PEMDAS Rules - Involving Decimals

We will follow the rules for simplifying an expression using PEMDAS rules - involving decimals for solving order of operations.


Follow the order of operation as:

1. Parenthesis β†’ Find the things inside the Parenthesis part before Exponent, Multiply, Divide, Add or Subtract.

For example:

7.04 Γ— (4.07 + 6.72)

= 7.04 Γ— 10.79

= 75.9616

2. Exponent β†’ Then do the Exponent part (Powers, Roots, etc.,) before Multiply, Divide, Add or Subtract.

For example:

3.05 Γ— (0.2)2 + 2

3.05 Γ— 0.2 Γ— 0.2 + 2

= 3.05 Γ— 0.04 + 2

= 0.122 + 2

= 2.122


3. Multiplication/ Division β†’ Then do Multiply or Divide part before Add or Subtract start from left to right.

For example:

5.75 Γ— 3.5 + 6.4 Γ· 1.6

= 20.125 + 6.4 Γ· 1.6

= 20.125 + 4

= 24.125


4. Addition/Subtraction β†’ At last do Add or Subtract start from left to right.

For example:

15.05 + (6.25 – 3.75) Γ— 2.05

= 15.05 + 2.5 Γ— 2.05

= 15.05 + 5.125

= 20.175



Worked-out problems for solving PEMDAS rules - involving decimals:

Simplify using PEMDAS rule:

(a) 16.5 – 16.5 Γ· 2.2 + 3 Γ— 5

Solution:

16.5 – 16.5 Γ· 2.2 + 3.2 Γ— 5.4

= 16.5 – 7.5 + 3.2 Γ— 5.4, (Simplifying β€˜division’ 16.5 Γ· 2.2 = 7.5)

= 16.5 – 7.5 + 17.28, (Simplifying β€˜multiplication’ 3.2 Γ— 5.4 = 17.28)

= 9 + 17.28, (Simplifying β€˜subtraction’ 16.5 – 7.5 = 9)

= 26.28, (Simplifying β€˜addition’ 9 + 17.28 = 26.28)

Answer: 26.28


(b) 10.75 - [3.25 + 3 of (19.45 – 2.65 Γ— 6.75)]

Solution:

10.75 - [3.25 + 3 of (19.45 – 2.6 Γ— 6.7)]

= 10.75 - [3.25 + 3 of (19.45 – 17.42)], (Simplifying 2.6 Γ— 6.7 = 17.42)

= 10.75 - [3.25 + 3 of 2.03], (Simplifying 19.45 – 17.42 = 2.03)

= 1.75 - [3.25 + 3 Γ— 2.03], (Simplifying β€˜of’)

= 10.75 - [3.25 + 6.09], (Simplifying β€˜multiplication’ 3 Γ— 2.03 = 6.09)

= 10.75 – 9.34, (Simplifying β€˜square brackets’ 3.25 + 6.09 = 9.34)

= 1.41, (Simplifying β€˜subtraction’ 10.75 – 9.34 = 1.41)

Answer: 1.41


(c) 20.76 - 4 of (6.82 – 4.42) + 8.5 Γ— 3.4

Solution:

20.76 - 4 of (6.82 – 4.42) + 8.5 Γ— 3.4

= 20.76 - 4 of 2.4 + 8.5 Γ— 3.4, (Simplifying β€˜parenthesis’ 7 - 2 = 5)

= 20.76 - 4 Γ— 2.4 + 8.5 Γ— 3.4, (Simplifying β€˜of)

= 20.76 – 9.6 + 8.5 Γ— 3.4, (Simplifying β€˜multiplication’ 4 Γ— 2.4 = 9.6)

= 20.76 – 9.6 + 28.9, (Simplifying β€˜multiplication’ 8.5 Γ— 3.4 = 28.9)

= 11.16 + 28.9, (Simplifying β€˜subtraction’ 20.76 – 9.6 = 2)

= 22, (Simplifying β€˜addition’ 11.16 + 28.9 = 40.06)

Answer: 40.06

● Related Concept

● Decimals

● Decimal Numbers

● Decimal Fractions

● Like and Unlike Decimals

● Comparing Decimals

● Decimal Places

● Conversion of Unlike Decimals to Like Decimals

● Decimal and Fractional Expansion

● Terminating Decimal

● Non-Terminating Decimal

● Converting Decimals to Fractions

● Converting Fractions to Decimals

● H.C.F. and L.C.M. of Decimals

● Repeating or Recurring Decimal

● Pure Recurring Decimal

● Mixed Recurring Decimal

● BODMAS Rule

● BODMAS/PEMDAS Rules - Involving Decimals

● PEMDAS Rules - Involving Integers

● PEMDAS Rules - Involving Decimals

● PEMDAS Rule

● BODMAS Rules - Involving Integers

● Conversion of Pure Recurring Decimal into Vulgar Fraction

● Conversion of Mixed Recurring Decimals into Vulgar Fractions




7th Grade Math Problems

From PEMDAS Rules - Involving Decimals to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More

  2. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

    Jul 17, 25 12:40 AM

    Most and Least Perimeter
    Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

    Read More

  3. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 11:46 PM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  4. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

    Jul 16, 25 02:33 AM

    Perimeter of a Figure
    Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

    Read More

  5. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 15, 25 11:46 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More