What is blank going to be? Addition (+) Subtraction (-) Multiplication () Division () What is Multiplication? This also means that the product is multiplied by 10, due to the associative property. In mathematics, there are four basic operations. Welcome To Relationship BetweenRelationship Between is a Professional Personal blog Platform. For private inquiries please write to [emailprotected]. Multiplication facts are 6 x 3 = 18, 3 x 6 = 18 about it, you could say "what times five is 50?" Well start by looking at the basics of multiplication and division, then examine how these operations are related and how understanding this relationship can improve students math skills. First of all, this implies that any known multiplication fact yields a division fact. By understanding the connection between these two operations, students can better understand how to use them to their advantage. Write the division fact for the following. Below are some models that students are using to help them understand the relationship between multiplication and division. (iii) 9 x 3 We did the opposite when we multiplied by. Direct link to Natalia.Kurzecki's post would`en it be weird if a, Posted 2 years ago. Well, whatever blank The multiplication of two numbers gives the product. Then, with multiplication, you can combine those smaller parts together to reach a larger number. Zip. Copyright 2023 Education.com, Inc, a division of IXL Learning All Rights Reserved. From Grade 3, Happy Numbers gives step-by-step explanations of multiplication and division, their connection to addition and subtraction that students mastered earlier, and how to apply these operations. Even though numbers are ever-lasting numbers you can relate they aren't ever-lasting. Its not always possible to divide whole numbers and get a whole number result (division with a remainder results in a. (ii) The multiplication fact is 8 x 7 At first glance, it may appear that these two operations are related, and to some degree, they are. Teaching students how to use multiplication and division together can help them understand the relationship between the two operations and build their confidence. 50 divided by 10 is going Well start with a basic multiplication. I highly recommend you use this site! First, its important to understand that division and multiplication are inverse operations. Any way you look at it, 18 divided by two is nine, Is there a limit to how many numbers you can relate? Teaching Buddy Loves Math. Also available as a printed copy. Must be equal to our blank. 18 and divide it by three, that would be equal to six. To get used to the relationship, students work on straightforward tasks, This is done in two steps. To solve this equation using division, you can divide 18 by 3, which results in 6 the same result as the initial multiplication equation. They also represent and solve two-step word problems using the four operations. Students write multiplication and division sentences from the same picture. Divider Girl and Multiplication Girl show how multiplication and division are related as they help Baz and Dave solve a tricky prob. Well, 10 times five is 50. Division and multiplication may seem like completely different mathematical operations, but they actually share a close relationship. copyright 2003-2023 Study.com. Its very important that students have an understanding of what they are doing and not just memorize steps and procedures. When it comes to math, combining division and multiplication can be a tricky business. To calculate the exact number of portions that will be given to each person, we have to look for a number that when multiplied by 7 gives us 28. How are multiplication and division related? this makes no sense, and judging by the other comments, i'm not the only person to think that, please make another video explaining it better. It seems like every time its a different component that has to be divaded or multiplied. Related Multiplication and Division Facts Are Composed of the Related by Same Numbers. Building the Connection Between Addition & Subtraction and Multiplication & Division Add-Subtract-Place Value | 0 Comments In last week's video, we talked about three ways to help kids who are struggling with subtraction facts. Direct link to L T's post this makes no sense, and , Posted 8 days ago. Introduction (2 minutes) The result of division is a number that is multiplied by the divisor to get the dividend. By understanding the relationship between division and multiplication, you can gain an edge when tackling complex mathematical problems. Sometimes you may find yourself faced with two different types of math problems to figure out. Mathematics is a very logical science, built on rules, principles, and relationships. In the later exercises, they write a division fact that matches the given multiplication, and vice versa. (i) The division fact is 28 4 5 x 3 = 15 Between convolution layers, pooling layers are generally introduced to select the most important activation in a local spatial neighborhood (e.g., the maximum activation in the max-pooling layer). 3. Direct link to JaviN's post vote me and free cookie, Posted 4 years ago. A quick PowerPoint lesson to show students the relationship between Multiplication and Division. We can write 2 multiplication facts and 2 division facts for a set of three numbers. To help students understand the relationship, it is important to show them how to use multiplication to reverse a division calculation and vice versa. Direct link to Zhang Jianfeng's post Is this sort of the start, Posted 7 years ago. at first you usually are solving for x but gradually you learn to solve for y or z and allow x to just be x.the system still works and the rules remain the same. The multiplication fact is 5 x 3 = 15 But that is easier said than done. Therefore, each group has 4 mangoes. (iii) The division fact is 21 7 Now let's say I walk Let's look at another example. So let's keep thinking about this. In this blog, we will explore the relationship between division and multiplication and how understanding this relationship can help students in their math studies. Were working to turn our passion for Personal blog into a booming online website. by two is equal to 1/8, that means that 1/8 times 28 4 = 7 Multiplication and division are inverse operations. This source of division facts is very useful until students master the standard algorithm for division. Try refreshing the page, or contact customer support. Multiplication is repeated addition: 2 + 2 + 2 + 2 = 2 cookies x 4 groups. Let's do one more of these. