Understanding the properties of equality is very important when solving linear equations, especially in GCSE Year 2 math. There are four main properties that students need to learn. These properties help you solve equations accurately and consistently. They are:
Each one lets you do things to both sides of an equation without changing the equality.
The Addition Property of Equality says that if you add the same number to both sides of an equation, the two sides stay equal.
You can write this as:
If ( a = b ), then ( a + c = b + c ).
This property is really helpful for isolating variables. For example, in the equation ( x - 5 = 10 ), you can use the Addition Property by adding 5 to both sides:
( x - 5 + 5 = 10 + 5 )
So, you get:
( x = 15 ).
The Subtraction Property of Equality works in a similar way. It says that if you subtract the same number from both sides of an equation, they stay equal.
You can write this as:
If ( a = b ), then ( a - c = b - c ).
This property is useful when you have equations that involve adding the variable. For example, in the equation ( x + 8 = 20 ), we can subtract 8 from both sides:
( x + 8 - 8 = 20 - 8 )
Now you get:
( x = 12 ).
The Multiplication Property of Equality says that if you multiply both sides of an equation by the same number (but not zero), the sides will still be equal.
You can write this as:
If ( a = b ), then ( a \cdot c = b \cdot c ).
This property is really helpful when you have numbers in front of the variable. For example, if you have the equation ( \frac{x}{3} = 4 ), you can get rid of the fraction by multiplying both sides by 3:
( 3 \cdot \frac{x}{3} = 4 \cdot 3 )
This gives you:
( x = 12 ).
The Division Property of Equality says that if you divide both sides of an equation by the same number (but not zero), they will still be equal.
You can write this as:
If ( a = b ), then ( \frac{a}{c} = \frac{b}{c} ) (where ( c \neq 0 )).
This property is useful for equations where the variable is multiplied. For example, if you have the equation ( 5x = 20 ), you can solve it by dividing both sides by 5:
( \frac{5x}{5} = \frac{20}{5} )
So, you find:
( x = 4 ).
These four properties of equality—Addition, Subtraction, Multiplication, and Division—are key skills for solving linear equations in math.
Getting a good grasp of these properties helps students in their GCSE studies and prepares them for tougher math concepts in the future.
When you use these properties correctly, they provide a clear way to find the value of variables in equations. With practice, students can improve their problem-solving skills and gain confidence in working with linear equations, which sets the stage for exploring more complex math later on.
Understanding the properties of equality is very important when solving linear equations, especially in GCSE Year 2 math. There are four main properties that students need to learn. These properties help you solve equations accurately and consistently. They are:
Each one lets you do things to both sides of an equation without changing the equality.
The Addition Property of Equality says that if you add the same number to both sides of an equation, the two sides stay equal.
You can write this as:
If ( a = b ), then ( a + c = b + c ).
This property is really helpful for isolating variables. For example, in the equation ( x - 5 = 10 ), you can use the Addition Property by adding 5 to both sides:
( x - 5 + 5 = 10 + 5 )
So, you get:
( x = 15 ).
The Subtraction Property of Equality works in a similar way. It says that if you subtract the same number from both sides of an equation, they stay equal.
You can write this as:
If ( a = b ), then ( a - c = b - c ).
This property is useful when you have equations that involve adding the variable. For example, in the equation ( x + 8 = 20 ), we can subtract 8 from both sides:
( x + 8 - 8 = 20 - 8 )
Now you get:
( x = 12 ).
The Multiplication Property of Equality says that if you multiply both sides of an equation by the same number (but not zero), the sides will still be equal.
You can write this as:
If ( a = b ), then ( a \cdot c = b \cdot c ).
This property is really helpful when you have numbers in front of the variable. For example, if you have the equation ( \frac{x}{3} = 4 ), you can get rid of the fraction by multiplying both sides by 3:
( 3 \cdot \frac{x}{3} = 4 \cdot 3 )
This gives you:
( x = 12 ).
The Division Property of Equality says that if you divide both sides of an equation by the same number (but not zero), they will still be equal.
You can write this as:
If ( a = b ), then ( \frac{a}{c} = \frac{b}{c} ) (where ( c \neq 0 )).
This property is useful for equations where the variable is multiplied. For example, if you have the equation ( 5x = 20 ), you can solve it by dividing both sides by 5:
( \frac{5x}{5} = \frac{20}{5} )
So, you find:
( x = 4 ).
These four properties of equality—Addition, Subtraction, Multiplication, and Division—are key skills for solving linear equations in math.
Getting a good grasp of these properties helps students in their GCSE studies and prepares them for tougher math concepts in the future.
When you use these properties correctly, they provide a clear way to find the value of variables in equations. With practice, students can improve their problem-solving skills and gain confidence in working with linear equations, which sets the stage for exploring more complex math later on.