MATHEMATICS
Simple Algebra
Learning Outcomes
- Use and interpret algebraic notation
- Substitute numerical values into formulae and expressions
- Solve simple linear equations
What is Algebra?
Mixing letters with numbers!
Lets first look at what Algebra actually is:
We use letters as indicators for an unknown value or variable - (something that can change, so we don't know the value of it.....yet!) Commonly used letters are a, b, c, x, y, z but you can use any letter or symbol you like! For example, Expressions: b + 6 = 17 a x 3 = 24 72/y = 9 c - 12 = 18 Equations: y = x + 4 b = a - 2 z = x + y q = f + k
What is Algebra?
Mixing letters with numbers! (Section 1)
Imagine - Bob has a drawer full of odd socks, he knows that there are 12 socks in total and he knows that there is a certain number of pairs.
= 12
Using Algebra - we can create an expression to represent how to calculate the number of Pairs
If the total number of socks is represented by the letter x and the number of pairs y
and we know that there are 2 socks in a pair, what would our expression be?
x = y/2
Once we have this equation, we can substitute the letter y, with any number of socks and find out how many pairs we can get!
In the previous example, there were 12 socks (y), so if we substitute into our expression we get: x= 12/2, so, x = ?
x = y/2
However, Bob opens the second drawer down and discovers there are another 42 socks in there, with the 12 he already has, he now has 12 + 42 socks.Which is how many?
If we now substitute the new number into our expression we get:
x = 54/2 x = ?
Let's remind ourselves of some more basics:
a + a = 2 x a b + b + b + b + b = 5 x b 2 x a can be written as 2a 5 x b can be written as 5b By putting a number before an algebraic letter, we are stating that there are that many of the given variable
What about minus operators?
a + a = 2 x ab + b + b + b + b = 5 x b And Division? a/2 = 1/2 a 6a/3 = 2a
Let's put some of these ideas into practice!
Using what you know now, can you help solve the following expressions to find the value of x:1. x + 5 = 10 2. x + 17 = 25 3. x - 6 = 14 4. x - 8 = 16 5. 2x = 16 6. 7x = 28 7. 9x = 63 8. x/ 4 = 8 9. x/7 = 5 10. BONUS Question - x3 = 8
Some Key Terms: Complete Section 3
· Solve - Finding the numerical value of all variables
· Coefficient - A number that multiplies a variable. In "2x," the "2" is the coefficient
· Subject - The term that is being defined by an equation, and therefore appears by itself on one half of the equation.
· Equation - A mathematical expression that includes an equals "=" symbol.
· Substitution - When you replace variables (letters) in an equation with numerical values.
· Expression - A mathematical statement i.e. a group of terms
· Term - One part of an equation. This can be a number, a variable, or a number multiplied with one or more variables
· Formula - A mathematical rule to explain the relationship between different terms. They use letters to represent changeable quantities.
· Variable - A letter or symbol that stands in for a number in an equation.
Sometimes you need to work out the formula yourself!
Question 1
Question 3
Question 2
A carpenter has a 3 metre length of studwork, which she needs to cut into 6 equal lengths, What length should she measure?She also needs to work out how many pieces she can get from a delivery of 900 metres.
The farm shop sells eggs for £3.60 per 6 eggs, allows customers to buy any number of eggs. How much would customers pay for 13, 27 and 33 eggs?
A farmer and his team can harvest 4 Fields in 1 day, how many can they harvest in 7 days, 22 days and 30 days?
THANKS!
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Nicholas Reynolds
Created on March 25, 2024
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Transcript
MATHEMATICS
Simple Algebra
Learning Outcomes
What is Algebra?
Mixing letters with numbers!
Lets first look at what Algebra actually is:
We use letters as indicators for an unknown value or variable - (something that can change, so we don't know the value of it.....yet!) Commonly used letters are a, b, c, x, y, z but you can use any letter or symbol you like! For example, Expressions: b + 6 = 17 a x 3 = 24 72/y = 9 c - 12 = 18 Equations: y = x + 4 b = a - 2 z = x + y q = f + k
What is Algebra?
Mixing letters with numbers! (Section 1)
Imagine - Bob has a drawer full of odd socks, he knows that there are 12 socks in total and he knows that there is a certain number of pairs.
= 12
Using Algebra - we can create an expression to represent how to calculate the number of Pairs
If the total number of socks is represented by the letter x and the number of pairs y
and we know that there are 2 socks in a pair, what would our expression be?
x = y/2
Once we have this equation, we can substitute the letter y, with any number of socks and find out how many pairs we can get!
In the previous example, there were 12 socks (y), so if we substitute into our expression we get: x= 12/2, so, x = ?
x = y/2
However, Bob opens the second drawer down and discovers there are another 42 socks in there, with the 12 he already has, he now has 12 + 42 socks.Which is how many?
If we now substitute the new number into our expression we get:
x = 54/2 x = ?
Let's remind ourselves of some more basics:
a + a = 2 x a b + b + b + b + b = 5 x b 2 x a can be written as 2a 5 x b can be written as 5b By putting a number before an algebraic letter, we are stating that there are that many of the given variable
What about minus operators?
a + a = 2 x ab + b + b + b + b = 5 x b And Division? a/2 = 1/2 a 6a/3 = 2a
Let's put some of these ideas into practice!
Using what you know now, can you help solve the following expressions to find the value of x:1. x + 5 = 10 2. x + 17 = 25 3. x - 6 = 14 4. x - 8 = 16 5. 2x = 16 6. 7x = 28 7. 9x = 63 8. x/ 4 = 8 9. x/7 = 5 10. BONUS Question - x3 = 8
Some Key Terms: Complete Section 3
· Solve - Finding the numerical value of all variables
· Coefficient - A number that multiplies a variable. In "2x," the "2" is the coefficient
· Subject - The term that is being defined by an equation, and therefore appears by itself on one half of the equation.
· Equation - A mathematical expression that includes an equals "=" symbol.
· Substitution - When you replace variables (letters) in an equation with numerical values.
· Expression - A mathematical statement i.e. a group of terms
· Term - One part of an equation. This can be a number, a variable, or a number multiplied with one or more variables
· Formula - A mathematical rule to explain the relationship between different terms. They use letters to represent changeable quantities.
· Variable - A letter or symbol that stands in for a number in an equation.
Sometimes you need to work out the formula yourself!
Question 1
Question 3
Question 2
A carpenter has a 3 metre length of studwork, which she needs to cut into 6 equal lengths, What length should she measure?She also needs to work out how many pieces she can get from a delivery of 900 metres.
The farm shop sells eggs for £3.60 per 6 eggs, allows customers to buy any number of eggs. How much would customers pay for 13, 27 and 33 eggs?
A farmer and his team can harvest 4 Fields in 1 day, how many can they harvest in 7 days, 22 days and 30 days?
THANKS!