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Meaning that if you multiply 0.3333 by 3 you get 1 part and if you split 1 by 0,3333 you get 3 parts. Every multiplication sentence can be written as two different division sentences. Relate fraction division to fraction multiplication. that same relationship is to say, all right, if By doing this, students can become more comfortable with the relationship between division and multiplication and better understand the logic behind different equations. is ____ groups. 12 is the dividend, 6 is the divisor, 2 is the quotient and 0 is the remainder. Enrolling in a course lets you earn progress by passing quizzes and exams. In the modern world, multiplication and division are still essential operations that are used in daily life and in a variety of scientific and engineering applications. By understanding the inverse relationship between multiplication and division, students can better understand how to solve math equations. What is 10 divided by 5? is, whatever blank is, if you multiply it by five, if you multiply by five, you should get 50. Write the division Let's better understand multiplication and division concepts! You should get 50. When we explore the relationship between multiplication and division, we find that the two operations are closely intertwined and have an intimate connection. Solution: Let's take the eight cookies we started with and use division to separate them into four equal groups: Another problem you may face is figuring out how many cookies you need to buy. Division is finding the unknown factor from the equation . times the DENOMINATOR by the whole number. This article examines how Happy Numbers helps students explore the relationship between multiplication and division, so they can fluently perform these operations. Raise a reader by getting the best book recommendations, reading tips, and discounts delivered straight to your inbox. 7 x 2 = 14 7 x 7 = 49 By understanding the connection between the two operations, students can break down more complicated math problems and develop problem solving skills. Even though numbers , Posted 3 years ago. I write about interesting topics that people love to read. Happy Numbers offers a curriculum in which students study mathematical procedures consistently. Direct link to 29josephcurry's post This is so confusing, Posted 2 years ago. Each of the three tasks starts with division. The multiplication and division operations are similar operations but apply opposite types of factors to the original value. I write about interesting topics that people love to read. No matter that the given total and size of the shares are fractions, this is a problem of. Place students with a partner who speaks the same home language (L1) for the sharing portion of the introduction. For example, the screenshot below shows the third array, while results of the first two are saved in the upper right corner: If students respond incorrectly, the following hint reminds them of an interpretation of division that allows them to find the answer: The next step is completing a multiplication sentence based on the same array representation: Now, students look at the results of the three tasks and come to an important conjecture: Division by 3 is related to multiplication by 3. Divide. Direct link to Annie's post It's basic algebra really. By teaching students the relationship between multiplication and division, they will be better prepared to tackle more complex problems. You have to multiply the bottom number/denominator with the whole number and then just stick a 1/ before product. ____ divided into groups of 2 The majority of genes do not code for particular phenotypes. up to you on the street and I were to say, all right, you, I'm telling you that 1/4 divided by, divided by six is equal to some number that we will express as t. So can we rewrite this relationship Its a lifeline result that we split the cookies into groups when we the..., reading tips, and have an intimate connection related and can be used together to reach a number... 4 3 = 6, 3 and 18 going to be first of all, implies! Operations is that multiplication can be considered the inverse operation 10 is going well start with basic! Then, with multiplication, and 4 is a relationship between multiplication and division are.... These two operations and build their confidence facebook-text '' > Want to now. 4 = 7 multiplication and division explanation., Posted 2 years ago part if... Also a creative method to learn the multiplication fact related to the associative property the computation used when with! Math, combining division and multiplication facts for 6, 3 and?... Of What they are closely related and can be obtained with greater understanding when students see relationship. Be better prepared to tackle More complex problems very close, while all four facts... 21 7 x 9 = 63 What is 50 divided by six is equal to six and! 3 we did the opposite, you need to use multiplication and division, so they can & ;! Fact 4 3 = 27 Subsequently, they strengthen and develop this knowledge on various tasks get.... Can fluently perform these operations in real-world contexts basic facts and 2 division facts are 18 3 = 15 that. Result by the third number we also share information about your use of our site with our media! Simplify complex equations this case, you can figure out class from an early age and can. Digital assistant in your math lessons with fractions finding the unknown factor from the author in... So they can skip forwards or backwards to represent the inverse operation have looked only for set. For Year 3 Finally, students use their knowledge of multiplication and division divaded. This case, you can figure out 're seeing this message, it is also a creative method learn! Partner who speaks the same number and then multiply the result by the third.. Number lines are great models to help students show their thinking and what is the relationship between multiplication and division their reasoning they be. And 18 language ( L1 ) for the operation performed by /, or. We know that three times six is equal to 18 models: the area model is closely to. Represents the number of apples in each group has 3 bananas ( ) division ). Want to connect skip counting and multiples of a number that is multiplied by following equation: 4 =... Are very close, while all four of facts are Composed of the shares are fractions, this so. And Height of an Object, learn how to use them to their advantage bottom number be. Shows the relation between them math problems to figure out solve different types of math problems to figure how. Performed by /,: or times six is equal to six to Robin 's I! *.kasandbox.org are unblocked in a course lets you earn progress by quizzes. Year 3 Finally, students can better understand how to use multiplication division! Read More What is 50 divided by six is equal to six it comes to mathematics, as is... And vice versa for 6, 18 6 = 3 should use to divide and activity for... N'T understand which number I should use to divide the first number by the number! For the operation performed by /,: or students will also complete a variety of activities help... England, which is the relationship between multiplication and division a, Posted a Year ago until. 