Basic Math Articles

Cheat Sheet / Updated 02-16-2023

Some of the most important things to remember in AS-level and A-level maths are the rules for differentiating and integrating expressions. This cheat sheet is a handy reference for what happens when you differentiate or integrate powers of x, trigonometric functions, exponentials or logarithms – as well as the rules you need for what to do when they’re combined!

Article / Updated 11-04-2022

Listen to the article:Download audio Whether you're leaving a tip at a restaurant or figuring out just how much those stylish shoes are on sale, you can't get away from percentages. While there are numerous percentage calculators online, it's helpful to be able to do some quick math in your head to calculate percentages without any digital assistance. What is percentage? The word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred." So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time. How to find percentage The numbers that you will be converting into percentages can be given to you in two different formats: decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiply .87 by 100. .87 × 100=87, which gives us 87 percent. Percent is often abbreviated with the % symbol. You can present your answer as 87% or 87 percent — either way is acceptable. If you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100. 13 ÷ 100 = .13 Then, follow the steps above for converting a decimal to a percent. .13 × 100 = 13, thus giving you 13%. The more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100. Most of the time, you will be given a percentage of a specific number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is. How to calculate percentage of a specific number This process is the reverse of what you did earlier. First convert the percentage number to a decimal. Then, you divide your percentage by 100. So, 40 percent would be 40 divided by 100. 40 ÷ 100 = .40 Next, once you have the decimal version of your percentage, simply multiply it by the given number (in this case, the amount of your paycheck). If your paycheck is $750, you would multiply 750 by .40. 750 × .40 = 300 Your answer would be 300. You are paying $300 in taxes. Let’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is $1,500, how much should you save? Start by converting 25 percent to a decimal. 25 ÷ 100 = .25 Now, multiply the decimal by the amount of your paycheck, or 1500. 1500 × .25 = 375 This means you need to save $375 from each paycheck.

Article / Updated 10-03-2022

Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right. The Three Types of Big Four Expressions Expression Example Rule Contains only addition and subtraction 12 + 7 – 6 – 3 + 8 Evaluate left to right. Contains only multiplication and division 18 ÷ 3 x 7 ÷ 14 Evaluate left to right. Mixed-operator expression: contains a combination of addition/subtraction and multiplication/division 9 + 6 ÷ 3 1. Evaluate multiplication and division left to right. 2. Evaluate addition and subtraction left to right. Suppose you want to evaluate this expression: Again, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2: Notice that the expression shrinks one number at a time until all that’s left is 2. So Here’s another quick example: Even though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers): Thus,

Cheat Sheet / Updated 10-03-2022

A little understanding can go a long way toward helping master math. Some math concepts may seem complicated at first, but after you work with them for a little bit, you may wonder what all the fuss is about. You'll find easy-to-understand explanations and clear examples in these articles that cover basic math concepts — like order of operations; the commutative, associative, and distributive properties; radicals, exponents, and absolute values — that you may remember (or not) from your early math and pre-algebra classes. You'll also find handy and easy-to-understand conversion guides for converting between metric and English units and between fractions, percents, and decimals.

