Question

Six friends share 4 sandwiches equally. What fraction of a sandwich does each friend get?

Answer 1

`4/6 = 2/3` of a sandwich each,

Explanation:

Students often find this type of question difficult at first, until they realise that the question is the answer!

We are used to questions such as "12 sweets are shared between 4 friends", because it is easy to visualise sharing them out.

"What is 12 divided by 4"? `rarr 12/4 = 3`

But in this case we are sharing a smaller number between a larger number of friends.

"What is 4 divided by 6"?

In real life this would mean cutting up the sandwiches into smaller pieces, but of what size?

Do exactly the same as with the sweets! `4/6 = 2/3`
Each friend will get `2/3` of a sandwich.

"What is 4 apples shared between 5 friends?"

"What is 4 divided by 5?" `rarr 4/5 = 4/5`

The question is the answer!

Answer 2

The same thing but from a different stand point

Explanation:

Consider the ratio written like a fraction:

`("Count of sandwiches")/("count of people")-> 4/6`

But we need the count of sandwiches for 1 person. So we need to change the 6 people into 1 person. To change 6 into 1 divide it by 6

`6-:6=1`

`color(brown)("For ratios, when multiplying or dividing, what we do to the bottom")` `color(brown)("we do to the top.")`

So to change `4/6` into what we want we apply

`(4-:6)/(6-:6)=(2/3)/1 larr" "("Count of sandwiches")/("count of people")`

So each person ends up with `2/3` of a sandwich

`color(green)("Now see where the shortcut comes from "4/6 = 2/3" of a sandwich"`