Introduction to Integers, Fractions and the Order of Operations

Everything to Know About Integers

Integers are positive whole numbers and negative numbers. They do not contain any fractions or decimals. Positive integers are numbers that are greater than zero, while negative integers are numbers that are smaller than zero. Some very basic examples include, the numbers one, two, three, negative four, negative seven and so much more.

Order of Operations for Integers

Here are the basic order of operations you can take note of when dealing with integers and all the four operations.

  • Always look for brackets and simplify expressions within the brackets first.
  • Starting from left to right, perform multiplication or division next (whichever comes earlier)
  • Again from left to right, perform addition or subtraction next (whichever comes earlier).
  • Simplify the expression.

Introducing Fractions

Now, let’s look into fractions. A fraction consists of a numerator (top number) and a denominator (bottom number). A proper fraction is one where the numerator is smaller than the denominator. For example, ½ and ¼ are proper fractions. An improper fraction, on the other hand, is one where the numerator is greater than the denominator. Some examples of improper fractions include 4/3 and 8/7. Equivalent fractions have the same value. For example ½ and 2/4 are equivalent fractions since both their values equal to 0.5. Lastly, a mixed number is the sum of a whole number and a fraction.

Adding and Subtracting Fractions

The basic methods for adding and subtracting fractions can be summed up below.

  • If the fractions have different denominators, you need to make them the same first.
  • Add or subtract the numerators but just copy back the denominator. Write down the solution of the adding or subtracting of the numerator on the top while the denominator is written at the bottom.
  • If need be, simplify the fraction into the lowest terms.

Multiplication of Fractions

For multiplication of fractions, there are a few rules to follow which may seem complicated at first. But once you have mastered them, it’s actually quite easy to handle multiplication of fractions.

The following summarises the basic steps when dealing with multiplication of fractions or mixed numbers:

Change all mixed numbers (if there are any) to improper fractions first.
Simplify the fractions by canceling from the top and bottom or sideways.
Multiply the numerators and then the denominators.
Simplify the answer to the simplest form (if required).

Division of Fractions

Now that you are clear about multiplying fractions, let’s delve into the division of fractions instead. The following summarises the basic steps when dealing with division of fractions or mixed numbers.

  • Change all mixed numbers (if there are any) to improper fractions first.
  • Turn the second fraction upside down and change the divide sign to multiply.
  • Simplify the fractions by canceling from the top and bottom or sideways.
  • Multiply the numerators and then the denominators.
  • Simplify the answer to the simplest form (if required).

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