Consider the formula 𝑡 is equal to 𝑣 minus 𝑢 all over 𝑎. Work out the value of 𝑡 when 𝑣 is equal to four, 𝑢 is equal to a half, and 𝑎 is equal to two.
Now this isn’t just a completely made-up formula. It’s actually a rearrangement of the formula 𝑣 equals 𝑢 plus 𝑎𝑡, which you may recognise as one of the equations of motion. These are a set of equations which describe the motion of an object travelling in a straight line, where 𝑣 and 𝑢 have meanings as the speed of an object, 𝑎 represents its acceleration, and 𝑡 represents the time taken. However, you don’t need to know this in order to answer the question, but it’s just a bit of background information.
We’ve been given a set of values for 𝑣, 𝑢, and 𝑎. And to work out the value of 𝑡, we need to substitute them into this formula. So this gives 𝑡 is equal to four minus a half in the numerator over two.
Now we break the calculation of this down into stages. In the numerator, we have four minus a half, which is equal to three and a half. Now we can convert this from a mixed number into a top heavy or improper fraction. And to do this, we multiply the whole number, three, by the denominator of two, which gives six, and then add the numerator of one to give seven. This is because there are two halves in each of the whole ones, so that will make six halves. And then adding the final half gives us seven halves or seven over two.
Now we could write this as seven over two all over two, but that looks horrible and it’s not particularly good practice to sort of stack fractions up like this. So instead, we can remember that the horizontal line in a fraction means divide. So rather than writing seven over two over two, we can write it as seven over two divided by two.
Now to divide by two, we can think of two as the fraction two over one. And then we need to remember our rules for dividing by a fraction. To divide by a fraction, we invert or flip the fraction, so the numerator becomes the denominator and the denominator becomes the numerator. And we change the divide sign to a multiply. So dividing by two over one is the same as multiplying by one over two.
Multiplying fractions is much more straightforward. We just multiply the numerators together and multiply the denominators. So we have seven multiplied by one in the numerator, which is seven, and two multiplied by two in the denominator, which is four. The value of 𝑡 then is equal to seven over four.
We could also give our answer as a mixed number if we wanted, in which case it would be one and three-quarters. But as we haven’t been asked for the value in a particular format, we’re fine to leave it as seven over four.