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Algebraic operations are critical to many fields of study. In science, they are used to calculate forces to accelerate a car or determine the rate of a chemical reaction. In engineering, they can be used to design safe and efficient systems. They also underpin algorithms and data structures, which are...
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What do I do with the brackets? Brackets are useful to group numbers, pronumerals and operations together as a whole. Whatever is around the brackets affects all the things inside the brackets. Brackets are commonly used to express mathematical formulae. In order to manipulate expressions containing brackets it is necessary...
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How do I deal with fractions involving pronumerals? Adding and subtracting fractions always requires a common denominator (which is the lower half of the fraction). These need to be the same before you can add or subtract. This means converting some of the fractions to forms that are consistent in...
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What is an algebraic fraction? The numerator (top) or denominator (bottom) of a fraction can be in algebraic form involving numbers and variables (represented by pronumerals or letters). We cover the multiplication and division of fractions containing algebraic terms. Simplifying fractions You have probably seen numerical fractions like \(\frac{18}{24}\) before....
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Let's take a look at algebraic fractions where the denominator is a quadratic expression. Such fractions are common in mathematics and engineering. More complicated algebraic fractions can involve polynomials of any order. However in your studies, it is unlikely that you will have to deal with polynomials higher than quadratics....
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Find out how to express an algebraic fraction as a sum of simpler algebraic fractions (partial fractions). The method of partial fractions involves breaking up an algebraic fraction into simpler parts that are added together. This is useful in integration and in finding inverse Laplace and Fourier transforms. Adding fractions...
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Rearranging formulas, also called transposition of formulas, is a necessary skill for most courses. Let's work on some essential skills in manipulating formulas. Introduction Some of the most important equations that we might be required to transpose occur frequently in science, engineering and economics. They are called formulae and give...
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Are you still trying to get that variable on its own from the formula, but it is in a tricky place – or maybe it appears more than once? Here we demonstrate manipulating or rearranging complex formulas, with overviews and practice questions. Let's look at some more complicated formulas where...
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The fundamentals Building on fundamentals Dive deeper...
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What is algebra? Why are there letters in the equation? This page links to resources that will help you answer these questions. Algebraic expressions involve pronumerals (letters) to represent values. Pronumerals can take many different values. We often need to plug our own values into a given formula for calculating...
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Links to videos explaining different aspects of arithmetic: decimals, fractions, numbers, percentages and surds, and measurement....
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Fractions Numbers Decimals Percentages and surds...
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The fundamentals Arithmetic Fractions Numbers Decimals Percentages and surds Measurement Dimensions Units, prefixes and conversions Errors in measurement Errors in calculations Scientific notation Engineering notation Rules for significant figures Calculations for significant figures Building on fundamentals Indices, logs, surds Indices Fractional indices Logarithms Exponential equations Simplifying surds Dive deeper Complex...
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What is a decimal? Decimals are another way to express fractions or parts of a whole. We need them for measurement, and it is the easiest way to express fractions on a computer or a calculator. Work through these videos to get a review of decimals overall. Adding decimals Subtracting...
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How do we use fractions? A fraction is the easiest way to express a part of a whole. On this page you will learn how to simplify, add, subtract, multiply and divide fractions. If you received 18/20 for your test, you got 18 marks correct out of the 20 marks...
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How do we use fractions? A fraction is the easiest way to express a part of a whole. On this page you will learn how to simplify, add, subtract, multiply and divide fractions. If you received 18/20 for your test, you got 18 marks correct out of the 20 marks...
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What is index notation? When a number such as 16 is written in the form 42 (which means 4 x 4) we say that it is written as an exponential, or in index notation. There are laws about multiplying and dividing indices as well as how to deal with negative...
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What is a unit of measurement? How do I deal with measurement errors? Measurement is an important skill for everyday life but especially in fields of STEM. These pages will enhance your understanding of measurement, units and how to deal with errors. Dimensions (PDF) All measurements need a value as...
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Where do you start counting from? Zero? Think again! Calculating with numbers is a basic skill for everyday life. Watch these videos to see how the number system of integers (counting numbers) works. Multiplying numbers Dividing numbers Order of operations Negative numbers: addition and subraction Negative numbers: multiplication and division...
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How can you turn a raw score in a test into a percentage? If you get 15/20 for a test, you have done as well as someone who got 75 out of 100! This page is full of information about percentages and surds. Percentages Percentages are another way to express...
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Arithmetic Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris dui ligula, accumsan vel diam et, maximus pellentesque erat. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Aenean sit amet fringilla augue. Mauris eu augue nulla. In ultrices commodo leo et pulvinar. Fractions Numbers Decimals...
