𝐴, 𝐵, and 𝐶 are three points on a line. Point 𝐴 is 4.2 centimetres from point 𝐵. The distance from 𝐵 to 𝐶 is one-seventh of the distance from 𝐴 to 𝐵. Calculate the distance from 𝐴 to 𝐶.
So, we’re told from the question the distance 𝐵𝐶 is a seventh of the distance 𝐴𝐵. So therefore, what we can do is say that 𝐵𝐶 is a seventh of 4.2 centimetres. And that’s because we know that 𝐴𝐵 is equal to 4.2 centimetres. So, thinking about when we’re dealing with a fraction, when we’re dealing with fractions, of means multiplied. So, what we could say is that 𝐵𝐶 is a seventh multiplied by 4.2 centimetres.
And if we want to multiply a seventh by 4.2, then what we do is just divide 4.2 by seven. That’s because if we think about it as fractions, 4.2 is the same as 4.2 over one. And if we’re multiplying fractions, you multiply the numerators. So, we’d have one multiplied by 4.2, which is 4.2. And then, you multiply the denominators, seven multiplied by one, which gives us seven. So, we just have 4.2 over seven, which is the same as 4.2 divided by seven. Or you could, alternatively, just type in one-seventh multiplied by 4.2 on your calculator.
And when we divide 4.2 centimetres by seven, we get 0.6 centimetres. And again, you could have done this in the calculator. Or if we wanted to use a mental method, we can think of it as 42 divided by seven. Well, 42 divided by seven is six cause six multiplied by seven is 42. And then, we put the decimal point back in, so we’ve got 0.6 centimetres.
So, have we solved the problem? Well, no, because we’re looking for the total distance. We’re looking for the distance from 𝐴 to 𝐶. And the distance 𝐴𝐶 is equal to 𝐴𝐵 plus 𝐵𝐶. So, this is gonna be 4.2 centimetres plus 0.6 centimetres. And again, you could have done this using a calculator. But if you wanted to, you could have used the column method. So therefore, 4.2 add 0.6. We add the tenths, so two and six, which gives us eight. Then, we line up the decimal point. And then, we have four units add zero units, which gives us four. So, we get a 4.8. So therefore, we can say that the distance from 𝐴 to 𝐶 is 4.8 centimetres.