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Linear equations with multiplication and division

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

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Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

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Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with Polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

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- Hi. Welcome to this question right here. So we're trying to solve the equations. Now, when you hear the word solving, it means you want to figure out what the x equals to, right? So basically, you have to remove anything that's around the x. So far you see there's a three beside it. Now, as you can see, the three is multiplied to the x, right? So if you want to remove the three, you're going to have to do something that's called the opposite. Okay? So what's the opposite of multiplying? It's dividing. So that means you have to divide the three away from the x. 
So if I'm going to show you all the work here, which I would, then you would just simply divide three to both sides. So negative nine over seven right here, if you divide it by three, you can actually just put divided by three here if you want. Okay? Now, this will cancel. Now, it's not the seven over three. It's the nine over seven divided by three. Now, somehow it looks kind of confusing, but technically when you divide. . . if you take a fraction and if you divide it by another number, you can actually just pretend that three is just down here. Okay? It's actually negative nine over seven, the original fraction, and there's a three right beside the seven. It's a denominator because you're dividing it. Okay? So you're left with just the x on this side and it's nine over three times the seven here. Or you can figure out the work between the seven and the three, which is 21, and then you will have this simplified at the end, which is nine over 21 will give you three over seven. So it's negative three over seven. And that will be your final answer, which is right here. Now, sometime the people don't like the idea where you have to divide both sides by the three. So what we can do is we can do something that's called the cross multiplying. So let's try this question one more time. Negative nine over seven is equal to 3x, right? So if you have two fractions. . . It doesn't have to be fractions, just two different terms on either side of the equation, which is the equal sign here. What you can do is you can actually do something that's called cross multiplying. So the cross multiplying meaning that if you pretend. . . Well, this 3x, technically there's a one underneath. What you can do is you can take the three here and you can multiply it to the bottom down here. It's called the cross multiply because if you're going to multiply, you have to go across. Now, you can go downwards, you can do upwards, you can go this way or this way. But again, remember you want to keep the x by itself. So we're not going to touch the x. We're just going to move the three down this way. So the three will be multiplied to the seven. So you're going to end up with exactly the same number and exactly the same answer, which is negative three over seven. Okay. Just two different methods for you to choose from. Thanks for watching.

In the previous lessons, we have learned what a linear relationship is and its graphs and tables. In this lesson here, we will then learn how to solve one-step linear equations by multiplication and division.


Solving linear equations using multiplicattion and division

Evaluating algebraic expressions

Solving one - step equations: x + a = b