Special Cases Order of Operations Practice with Fractions

Master order of operations with special cases including 0, 1, inverse, and fraction lines. Practice PEMDAS/BODMAS with fractions, decimals, and reciprocals.

馃摎Practice Order of Operations with Special Cases and Fractions
  • Apply PEMDAS/BODMAS rules when working with fractions and decimal numbers
  • Solve expressions involving 0 and 1 as special case multipliers
  • Master operations with reciprocals and inverse fraction calculations
  • Handle fraction bars as grouping symbols in complex expressions
  • Practice left-to-right evaluation of equal-priority operations with fractions
  • Simplify mixed number results from fraction order of operations

Understanding Order or Hierarchy of Operations with Fractions

Complete explanation with examples

Order or Hierarchy of Operations with Fractions

Fractions do not influence the order of operations, therefore, you should treat them like any other number in the exercise.

The correct order of mathematical operations is as follows:

  1. Parentheses
  2. Multiplications and divisions in the order they appear in the exercise
  3. Additions and subtractions in the order they appear in the exercise

Comprehensive explanation of BODMAS/PEMDAS rules with additional notes: fraction bars treated as parentheses and inclusion of reciprocal numbers, detailing brackets, order, division, multiplication, addition, and subtraction in mathematical operations.

Detailed explanation

Practice Order or Hierarchy of Operations with Fractions

Test your knowledge with 21 quizzes

Solve the following exercise:

\( 2+0:3= \)

Examples with solutions for Order or Hierarchy of Operations with Fractions

Step-by-step solutions included
Exercise #1

0+0.2+0.6= 0+0.2+0.6= ?

Step-by-Step Solution

According to the order of operations, the exercise is solved from left to right as it contains only an addition operation:

0+0.2=0.2 0+0.2=0.2

0.2+0.6=0.8 0.2+0.6=0.8

Answer:

0.8

Video Solution
Exercise #2

12+30= 12+3\times0=

Step-by-Step Solution

According to the order of operations, we first multiply and then add:

30=0 3\times0=0

12+0=12 12+0=12

Answer:

12

Video Solution
Exercise #3

12+1+0= 12+1+0= ?

Step-by-Step Solution

According to the order of operations, the exercise is solved from left to right as it only involves an addition operation:

12+1=13 12+1=13

13+0=13 13+0=13

Answer:

13

Video Solution
Exercise #4

9(21)= 9 \times (2 \times 1) =

Step-by-Step Solution

First, calculate the expression within the parentheses:

21=2 2 \times 1 = 2

Now, multiply the result by 9:

92=18 9 \times 2 = 18

Thus, the final answer is 18.

Answer:

18

Exercise #5

8(51)= 8\times(5\times1)=

Step-by-Step Solution

According to the order of operations, we first solve the expression in parentheses:

51=5 5\times1=5

Now we multiply:

85=40 8\times5=40

Answer:

40

Video Solution

Frequently Asked Questions

Do fractions change the order of operations rules?

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No, fractions do not change the order of operations. You treat fractions like any other number and follow PEMDAS/BODMAS: parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right.

How do you handle fraction bars in order of operations?

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Fraction bars act as grouping symbols, similar to parentheses. You must complete all operations in the numerator and denominator separately before dividing. This gives fraction bars higher priority than regular division symbols.

What happens when you multiply or divide by 0 in order of operations?

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When multiplying any number by 0, the result is always 0, regardless of other operations. Division by 0 is undefined and cannot be performed. These special cases follow normal order of operations timing.

How do you solve order of operations with reciprocals?

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Reciprocals (like 1/3 or inverse fractions) follow the same order of operations rules. Multiply by the reciprocal instead of dividing by the original fraction. For example, 梅(2/3) becomes 脳(3/2).

Why does multiplying by 1 not change the order of operations?

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Multiplying by 1 gives the identity property - any number times 1 equals itself. This doesn't change the order of operations, but it can simplify expressions. You still perform multiplication at the correct step in PEMDAS/BODMAS.

What's the correct order for: 3 + 6 脳 1/3?

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Follow PEMDAS: multiplication before addition. First calculate 6 脳 1/3 = 2, then add: 3 + 2 = 5. The fraction 1/3 is treated as a regular number in the multiplication step.

How do you handle decimal fractions in order of operations?

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Decimal fractions (like 0.3 or 0.5) follow identical order of operations rules as common fractions. There's no difference in priority - both are simply numbers that get processed according to PEMDAS/BODMAS timing.

When do you simplify fractions during order of operations?

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Simplify fractions after completing each operation step, not before following order of operations. For example, if you get 8/8 during multiplication step, simplify it to 1, then continue with the next operation in sequence.

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