Basic Math Articles

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 03-21-2022

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.

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.

Article / Updated 08-26-2021

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. Before you can calculate a percentage, you should understand exactly what a percentage is. 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. 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. To calculate the percentage of a specific number, you first convert the percentage number to a decimal. This process is the reverse of what you did earlier. You divide your percentage by 100. So, 40 percent would be 40 divided by 100. 40 ÷ 100 = .40 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 07-24-2021

Sometimes, when you are subtracting large numbers, the top digit in a column is smaller than the bottom digit in that column. In that case, you need to borrow from the next column to the left. Borrowing is a two-step process: Subtract 1 from the top number in the column directly to the left. Cross out the number you’re borrowing from, subtract 1, and write the answer above the number you crossed out. Add 10 to the top number in the column you were working in. For example, suppose you want to subtract 386 – 94. The first step is to subtract 4 from 6 in the ones column, which gives you 2: When you move to the tens column, however, you find that you need to subtract 8 – 9. Because 8 is smaller than 9, you need to borrow from the hundreds column. First, cross out the 3 and replace it with a 2, because 3 – 1 = 2: Next, place a 1 in front of the 8, changing it to an 18, because 8 + 10 = 18: Now you can subtract in the tens column: 18 – 9 = 9: The final step is simple: 2 – 0 = 2: Therefore, 386 – 94 = 292. In some cases, the column directly to the left may not have anything to lend. Suppose, for instance, you want to subtract 1,002 – 398. Beginning in the ones column, you find that you need to subtract 2 – 8. Because 2 is smaller than 8, you need to borrow from the next column to the left. But the digit in the tens column is a 0, so you can’t borrow from there because the cupboard is bare, so to speak: When borrowing from the next column isn’t an option, you need to borrow from the nearest non-zero column to the left. In this example, the column you need to borrow from is the thousands column. First, cross out the 1 and replace it with a 0. Then place a 1 in front of the 0 in the hundreds column: Now, cross out the 10 and replace it with a 9. Place a 1 in front of the 0 in the tens column: Finally, cross out the 10 in the tens column and replace it with a 9. Then place a 1 in front of the 2: At last, you can begin subtracting in the ones column: 12 – 8 = 4: Then subtract in the tens column: 9 – 9 = 0: Then subtract in the hundreds column: 9 – 3 = 6: Because nothing is left in the thousands column, you don’t need to subtract anything else. Therefore, 1,002 – 398 = 604.

Article / Updated 07-24-2021

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:

Article / Updated 07-09-2021

The center of a circle is a point that's the same distance from any point on the circle itself. This distance is called the radius of the circle, or r for short. And any line segment from one point on the circle through the center to another point on the circle is called a diameter, or d for short. The diameter As you can see, the diameter of any circle is made up of one radius plus another radius — that is, two radii (pronounced ray-dee-eye). This concept gives you the following handy formula: For example, given a circle with a radius of 5 millimeters, you can figure out the diameter as follows: The circumference Because the circle is an extra-special shape, its perimeter (the length of its "sides") has an extra-special name: the circumference (C for short). Early mathematicians went to a lot of trouble figuring out how to measure the circumference of a circle. Here's the formula they hit upon: Note: Because 2 x r is the same as the diameter, you also can write the formula as C = π x d. The symbol π is called pi (pronounced "pie"). It's just a number whose approximate value is as follows (the decimal part of pi goes on forever, so you can't get an exact value for pi): So given a circle with a radius of 5 mm, you can figure out the approximate circumference: The area of a circle The formula for the area (A) of a circle also uses π: Here's how to use this formula to find the approximate area of a circle with a radius of 5 mm: