### Video Transcript

๐ด, ๐ต, and ๐ถ are three points on a line. Point ๐ด is 4.2 centimetres from point ๐ต. The distance from ๐ต to ๐ถ is one-seventh of the distance from ๐ด to ๐ต. Calculate the distance from ๐ด to ๐ถ.

So, weโre told from the question the distance ๐ต๐ถ is a seventh of the distance ๐ด๐ต. So therefore, what we can do is say that ๐ต๐ถ is a seventh of 4.2 centimetres. And thatโs because we know that ๐ด๐ต is equal to 4.2 centimetres. So, thinking about when weโre dealing with a fraction, when weโre dealing with fractions, of means multiplied. So, what we could say is that ๐ต๐ถ 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. Thatโs because if we think about it as fractions, 4.2 is the same as 4.2 over one. And if weโre multiplying fractions, you multiply the numerators. So, weโd 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 weโve got 0.6 centimetres.

So, have we solved the problem? Well, no, because weโre looking for the total distance. Weโre looking for the distance from ๐ด to ๐ถ. And the distance ๐ด๐ถ is equal to ๐ด๐ต plus ๐ต๐ถ. 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 ๐ด to ๐ถ is 4.8 centimetres.