ISEE Middle Level Math

ISEE Middle Level Math covers essential mathematical concepts and problem-solving skills needed for middle school students preparing for the ISEE exam.

Number Operations & PropertiesFractions, Decimals, and PercentsRatios, Proportions, and Rates
Algebraic Expressions & EquationsGeometry: Area, Perimeter, and VolumeData Analysis & Probability
Budgeting and Money MathTravel and Distance ProblemsCooking and Recipes
Time Management During the TestElimination and Guessing
Number Operations & ...Fractions, Decimals,...Ratios, Proportions,...Algebraic Expression...Geometry: Area, Peri...Data Analysis & Prob...Budgeting and Money ...Travel and Distance ...Cooking and RecipesTime Management Duri...Elimination and Gues...
Basic Concepts

Number Operations & Properties

Understanding Numbers

Numbers are everywhere! From counting your steps to figuring out the cost of lunch, you use numbers every day. In math, it's important to understand how numbers work and how you can manipulate them.

Types of Numbers

  • Whole numbers: 0, 1, 2, 3, ...
  • Integers: ..., -2, -1, 0, 1, 2, ...
  • Fractions: \( \frac{3}{4} \), \( \frac{1}{2} \)
  • Decimals: 0.5, 2.75, 10.0

Operations

The four basic operations are:

  • Addition
  • Subtraction
  • Multiplication
  • Division

It's important to remember the order of operations, often remembered as PEMDAS:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (left to right)
  4. Addition and Subtraction (left to right)

Properties

Some important properties help you solve problems:

  • Commutative Property: \( a + b = b + a \)
  • Associative Property: \( (a + b) + c = a + (b + c) \)
  • Distributive Property: \( a \times (b + c) = a \times b + a \times c \)

Why It Matters

Mastering number operations makes everyday tasks easier, like budgeting, shopping, or cooking!

Key Formula

\[a \times (b + c) = a \times b + a \times c\]

Examples

  • Adding fractions: \( \frac{1}{4} + \frac{1}{2} = \frac{3}{4} \)

  • Using the distributive property: \( 3 \times (2 + 5) = 3 \times 2 + 3 \times 5 = 21 \)

In a Nutshell

Number operations and properties are the building blocks of all math.

Key Terms

Commutative Property
A property where the order doesn't affect the result, like \( a + b = b + a \).
Associative Property
A property where how you group numbers doesn't affect the result, like \( (a + b) + c = a + (b + c) \).
Distributive Property
A property that lets you multiply a number by a group of numbers, like \( a \times (b + c) = a \times b + a \times c \).
Next
Fractions, Decimals, and Percents