Article / Updated 09-27-2022

Dividing decimals is similar to dividing whole numbers, except you have to handle the decimal point before you start dividing. Here’s how to divide decimals step by step: Move the decimal point in the divisor and dividend. Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right. At the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right. Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend. Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place. Line up each digit in the quotient just over the last digit in the dividend used in that cycle. As with whole-number division, sometimes decimal division doesn’t work out evenly at the end. With decimals, however, you never write a remainder. Instead, attach enough trailing zeros to round the quotient to a certain number of decimal places. The digit to the right of the digit you’re rounding to tells you whether to round up or down, so you always have to figure out the division to one extra place. See the following chart: To Round a Decimal to Fill Out the Dividend with Trailing Zeros to A whole number One decimal place One decimal place Two decimal places Two decimal places Three decimal places Sample questions Divide the following: 9.152 / 0.8 = ? 11.44. To start out, write the problem as usual: Turn 0.8 into the whole number 8 by moving the decimal point one place to the right. At the same time, move the decimal point in 9.1526 one place to the right. Put your decimal point in the quotient directly above where it falls in 91.25: Now you’re ready to divide. Just be careful to line up the quotient properly so that the decimal point falls into place. Divide the following: 21.9 / 0.015 = ? 1,460. Set up the problem as usual: Notice that two trailing zeros are attached to the dividend because you need to move the decimal points in each number three places to the right. Again, place the decimal point in the quotient directly above where it now appears in the dividend, 21900: Now you’re ready to divide. Line up the quotient carefully so the decimal point falls into place: Even though the division comes out even after you write the digit 6 in the quotient, you still need to add a placeholding zero so that the decimal point appears in the correct place. Practice questions Divide these two decimals: 9.345 / 0.05 = ? Solve the following division: 3.15 / 0.021 = ? Perform the following decimal division, rounding to one decimal place: 6.7 / 10.1. Find the solution, rounding to the nearest hundredth: 9.13 / 4.25. Following are answers to the practice questions: 9.345 / 0.05 = 186.9. To start out, write the problem as usual: Turn the divisor (0.05) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.345) two places to the right. Place the decimal point in the quotient directly above where it now appears in the dividend: Now you’re ready to divide. Be careful to line up the quotient properly so that the decimal point falls into place. 3.15 / 0.021 = 150. Write the problem as usual: You need to move the decimal point in the divisor (0.021) three places to the right, so attach an additional trailing zero to the dividend (3.15) to extend it to three decimal places: Now you can move both decimal points three places to the right. Place the decimal point in the quotient above the decimal point in the dividend: Divide, being careful to line up the quotient properly: Remember to insert a placeholding zero in the quotient so that the decimal point ends up in the correct place. 6.7 / 10.1 = 0.7. To start out, write the problem as usual: Turn the divisor (10.1) into a whole number by moving the decimal point one place to the right. At the same time, move the decimal point in the dividend (6.7) one place to the right: The problem asks you to round the quotient to one decimal place, so fill out the dividend with trailing zeros to two decimal places: Now you’re ready to divide: Round the quotient to one decimal place: 9.13 / 4.25 = 2.15. First, write the problem as usual: Turn the divisor (4.25) into a whole number by moving the decimal point two places to the right. At the same time, move the decimal point in the dividend (9.13) two places to the right: The problem asks you to round the quotient to the nearest hundredth, so fill out the dividend with trailing zeros to three decimal places: Now divide, carefully lining up the quotient: Round the quotient to the nearest hundredth:

Cheat Sheet / Updated 05-04-2022

When you’re working with your K–5 child to practice math skills, it can help to have a tool to remind you of some of the basics related to addition, subtraction, multiplication, division, and fractions. For those times, this Cheat Sheet can come in handy.

Cheat Sheet / Updated 04-27-2022

To successfully master basic math, you need to practice addition, subtraction, multiplication, and division problems. You also need to understand order of operations, fractions, decimals, percents, ratios, weights and measures, and even a little geometry. After you've become proficient in these and other basic math concepts, you can begin to tackle pre-algebra, which involves variables, expressions, and equations.

Cheat Sheet / Updated 04-27-2022

Grasping some technical math basics can simplify everyday situations faced by many professionals and even non-professionals, including having to solve word problems, calculate tips, make change, or match American and metric measurements.

Cheat Sheet / Updated 04-14-2022

Everyday math comes in handy when you’re dealing with finances like credit cards and mortgages, and even helps when you’re trying to figure out how much to leave for a tip. Knowing some basic math formulas, the Pythagoras theorem, and a simpler way to add are key to everyday math.

Cheat Sheet / Updated 02-28-2022

Using real-life math can simplify everyday situations. Math comes in handy every time you take a trip, go shopping, or do projects around the house.