Learn About the Associative Property in Math

Learn About the Associative Property in Math According to the associative property, the addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property will involve 3 or more numbers. The parenthesis indicates the terms that are considered one unit. The groupings (Associative Property) are within the parenthesis. Hence, the numbers are associated together. In multiplication, the product is always the same regardless of their grouping. The Associative Property is pretty basic to computational strategies. Remember, the groupings in the brackets are always done first, this is part of the order of operations. Addition Example of the Associative Property When we change the groupings of addends, the sum does not change:(2 5) 4 11 or 2 (5 4) 11(9 3) 4 16 or 9 (3 4) 16Just remember that when the grouping of addends changes, the sum remains the same. Multiplication Example of the Associative Property When we change the groupings of factors, the product does not change:(3 x 2) x 4 24 or 3 x (2 x 4) 24.Just remember that when the grouping of factors changes, the product remains the same. Think Grouping! Changing the grouping of addends does not change the sum, changing the groupings of factors, does not change the product. Simply put, regardless of whether you show 3 x 4 or 4 x 3, the final result is the same. In addition, 4 3 or 3 4, you know that the outcome is the same, the answer remains the same. However, this is NOT the case in subtraction or division so when you think of the associative property, remember that the final result or answer remains the same or its not the associative property. The understanding of the concept of associative property is much more important that the actual term associative property. Titles often confuse students and youll discover that youll ask what the associative property is, only to be returned with a blank look. However, if you say to a child something like If I change the numbers in my addition sentence, does it matter? In other words, can I say 5 3 and 3 5, will the child that understands say yes because its the same? When you ask if you can do this with subtraction, theyll laugh or tell you that you cant do that. So in essence, a child knows about the associative property which is really all that matters even though you may stump them when you ask for a definition of the associative property. Do I care that the definition escapes them? Not at all, if they indeed know the concept. Lets not trip our students up with labels and definitions when concept understanding is the key ingredient in math.

The Real Marketing Value of a Professional Book Cover

The Real Marketing Value of a Professional Book Cover Revealed: The Real Marketing Value of a Professional Book Cover Most self-published authors already understand the importance of great cover design. When it comes to marketing their book, the cover design is their primary sales tool, the face of their project, and the thing that can elevate them to a professional standard in the eyes of readers. But, if authors know this, why do so many still create their own book covers?Most often, it comes down to resources. Professionally designed book covers cost money (but not as much as you might think), and often, authors end up asking themselves: does a professional book cover actually get you more clicks and sales? The Professional Cover TestTo answer this question once and for all, we recently ran an experiment, in which self-published authors were invited to get their book covers re-designed by an experienced professional on Reedsy.Four titles from a range of genres were selected and entered into an A/B test: over the period of a week, we ran two Facebook ads for each book. Both ads were identical in every way - except for the cover image - and exposed to approximately 1,000 users from the same audience set. That way, we would discover how much the re-designed cover impacts the click-rate rate of an advert.On average, we saw a 35% increase in the marketability of books with professional covers.What does this mean? For each test, the professionally designed cover had a click-through rate that was 12.5–50% higher than their non-professional counterparts. Let’s take a quick look at each of the redesigns and let our designers explain their approaches.Once a Bridesmaid -   48% mo re clicksBuy The Fire Within on AmazonWhy do professional covers matter?An effective cover will get relevant readers responding to your ads and heading to your Amazon page. Once there, the design will communicate the tone and content of your book and get more (of the right) readers to buy or download it. This, in turn, improves your chances of positive reviews and ratings, which will send you up Amazon’s rankings, giving your book greater visibility, leading to even more downloads. More so than in most markets, self-publishing benefits heavily from the snowball effect.And we haven’t even touched on how your cover can be used for reader magnets  and crowdfunding campaigns!To see about maximize your book’s marketing potential, head over to the Reedsy Marketplace and request free quotes from over 200 experienced book designers with experience in almost every imaginable genre.Sign up for our free online marketing course and learn how to use Facebook advertising to market your own books.If you've had a re-design of your book cover - or if you've considered getting a professional cover but decided not to - share your thoughts in the comments below.