Subjects

Maths

Algebra

Expressions & formulae

Free Maths Notes PDF & Fun Guides for Kids

Name: Knowunity
Brand: Knowunity

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Free Maths Notes PDF & Fun Guides for Kids

Lauren Edwards

@laurenedwards_gdhx

11 Followers

This document covers key mathematical concepts including multiplying numbers without decimals, estimating significant figures calculations, and converting numbers to standard form. It provides detailed explanations, examples, and practice problems to help students master these important mathematical skills.

• The content focuses on decimal operations, powers of 10, estimation techniques, and standard form notation.
• It includes step-by-step instructions for performing calculations and converting between different numerical representations.
• Practice problems are provided throughout to reinforce learning and application of concepts.
• The material is suitable for students learning advanced arithmetic and pre-algebra skills.

28/02/2023

1597

<p>When multiplying without decimals, the answer will have the same number of decimal places as the question. For example, 0.007 x 0.03 = 0

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Expanding and Simplifying Expressions

This page covers techniques for expanding and simplifying algebraic expressions.

Key concepts:

Expanding brackets in algebraic expressions
Simplifying expressions by combining like terms
Solving equations

Example: (3x + 1)(x + 2) = 3x^2 + 6x + x + 2 = 3x^2 + 7x + 2

The page also includes a section on solving word problems, including a problem about sets and probability using Venn diagrams.

Vocabulary: Venn diagram - A diagram that shows all possible logical relations between a finite collection of different sets.

View

Solving Inequalities

This final page focuses on techniques for solving inequalities, also known as compound inequalities.

Key steps:

Isolate the variable term
Solve each part of the inequality separately
Combine the solutions

Example: -7 ≤ 3x ≤ 4 Solving: -7/3 ≤ x ≤ 4/3 -2.33 ≤ x ≤ 1.33

The page includes several practice problems for students to apply these techniques and gain proficiency in solving inequalities.

Highlight: When solving inequalities, remember that the direction of the inequality sign changes when multiplying or dividing by a negative number.

View

Inequalities

This page introduces the concept of inequalities and how to represent them graphically.

Key symbols:

< : less than
: greater than
≤ : less than or equal to
≥ : greater than or equal to
≠ : not equal to

Definition: Inequality - A mathematical statement that compares two expressions using inequality symbols.

The page includes a number line representation of inequalities and introduces the concept of compound inequalities.

View

Practice Problems and Conversions

This page provides a series of practice problems focused on converting numbers to and from standard form.

Key points:

Converting large numbers to standard form
Converting small numbers (less than 1) to standard form
Adjusting the power of 10 when moving the decimal point

Highlight: When converting to standard form, remember that the number before the power of 10 must be between 1 and 10.

Example: 0.000074 = 7.4 x 10^-5

The page also includes rules for manipulating powers of 10:

To make a number smaller, add to the power
To make a number bigger, subtract from the power

View

Standard Form Operations

This page focuses on operations with numbers in standard form, including addition, subtraction, multiplication, and division.

Key techniques:

Rewriting numbers to the same power of 10 before adding or subtracting
Adding or subtracting the numbers, keeping the power of 10 the same
Checking if the result is in standard form and adjusting if necessary

Example: (1.87 x 10^4) + (6.24 x 10^3)

Rewrite to largest power: 1.87 x 10^4 + 0.624 x 10^4

Add: 2.494 x 10^4

Result is already in standard form

The page includes multiple practice problems for students to work through, reinforcing the concepts of standard form operations.

View

Multiplying and Dividing in Standard Form

This page covers techniques for multiplying and dividing numbers in standard form.

Key rules:

When multiplying, add the powers of 10
When dividing, subtract the powers of 10
Always check if the result is in standard form and adjust if necessary

Example: (7 x 10^20) x (8 x 10^19) = 56 x 10^39 = 5.6 x 10^40

Highlight: Remember that 10^a x 10^b = 10^(a+b)

The page includes several practice problems for students to apply these rules and gain confidence in working with standard form.

View

Decimal Operations and Powers of 10

This page covers techniques for multiplying and dividing decimals, as well as working with powers of 10.

Key points:

When multiplying decimals, the answer will have the same number of decimal places as the question.
To divide decimals, make the divisor a whole number by multiplying both numbers by a power of 10.
Powers of 10 are used to represent very large or very small numbers.

Example: 0.007 x 0.03 = 0.00021 (5 decimal places)

Highlight: When estimating, round each number to one significant figure unless there are decimals involved.

Vocabulary: Significant figure - The digits of a number that carry meaning contributing to its measurement precision.

The page also covers techniques for rounding to the nearest perfect square and estimating calculations involving large numbers.

View

Standard Form and Powers of 10

This page delves deeper into standard form and the use of powers of 10 to represent very large or small numbers.

