· The answer.
A car that can travel 12km with a 4/5 filled tank can travel 5km with a 1/3 filled tank.
· How this is worked out
As these two fractions are totally different, we must find a common denominator; the denominator is the bottom value on a fraction; by finding a common one, we are making this value the same on both divisions.
To do this, we must find a number that is divisible by both of the denominators in our equations. In this example, the smallest numerical value that is applicable is 15.
Now that we know this, we must multiply the bottom of the fraction by a value that would give us our common denominator. For example, we know that 5 multiplied by 3 equals 15.
Whatever we do to the bottom of a fraction we must also do to the top, and so we must multiply 4 by 3, equalling 12, and an overall new fraction of 12/15.
Looking at our other fraction, we can see that 3 must be multiplied by 5 to give us our wanted value and so, by following the theory above, we know that this means that 1 must be multiplied by 5, giving us 5/15.
Now that, we have converted our fractions into more similar looking ones, we can see what it is that our question is actually asking us; we are told that 12/15 will allow the car to travel 12km, and so must work out how many kilometres 1/15 would take it.
We can work this out by dividing the 12km by the top part of our fraction, giving us 12 divided by 12, which we know equals 1. All that we have to do now is to multiply this one by the number on the top of our other fraction, giving us 1 multiplied by 5, which we know equals 5. This is our final answer.
A car that can travel 12km with a 4/5 filled tank can travel 5km with a 1/3 filled tank.
· How this is worked out
As these two fractions are totally different, we must find a common denominator; the denominator is the bottom value on a fraction; by finding a common one, we are making this value the same on both divisions.
To do this, we must find a number that is divisible by both of the denominators in our equations. In this example, the smallest numerical value that is applicable is 15.
Now that we know this, we must multiply the bottom of the fraction by a value that would give us our common denominator. For example, we know that 5 multiplied by 3 equals 15.
Whatever we do to the bottom of a fraction we must also do to the top, and so we must multiply 4 by 3, equalling 12, and an overall new fraction of 12/15.
Looking at our other fraction, we can see that 3 must be multiplied by 5 to give us our wanted value and so, by following the theory above, we know that this means that 1 must be multiplied by 5, giving us 5/15.
Now that, we have converted our fractions into more similar looking ones, we can see what it is that our question is actually asking us; we are told that 12/15 will allow the car to travel 12km, and so must work out how many kilometres 1/15 would take it.
We can work this out by dividing the 12km by the top part of our fraction, giving us 12 divided by 12, which we know equals 1. All that we have to do now is to multiply this one by the number on the top of our other fraction, giving us 1 multiplied by 5, which we know equals 5. This is our final answer.
