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The Order of Operations: PEMDAS

The Order of Operations: PEMDAS
Purplemath If you are asked to simplify something like "4 + 2×3", the question that naturally arises is "Which way do I do this? Because there are two options!" I could add first: ...or I could multiply first: Which answer is the right one? MathHelp.com It seems as though the answer depends on which way you look at the problem. To eliminate this confusion, we have some rules of precedence, established at least as far back as the 1500s, called the "order of operations". A common technique for remembering the order of operations is the abbreviation (or, more properly, the "acronym") "PEMDAS", which is turned into the mnemonic phrase "Please Excuse My Dear Aunt Sally". Parentheses (simplify inside 'em) Exponents Multiplication and Division (from left to right) Addition and Subtraction (from left to right) When you have a bunch of operations of the same rank, you just operate from left to right. Content Continues Below Simplify 4 + 32. Simplify 4 + (2 + 1)2. Simplify 4 + [–1(–2 – 1)]2.

Contents, Interactive Mathematics Miscellany and Puzzles Since May 6, 1997You are visitor number E66B7E in base 20 Raymond Smullyan, a Mathematician, Philosopher and author of several outstanding books of logical puzzles, tells, in one of his books, a revealing story. A friend invited him for dinner. Having told this story, would it be wise to announce up front what this site is about? |Contact||Front page||Index||Store| History of Normal Distribution History of the Normal Distribution Author(s) David M. Lane Prerequisites Distributions, Central Tendency, Variability, Binomial Distribution In the chapter on probability, we saw that the binomial distribution could be used to solve problems such as "If a fair coin is flipped 100 times, what is the probability of getting 60 or more heads?" where x is the number of heads (60), N is the number of flips (100), and π is the probability of a head (0.5). Abraham de Moivre, an 18th century statistician and consultant to gamblers, was often called upon to make these lengthy computations. de Moivre noted that when the number of events (coin flips) increased, the shape of the binomial distribution approached a very smooth curve. Figure 1. de Moivre reasoned that if he could find a mathematical expression for this curve, he would be able to solve problems such as finding the probability of 60 or more heads out of 100 coin flips much more easily. Figure 2.

Sudoku - Play, Share & Print Sudoku puzzles for free! u36824 Easy What is Sudoku? Sudoku is a number-placement puzzle. You start with an almost empty puzzle, which has some of the cells already filled with numbers. Your objective is to fill in the rest of the empty cells. How do I start a Sudoku puzzle? The easiest way to begin is to choose a number and try to fill in all the places in the puzzle where it must appear, according to the Sudoku rules. Now what? Now go ahead! Mathematical Images: Symmetry | MissQuinnMaths I love finding ‘maths pictures’, and thought it would be nice to start collecting and sharing them. Symmetry is the easiest to begin with, unsurprisingly. Images with simple line symmetry can be great for young (i.e. Y7) pupils to engage with, allowing for discussions about strategies to ‘test’ to how symmetrical an image is and how it could be improved to be ‘more’ symmetrical (this is a good ‘way in’ to using squared paper to complete reflections). Rotational symmetry is fun to explore with an interactive whiteboard, and more practical activities abound (e.g. for homework pupils can draw their own Rangoli patterns, or make patterned wedges that can be repeated to build up a whole shape). Some examples of line symmetry: Some examples of rotational symmetry: Post links to any images of your own! Like this: Like Loading...

The T-Test The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design. Figure 1 shows the distributions for the treated (blue) and control (green) groups in a study. Actually, the figure shows the idealized distribution – the actual distribution would usually be depicted with a histogram or bar graph. The figure indicates where the control and treatment group means are located. What does it mean to say that the averages for two groups are statistically different? This leads us to a very important conclusion: when we are looking at the differences between scores for two groups, we have to judge the difference between their means relative to the spread or variability of their scores. The formula for the t-test is a ratio. SE(XˉT​−XˉC​)=nT​varT​​+nC​varC​​​

Khan Academy From kindergarten to calculus, Khan Academy is here to help. Sharpen your skills with over 100,000 interactive exercises. Over 100,000 interactive exercises. You may have heard about our videos, but did you know that Khan Academy has fun interactive math exercises that cover skills ranging from counting to calculus, grade by grade? Created and peer-reviewed by a team of math educators, our exercises include full coverage of US Common Core and beyond, ranging from early math through calculus. Review student progress in real time. You will be empowered with instant, in-depth feedback and reports so you’ll know exactly where each student and your class as a whole stand at any time throughout the year. Stay up to date with your child’s progress. You’ll get quick email updates so you can see your children’s progress as they learn, both when they’ve mastered new skills and when they might be struggling.

Word Problems This page contains links to free math worksheets for Word Problems problems. Click one of the buttons below to view a worksheet and its answer key. You can also use the 'Worksheets' menu on the side of this page to find worksheets on other math topics. Addition Word Problems Introductory word problems for addition Subtraction Word Problems Introductory word problems for subtraction Mixed Addition and Subtraction Word Problems Mixed addition and subtraction word problems. Multiplication Word Problems Introductory word problems for multiplication. Division Word Problems Introductory word problems for division. Girl Scout Cookie Division If you've been working as Troop Cookie Mom (or Dad!) Division With Remainders Word Problems Story problems using division and involving remainders. Mixed Multiplication and Division Word Problems Mixed multiplication and division word problems. Mixed Operation Word Problems Mixed addition, subtraction, multiplication and division word problems. Printable Flash Cards

ONE-WAY ANOVA Analysis of variance (ANOVA) for comparing means of three or more variables. Use this test for comparing means of 3 or more samples/treatments, to avoid the error inherent in performing multiple t-tests Background. Ideally, for this test we would have the same number of replicates for each treatment, but this is not essential. An important assumption underlies the Analysis of Variance: that all treatments have similar variance. Procedure (see worked example) Don't be frightened by this! Assume that we have recorded the biomass of 3 bacteria in flasks of glucose broth, and we used 3 replicate flasks for each bacterium. Step 1. Step 2. , S x2, and Sd2 (click here for method) Step 3. Step 4. Step 5. and call the sum B. Step 6. Step 7. Step 8. Step 9. Step 10. Step 11. [The total df is always one fewer than the total number of data entries] Step 12. F = Between treatments mean square / Residual mean square Step 13. What does all this mean? Analysis of variance: worked example D = (Grand total)2

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