Lesson video

Hi, I'm Miss Davies.

In this lesson we're going to be substituting negative terms into formula.

In this first example, we have been given that a is equal to negative five and b is equal to negative seven.

The first part, we've been asked to work out the value of four a.

This means four multiplied by a.

By substituting negative five in four a, we can rewrite this as four multiplied by negative five.

This gives us an answer of negative 20.

Our next question is seven a subtract three.

This can be rewritten as seven multiplied by negative five subtract three.

This is equivalent to negative 35 subtract three.

This gives us an answer of negative 38.

Our final question is to work out the value of a squared subtract b.

By substituting in the values, we can rewrite this as negative five squared subtract negative seven.

Negative five squared means negative five multiplied by negative five.

This gives 25.

This is equivalent to 25 add seven, as subtracting a negative is the same as adding.

This gives us an answer of 32.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Make sure you are following the order of operations to complete these calculations.

The first thing you need to do is complete any calculations in brackets.

Then complete any calculations that involve indices or powers.

This is then followed by multiplication and division, and finally, addition and subtraction.

In this next example we have been given the formula t is equal to negative three k.

Negative three k means negative three multiplied by k.

We've been asked to find the value of t when k is equal to negative four.

We can substitute this value into our formula to give t is equal to negative three multiplied by negative four.

This gives a solution of t equals 12.

In the next part of this question we have been asked to find the value of k when t is equal to 51.

If we substitute this into our formula, it gives us 51 is equal to negative three multiplied by k.

To solve this equation to find the value of k, we're going to use inverse operations.

The inverse of multiplying by negative three is dividing by negative three.

We can find the value of k by calculating 51 divided by negative three.

This gives a solution of k is equal to negative 17.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

After substituting the values into part a, you are left with the calculation four multiplied by negative two subtract seven.

This simplifies to negative eight subtract seven, which gives the answer of y equals negative 15.

In part b, after substituting in the values, you've got the equation negative 17 equals four f subtract seven.

To solve this equation, we're going to start off by adding seven to both sides.

This gives negative 10 is equal to four f.

To find the solution for f, you need to divide both sides by four.

Negative 10 divided by four is negative 2.

5.

In this next example we have been given the formula t equals three k squared.

We're going to find the value of t when k equals negative four.

We need to follow the order of operations and work out negative four squared before multiplying it by three.

Negative four squared means negative four multiplied by negative four, which is 16.

This means that t is equal to 48.

In the next part we're going to find the value of k when t is equal to 363.

If we substitute this into the formula, we get 363 is equal to three multiplied by k squared.

Using inverse operations, we're going to solve this equation.

The inverse of multiplying by three is dividing by three.

This means that k squared is equal to 121.

To find k, we're going to find the square root of 121.

This gives us two solutions, 11 and negative 11.

Both of these numbers squared gives 121.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

In part a, after substituting in these terms, you have got negative three multiplied by negative four squared add eight.

Negative four squared is 16.

When we add 16 and eight together, this gives 24.

The answer is negative 72, as this is negative three multiplied by 24.

In part b, after substituting in the values, you've got the equation negative 60 is equal to negative three multiplied by a squared add negative five.

The first thing we're going to do to solve this equation is divide both sides by negative three.

This gives 20 is equal to a squared add negative five.

We can write that as a squared subtract five.

The next thing we're going to do is add five to both sides.

This gives us 25 is equal to a squared.

The inverse of a squared is the square root.

The square root of 25 gives a solution of negative five or positive five.

That's all for this lesson.

Thanks for watching.