# Video: Pack 3 • Paper 3 • Question 2

Pack 3 • Paper 3 • Question 2

04:01

### Video Transcript

Marie is weighing some cakes. She wishes to know the weight of the cakes in both grams and ounces. However, her scales only measure in grams. She finds out that one gram is equal to 0.035274 ounces. Marie puts a fruit cake on the scales. It weighs 657 grams. Find the weight of this fruit cake in ounces. Give your answer to one decimal place.

In the question, we’re given the conversion that we can use to convert between grams and ounces: one gram is equal to 0.035274 ounces. We want to know what 657 grams is equivalent to in ounces. To do so, we can scale up. The left-hand side of this ratio has been multiplied by 657. So we can do the same on the right-hand side, 0.035274 multiplied by 657 is 23.175018. The question asks us to give our answer to one decimal place. And as the second decimal place is a seven, we’re rounding up. The weight of the fruit cake is 23.2 ounces to one decimal place.

Marie’s scales run out of battery. But she notices the on the packaging of a battenberg cake, it says that it weighs 24.5 ounces. Marie does not have a calculator. So she uses the conversion 200 grams is equal to seven ounces in order to approximate the weight in grams. Use Marie’s conversion to show that the weight of this battenberg cake is approximately 700 grams.

So Marie is using an approximate conversion here of 200 grams is equal to seven ounces. We can divide both sides of this ratio by seven. So we have that 200 over seven grams is equal to one ounce and remember that’s still approximate. The battenberg cake weighs 24.5 ounces. So to convert this to grams, we need to multiply by 200 over seven. Now, we do have a calculator in this question, but Marie doesn’t. So let’s think about how we should answer this if we don’t have a calculator.

Division and multiplication can be performed in any order. So let’s divide 24.5 by seven first and then multiply by 200. We can divide 24.5 by seven using short division. Firstly, sevens into two we can’t do. So we carry the two. Seven goes into 24 three times with a remainder of three. Seven goes into 35 exactly five times. The calculation therefore becomes 3.5 multiplied by 200. 3.5 multiplied by two is seven. And then multiplying by 100, we get the 700 grams that we were asked to show.

Is using this approximate conversion, instead of the original conversion, a sensible start for Marie to calculate the weight of this battenberg cake in grams? You must justify your answer.

Remember the approximate conversion that Marie was using was that 200 grams is equal to seven ounces. If we divide both sides of this ratio by 200, it becomes one gram is equal to 0.035 ounces. The original conversion was one gram is equal to 0.035274 ounces. And these ratios are very, very similar.

Therefore, this is a very sensible starting point as she can do the calculation without a calculator and it’s still quite accurate. Seven over 200 is very close to 0.035274.