A Review on Operations on Real Numbers

We had just finished discussing the different operations on integers: addition, subtraction, multiplication and division. Since you are already familiar with these operations on integers, the operations on real numbers (integers, decimals, and fractions) will be very easy for you because the process is just the same. For example, positive a real number 0.4 is multiplied by a negative real number 0.1, the result is negative just like multiplying positive and negative integers. 

Below are worked examples on the operations on real numbers. I made the examples easy so that you can recognize the pattern even if you forgot the rules on operating with decimals and fractions. Do not worry though if you have forgotten the rules because I will have separate posts about them. For now, try to solve and by compare your answer with the calculated results below.

Addition

Rules:

  • Positive Number + Positive Number = Positive Number
  • Negative Number + Negative Number = Negative Number
  • Positive Number + Negative Number: Subtract, and then take the sign of the larger number when the negative sign is disregarded.

Worked Examples on Addition of Real Numbers

1.  4.3 + 2.5 = 6.8

2. 8.7 + -3.7 = 5 (8.7 is larger whether the negative sign is disregarded or not)

3. -1/5 + -2/5 = -3/5

4. -10.3 + 2.2  = 10.3 – 2.2 = -8.1 (-10.1 is larger when the negative sign is disregarded, so the answer is negative)

Subtraction

Rule: Change the subtraction to addition, then use the addition rules.

Worked Examples on Subtraction of Real Numbers

1. 8.9 – 7.2 = 1.7

2. 4.3 – (-3) = 4.3 + 3 = 7.3

3. -2/5 – 1/5 = -2/5 + -1/5 = -3/5

4. -2/7 – (-1/7)  = -2/7 + 1/7  = -1/7

Multiplication

Rules

  • Positive Number x Positive Number = Positive Number
  • Positive Number x Negative Number = Negative Number
  • Negative Number x Positive Number = Negative Number
  • Negative Number x Negative Number = Positive Number

Worked Examples on Multiplication of Real Numbers

1. 2.3 x 1.2 = 2.76

2. 1.6 x -3 = -4.8

3. -2.5 x 4 = -10

4. – 0.5 x -1.2 = 0.6

Division

Rules

  • Positive Number ÷ Positive Number = Positive Number
  • Positive Number ÷ Negative Number = Negative Number
  • Negative Number ÷ Positive Number = Negative Number
  • Negative Number ÷ Negative Number = Positive Number

Worked Examples on Division of Real Numbers

1.  4/7  ÷ 2/7 = 2

2. 5.2 ÷ -2 = -2.6

3. -3.2 ÷ 1.6 = -2

4. -7.5 ÷ -2.5 = 3

That completes are worked examples on operations on integers. In the next posts, we will be discussing operations on fractions and decimals.

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1 Response

  1. August 30, 2013

    […] the previous post we have discussed how to divide integers. Operations on real numbers, particularly integers, is one of the scopes of the Civil Service Examinations both Professional […]

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