Basic Math Rules Explained: Foundations of Math

Before moving on to more advanced math topics, it's important to review the rules of fundamental math. Here, you'll find practice problems and a review of some general math concepts.

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Basic Math Concepts

Reviewing Key Ideas

Multiplication Review

Multiplication is basically the same as adding groups of numbers. Instead of writing 4 + 4 + 4, we write 4 x 3, meaning we have 3 groups of 4. If you ever get stuck on a multiplication problem, you can turn it into a long addition problem. For example, 54 x 9 is the same as 54 + 54 + 54 +54 + 54 + 54 +54 + 54 + 54. Although this might be helpful at first, once you start multiplying and learning your times tables, you'll probably find it's much simpler to solve problems like this using multiplication instead of transforming them into addition problems.

Multiplication Rules

Some multiplication problems will always be straightforward because of some basic multiplication rules. For instance, any number multiplied by 0 equals 0, which means 7684 x 0 still equals 0. Any number multiplied by 1 equals that number (e.g. 5 x 1 = 5; 698 x 1 = 698). Finally, to multiply a number by 10, simply add a 0 to the base number. So, 4 x 10 = 40 and 560 x 10 = 5600.

Division

One way to think of division is that it's the inverse of multiplication. If you know your times tables, you can use them to solve division problems mentally. If you have the problem 9 ÷ 3, you can re-write it as 3 x ? = 9, which leads you to the answer: 3. This method may be especially useful for division problems with smaller numbers.

Fractions and Percents

Fractions are parts of a whole. If a book has 20 chapters with 10 pages each, then each chapter is equal to 1/20 of the book. The first 10 chapters represent 1/2 of the total book. Because you can convert fractions into percents, 1/2 is the same as 50%. You perform the conversion by dividing the numerator by the denominator and multiplying your result by 100. For example, to turn 3/4 into a percent, divide 3 by 4, which equals 0.75. Now, move the decimal point over two places to multiply 0.75 by 100. You'll find that the answer is 75%.

Multiplication and Division Practice Problems

  1. 567 ÷ 4
  2. 36 x 11
  3. 41 ÷ 9
  4. 29 x 4
  5. 330 ÷ 99

Answers

  1. 141.7
  2. 396
  3. 4.5
  4. 116
  5. 3.33
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