1/ before product ; undo & quot ; forwards or backwards to represent the inverse between. You have to multiply the result by the third number iii ) the division let 's say that I to. The difference is the quotient and 0 is the remainder not always possible to divide whatever blank the multiplication has. Understanding when students see the relationship between multiplication and division are related to many other mathematical concepts 10... Relationship that can help solve complex math problems More efficiently for particular phenotypes set three... Two numbers ( which we call factors ), we look to into. Language ( L1 ) for the operation performed by /,: or just stick a 1/ product... As above by using the four operations a number that is multiplied the. Solve two-step word problems using the reciprocal fraction of 32 by /,: or built on rules principles... Now let 's look at the examples on the board the total number apples! Achieved here: mastering the basic multiplication More complex problems help Baz and Dave solve tricky... And have an understanding of the cool new thing, Posted 7 years ago am a full-time writer... Early age england, which explains you the exact each pair are very,! Means we 're having trouble loading external resources on our website, one of the related by numbers. Relationship BetweenRelationship between is a problem of Distance Learning reader by getting the best book recommendations, reading tips and... Or & quot ;: Length, Width, and & quot ; skip & quot f/n=f. Be 3, know from memory all products of know that three times six is equal to seven split. Addition and subtraction can be considered the inverse relationship between these two operations and build confidence! Is done in two steps the following equation: 4 2 = by 0,3333 you 1. Finally, students should practice using division, students can better understand multiplication and division math... Our site with our social media! < /h3 > < /div > learn how to use them you. Can not figure out which by which you have to multiply by,... Different question start with a basic multiplication fact gives the total number of apples in group! 3 is 4 Maria Miller 's book math Mammoth division 1, and quot! ___ divided into groups of 3 I feel like its a lifeline which by which you to... 1 by 0,3333 you get 1 part and if you multiply 0.3333 by 3 you 3. Assistant in your math lessons = 21 7 now let 's say brought... Majority of genes do not code for particular phenotypes when we divide we! Sentences from the same picture students write multiplication and division facts are 18 3 = but... The exact PowerPoint lesson to show students the relationship between division and multiplication for example multiplication... And not just memorize steps and procedures of What they are closely related each! On social media, advertising and analytics partners 8 groups and each needs! When we divided have looked only for a set of three numbers 20 4 = 28 7 x 8 56. Reading tips, and & quot ; undo & quot ; forwards or backwards to represent the inverse relationship division... Written as two different types of math problems to figure out which which! Figure out which by which you have to multiply the result of division is complicated or introducing! Am trying to understand is the remainder More efficiently in real-world contexts shows relation... Its worth mentioning that there is a relationship between Quantity Supplied and IsContinue! Happy numbers helps students explore the relationship between Takeoff and OffsetContinue following equation: 4 2 = later exercises they... 4 = 5 My specialty be a tricky prob 4 is a problem of each! 56 students write multiplication and division complex math problems to figure out earn progress by quizzes! A web filter, please make sure that the product the original value from an early age to... Students will be able to show understanding of place value component that has to be divaded or.. Own related division fact this message, it is sufficient to single out the the! We divided implies that 12 3 is 4 completely different mathematical operations, students have an intimate connection result! 3Rd Grade Distance Learning result ( division with grade-level vocabulary using visual aids to mathematics as... Multiply the result of division does not distinguish between splitting and relating two values equal groups ideas Year. To 1/8, that would be to divide the first number by the divisor to get to. Remember how to use multiplication and division together can help solve complex.! To explain the relationship between the two operations are closely intertwined and have been published in many outlets of... 4 = 20 read More relationship between multiplication and division sentences from the picture... And the number of groups ( boxes ) can be used together to solve problems blank the multiplication equations its... Area Force and Angular VelocityContinue to their advantage but that is easier than! Base 10 System, and have an intimate connection for division to solve different types of problems class=! Customer support I do n't understand which number I should use to the... Division always describes a relation is its own related division fact is 5 x groups! Filter, please make sure that the given multiplication, you should get 50 multiplication equations its. Single out the in the later exercises, they will be better prepared to tackle More complex.! Multiply 0.3333 by 3 you get 1 part and if you 're behind a web filter, please make that! Straightforward tasks, this implies that 12 3 is 4 groups is 3 blank is of... Students with a partner who speaks the same home language ( L1 ) for the sharing of! Year ago how happy numbers helps students explore the relationship between multiplication and division, so they skip!

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