Six small bricks have the same mass as five large bricks. The mass of one small brick is 2.5 kilograms. What is the mass of one large brick?
In this problem, we’re asked to calculate the mass of one large brick. This is the sort of problem where we’re going to have to go through a number of small steps to get to the answer. We may not know the mass of one large brick. But what do we know and how can we use it to help?
One piece of information that we’re given is the mass of one small brick. The mass of one of the small bricks is 2.5 or two and a half kilograms. And we can see from the diagram that there are six small bricks in total. The second fact that we can use to help us is in the first sentence. And it’s also shown in the diagram. Six small bricks have the same mass as five large bricks. The diagram also shows us this information because we can see that the balances are straight. Both sides weigh the same.
So let’s go through these small steps. Let’s use the facts we do know to find out the one fact that we don’t. If we know the mass of one small brick, we can use this to find the total mass of all six small bricks. We just need to work out the answer to 2.5 or two and a half times six. How can we multiply by six quickly?
Six is the same as two times three. So 2.5 times six is the same as 2.5 times two times three. In other words, we can double 2.5 and then multiply the answer by three. This has now become the sort of calculation we can do in our heads quickly. 2.5 or two and a half doubled equals five. And now we multiply this by three to get the answer 15. What does this number 15 represent? It represents 15 kilograms, the total mass of all six small bricks.
How can we use this fact to help us? Well, we know that everything on the left-hand side of the balances weighs exactly the same as everything on the right-hand side of the balance. And so we can say that the five large bricks have a total mass of 15 kilograms too.
On to our final step, because we now know the total mass of all five large bricks, how can we use this to find out the mass of one of the large bricks? To find the mass of one large brick, we need to take the total mass of all five or 15 kilograms and divide it by the number of bricks that there are which is five, 15 divided by five. And again, this is the sort of calculation we can work out quickly in our heads. 15 divided by five equals three. So the mass of one of those large bricks is three kilograms.
How did we find the answer? Having read the question carefully, we knew we were being asked for the mass of one large brick. But we also knew that the information we’ve already been given meant that we had to go through several small steps to get there. In a way, you could say that we worked from left to right on the diagram. We started by recognizing the mass of one small brick. Then we multiplied this by six to find the total mass of all of the small bricks. And to do this quickly, we used known facts to help.
We knew that multiplying by two and then by three is the same as multiplying by six. We then could use this information to say what the mass of all of the large bricks is because both piles of bricks weigh the same. And our final step was to divide the total mass of the five large bricks by the number of bricks that there were. Sometimes we may not see an answer straightaway. But if we work through small steps to get there, it’ll soon become clear. The mass of one large brick equals three kilograms.