# Mathematical Operations Flashcards

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(5/6) ÷ (1/3) = (5/6) * (3/1) = 15/6 = 2 3/6 = 2 1/2

5/13 ÷ 10 = (5/13) * (1/10) = 5/130 = 1/26

1/(4/17) = 17/4 = 4 1/4

The result of dividing the number one by a number

Example: the reciprocal of 5 is 1/5; the reciprocal of 3/5 is 1/(3/5) or 5/3

9 ÷ 1/3 = 9 * 3/1 = 27

(7/8) * 3 = 21/8 = 2 5/8

5/6 - 1/6 = 4/6 = 2/3

2 4/5 = 14/5 = 28/10

28/10 + 9/10 = 37/10 = 3 7/10

Order of operations: PE(MD)(AS)

Parentheses: 5 - 3 = 2, expression is now 2^3 * 4

Exponent: 2^3 = 8, expression is now 8 * 4

Multiplication: 8 * 4 = 32

The order of steps to solve mathematical expressions

PE(MD)(AS): *P*lease *E*xcuse *M*y *D*ear *A*unt *S*ally

Stands for parentheses, exponents, multiplication and division, addition and subtraction

Simplify parentheses, simplify exponents, simplify multiplication and division from left to right, simplify addition and subtraction from left to right

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## Flashcard Content Overview

When you see a complicated mathematical expression, the first thing to do is identify the operations present and determine the order in which they need to be solved. These flashcards will help you review that process. They will also help you review how to deal with tricky situations involving rational numbers, including decimals, improper fractions, and mixed numbers.

Simplify parentheses, simplify exponents, simplify multiplication and division from left to right, simplify addition and subtraction from left to right

The order of steps to solve mathematical expressions

PE(MD)(AS): *P*lease *E*xcuse *M*y *D*ear *A*unt *S*ally

Stands for parentheses, exponents, multiplication and division, addition and subtraction

Order of operations: PE(MD)(AS)

Parentheses: 5 - 3 = 2, expression is now 2^3 * 4

Exponent: 2^3 = 8, expression is now 8 * 4

Multiplication: 8 * 4 = 32

2 4/5 = 14/5 = 28/10

28/10 + 9/10 = 37/10 = 3 7/10

5/6 - 1/6 = 4/6 = 2/3

(7/8) * 3 = 21/8 = 2 5/8

9 ÷ 1/3 = 9 * 3/1 = 27

The result of dividing the number one by a number

Example: the reciprocal of 5 is 1/5; the reciprocal of 3/5 is 1/(3/5) or 5/3

1/(4/17) = 17/4 = 4 1/4

5/13 ÷ 10 = (5/13) * (1/10) = 5/130 = 1/26

(5/6) ÷ (1/3) = (5/6) * (3/1) = 15/6 = 2 3/6 = 2 1/2

An operation that cancels out another operation

Example inverse operation pairs: multiplication-division, addition-subtraction, exponent-root, logarithm-10^*x*

Inverse of 5^3 = cube root of 125

5^3 = 125; cube root of 125 = 5

A fraction in which the number in the numerator is greater than the number in the denominator

Improper fractions: numerator > denominator

11/5 and 4/3 are improper fractions

3 * 4 = 12 + 1 = 13

4 1/3 = 13/3

18 ÷ 7 = 2 remainder 4

18/7 = 2 4/7

A fraction that includes a whole number in addition to a numerator and a denominator

1 * 2 = 2

3 * 9 = 27

(1/3) * (2/9) = 2/27

2 1/5 = 11/5

4 = 4/1

11 * 4 = 44

5 * 1 = 5

(11/5) * 4 = 44/5 = 8 4/5

6 1/3 = 19/3

5 1/2 = 11/2

(19/3) * (11/2) = 209/6 = 34 5/6

(5/6) ÷ (1/4) = (5/6) * (4/1)

5 * 4 = 20

6 * 1 = 6

(5/6) ÷ (1/4) = 20/6 = 3 2/6 = 3 1/3

5 1/6 = 31/6

4 1/2 = 9/2

(31/6) ÷ (9/2) = (31/6) * (2/9)

31 * 2 = 62

6 * 9 = 54

(5 1/6) ÷ (4 1/2) = 62/54 = 1 8/54 = 1 4/27

Number of months: 12/year - 1 = 11 months

Expression: 5 1/3 * 11

5 1/3 = 16/3

11 = 11/1

16 * 11 = 176

3 * 1 = 3

5 1/3 * 11 = 176/3 = 58 2/3 books

Expression: 1 3/4 * 5

1 3/4 = 7/4

5 = 5/1

7 * 5 = 35

4 * 1 = 4

1 3/4 * 5 = 35/4 = 8 3/4 cups of flour

*A*: 3 1/4 yards = 13/4 yards

*B* = *A* + 3 1/2 yards = 13/4 + 7/2 = 13/4 + 14/4 = 27/4 = 6 3/4 yards

*C* = *B* + 2 1/2 yards = 27/4 + 5/2 = 27/4 + 10/4 = 37/4 = 9 1/4 yards

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Math 99: Essentials of Algebra and Statistics22 chapters | 127 lessons | 11 flashcard sets

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- Problem Solving & Math Models Flashcards
- Working with Integers & Exponents Flashcards
- Mathematical Operations Flashcards
- Equations, Expressions & Systems of Equations Flashcards
- Rational Numbers, Functions & Inequalities Flashcards
- Solving & Graphing Linear Equations Flashcards
- Understanding Basic Geometry Flashcards
- Basic Probability & Statistics Flashcards
- Understanding Graphs & Charts Flashcards
- Data Sets, Sequences & Unit Conversion Flashcards
- Math 99: Algebra & Statistics Formulas & Properties
- Go to Studying for Math 99