Key concepts:

Standard form expresses a number as a value between 1 and 10 multiplied by a power of 10.
Positive powers of 10 represent big numbers, while negative powers represent small numbers.
Converting between standard form and regular notation.

Definition: Standard form - A way of writing very large or very small numbers in scientific notation, expressed as a x 10^n, where 1 ≤ a < 10 and n is an integer.

Example: 1,735,000 = 1.735 x 10^6

The page includes multiple examples of converting numbers to and from standard form, as well as practice problems for students to work through.

View

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Subjects

Maths

Algebra

Expressions & formulae

Free Maths Notes PDF & Fun Guides for Kids

Lauren Edwards

@laurenedwards_gdhx

11 Followers

28/02/2023

1597

Maths

124

Expanding and Simplifying Expressions

This page covers techniques for expanding and simplifying algebraic expressions.

Key concepts:

Expanding brackets in algebraic expressions
Simplifying expressions by combining like terms
Solving equations

Example: (3x + 1)(x + 2) = 3x^2 + 6x + x + 2 = 3x^2 + 7x + 2

The page also includes a section on solving word problems, including a problem about sets and probability using Venn diagrams.

Vocabulary: Venn diagram - A diagram that shows all possible logical relations between a finite collection of different sets.

Solving Inequalities

This final page focuses on techniques for solving inequalities, also known as compound inequalities.

Key steps:

Isolate the variable term
Solve each part of the inequality separately
Combine the solutions

Example: -7 ≤ 3x ≤ 4 Solving: -7/3 ≤ x ≤ 4/3 -2.33 ≤ x ≤ 1.33

The page includes several practice problems for students to apply these techniques and gain proficiency in solving inequalities.

Highlight: When solving inequalities, remember that the direction of the inequality sign changes when multiplying or dividing by a negative number.

Inequalities

This page introduces the concept of inequalities and how to represent them graphically.

Key symbols:

< : less than
: greater than
≤ : less than or equal to
≥ : greater than or equal to
≠ : not equal to

Definition: Inequality - A mathematical statement that compares two expressions using inequality symbols.

The page includes a number line representation of inequalities and introduces the concept of compound inequalities.

Practice Problems and Conversions

This page provides a series of practice problems focused on converting numbers to and from standard form.

Key points:

Converting large numbers to standard form
Converting small numbers (less than 1) to standard form
Adjusting the power of 10 when moving the decimal point

Highlight: When converting to standard form, remember that the number before the power of 10 must be between 1 and 10.

Example: 0.000074 = 7.4 x 10^-5

The page also includes rules for manipulating powers of 10:

To make a number smaller, add to the power
To make a number bigger, subtract from the power

Standard Form Operations

This page focuses on operations with numbers in standard form, including addition, subtraction, multiplication, and division.

Key techniques:

Rewriting numbers to the same power of 10 before adding or subtracting
Adding or subtracting the numbers, keeping the power of 10 the same
Checking if the result is in standard form and adjusting if necessary

Example: (1.87 x 10^4) + (6.24 x 10^3)

Rewrite to largest power: 1.87 x 10^4 + 0.624 x 10^4

Add: 2.494 x 10^4

Result is already in standard form

The page includes multiple practice problems for students to work through, reinforcing the concepts of standard form operations.

Multiplying and Dividing in Standard Form

This page covers techniques for multiplying and dividing numbers in standard form.

Key rules:

When multiplying, add the powers of 10
When dividing, subtract the powers of 10
Always check if the result is in standard form and adjust if necessary

Example: (7 x 10^20) x (8 x 10^19) = 56 x 10^39 = 5.6 x 10^40

Highlight: Remember that 10^a x 10^b = 10^(a+b)

The page includes several practice problems for students to apply these rules and gain confidence in working with standard form.

Decimal Operations and Powers of 10

This page covers techniques for multiplying and dividing decimals, as well as working with powers of 10.

Key points:

When multiplying decimals, the answer will have the same number of decimal places as the question.
To divide decimals, make the divisor a whole number by multiplying both numbers by a power of 10.
Powers of 10 are used to represent very large or very small numbers.

Example: 0.007 x 0.03 = 0.00021 (5 decimal places)

Highlight: When estimating, round each number to one significant figure unless there are decimals involved.

Vocabulary: Significant figure - The digits of a number that carry meaning contributing to its measurement precision.

The page also covers techniques for rounding to the nearest perfect square and estimating calculations involving large numbers.

Standard Form and Powers of 10

This page delves deeper into standard form and the use of powers of 10 to represent very large or small numbers.

Key concepts:

Standard form expresses a number as a value between 1 and 10 multiplied by a power of 10.
Positive powers of 10 represent big numbers, while negative powers represent small numbers.
Converting between standard form and regular notation.

Definition: Standard form - A way of writing very large or very small numbers in scientific notation, expressed as a x 10^n, where 1 ≤ a < 10 and n is an integer.