Variables (Level 2)
Alright let's jump straight into some examples.
Tell whether each statement is true or false and explain your reasoning.
seven times five is equal to to twenty plus 15
Alright so the first thing we need to do is we need to simpify each side of the expression
to be able to compare them.
The left hand side simplifies to 35 and the right hand side simplifies to 35.
Since 35 is equal to 35 this is a true statement.
How about the next statement?
Three plus three does not equal three times three. Once again we need to simplify,
each side of the statement in order to approprietly compare them
the left hand side simplifies to 6 and the right hand side simplifies to 9.
6 does not equal to 9.
This is true. Let's try the next statement.
4 times 0 is equal to 0 times 6.
Again we need to simplify each expression to appropriately compare them.
The left hand side simplifies to 0, and the right hand side simplifies to 0,
and it turns out that 0 is equal to 0. This statement is absolutely true.
Alright let's try the next statement. 8 divided by one does not equal 1 divided by 8.
Like always we need to simplify each side of the expression,
the left hand side simplifies to 8 and the right hand side simplifies to 1 over 8.
So the statement simplifies to 8 does not equal to 1/8,
and this is once again true. 8 does not equal 1/8.
How about the next statement?
54 times 1/2 does not equal 54 times 0.5.
We need to simplify each side of the statement to compare them the left hand side simplifies to 27
and the right hand side also simplifies to 27.
Remember that the decimal 0.5 can be rewritten as 1/2.
So the statement simplifies to 27 does not equal 27.
This is absolutely false.
27 does not equal 27.
27 actually equals 27, so this statement is false.
Alright now let's work on simplifying numerical expressions.
Simplify the expression the quantity 8 minus 3 plus 3.
The expression in the parenthesis is simplified first.
So doing that we have that 8 minus 3 is equal to 5
and we add 3 to the result.
Which simplifies to 8.
Alright so let's simplify the expression 5 times the quantity 11 plus 1.
Once again the expression within the parenthesis is simplified first.
So we have that 11 plus 1 is equal to 12,
and then we multiply that by 5 which is equal to 60.
Alright let's try the next expression. 6 plus the quantity 12 divided by 3.
We work with the parenthesis first so we get that 12 divided by 3 is equal to 4.
We add that to 6 which is equal to 10.
Try the next one, 29 minus the quantity 0 times 9.
Zero times anything is always equal to zero.
So this simplifies to 29 minus 0 which is equal to 29.
Alright let's try the next example, simplify the quantity 12 times 10 minus 2 times 11.
So here we have an expression with 2 parenthesis.
So left hand side reduces to 120,
and the right hand side reduces to 22, and now we subtract these two quantities,
and now we have 120 minus 22 which simplifies to 98.
Let's try the next one.
Simplify the quantity 40 divided by 10 divided by 1 times 4.
So here once again we simplify the expressions within the parenthesis.
So the left hand parenthesis simplifies to 4,
and the right expression within the parenthesis simplifies to 4.
So now we need to simplify 4 divided by 4 which is equal to 1.
Now let's practice evaluating expressions. Evaluate each expression
if x = 1, y = 2, and z = 3.
Notice that we have three different variables and each and variable has a corresponding value.
The goal is to use these expressions to substitute the values of these variables
into the following expressions. Ok, so first expression is
5x, the variable here is x, so we need to substitute x
with the corresponding value in this case it's equal to 1,
and always we use parenthesis to substitute any variables
this is going to be key as we work with more complicated algebraic expressions.
So now we evaluate the expression, so 5 times 1 simplifies to 5.
Let's try the next variable expression, x times y.
So once again we substitute each variable, in this case we have two different variables, x and y.
So x is actually equal to 1, and y is equal to 2.
So substituting the expressions we have the following, and now we simplify the expression
and it turns out that it is equal to 2.
Let's try the next variable expression.
3y minus 6, so here notice that we have a parenthesis,
we need to work on these expressions first, so first of all we need to substitute the variable in this case y,
with two and as always make sure you use parenthesis when you are substituting
so now we have three times 2 which simplifies to 6,
and then 6 minus 6 is equal to 0.
Let's try the next expression.
The quantity 3 time z minus the quantity 4 times x.
So here we have 2 parenthesis we need to work on each one before we subtract them.
So first of all we need to substitute z with 3,
again using parenthesis and substitute x with 1.
Left hand side simplifies to 9 and the right hand side simplifies to 4.
Subtracting these two values we have that the final answer is equal to 5.
Let's try the next expression.
One half times the quantity z minus x. We need to work with the values in the parenthesis first.
So we substitute each value and we have 3 minus 1 which is equal to 2.
and then 2 times 1/2 is just equal to 2/2 which reduces 1.
Let's try the next expression.
Simplify the quantity z plus y over z minus y.
We substitute each variable with the appropriate value.
So we have the quantity 3 plus 2 which is equal to 5.
Over the quantity 3 minus 2 which is equal to 1.
5 over 1 reduces to 5.
Let's try the final variable expression.
Simplify the expression 8 plus the quantity 9 times x times y or 9xy.
We need to substitute the variables with the appropriate value.
In this case x = 1 and y = 2
So we evaluate the quantity in the parenthesis first, that expression simplifies to 18,
and we add 8 to that.
So we have that the final answer is equal to 26.
Alright in our next video we will learn how to simplify expressions with and without grouping symbols.