Question

Sasha, Rudy, and Mario each have `1 3/4` cups of flour. Can they make a recipe for bread that needs 5 cups of flour?

Answer 1

`"yes"`

Explanation:

`"calculate the total amount of flour they have"`

`rArr3xx1 3/4`

`"change "1 3/4" to an "color(blue)"improper fraction"`

`=3/1xx7/4=(7xx3)/(1xx4)=21/4=5 1/4`

`"they have the required 5 cups with "1/4" left over"`

Answer 2

Yes there is enough flour to make the bread.

Over the top explanation given so you can see where everything comes from.

Explanation:

`color(blue)("Three very important facts")`

`color(brown)("Fact 1: ")`

A structure of a fraction consists of

`color(white)("bbbbbb.")("count")/("size indicator of what you are counting")`

`color(white)("ccccccccccc")("count")/("size indicator")->("numerator")/("denominator")`

..............................................................
`color(brown)("Fact 2: ")`

You can not `ul("directly compare")` counts (numerators) unless the size indicators (denominators) are the same.

.................................................................
`color(brown)("Fact 3: ")`

Multiply by 1 and you do not change the 'true' value of a fraction or number. However, 1 comes in many forms so you can change the way a fraction looks without changing its value.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

I chose to make the size indicator such that we are counting quarters.

Converting 5 into quarters:

`color(green)(5color(red)(xx1)color(white)("cccc") ->color(white)("c"vvvv) 5color(red)(xx4/4) = 20/4)`

Converting `1 3/4` into all quarters:

`color(green)(1 3/4color(white)("cccc")->color(white)("cccc") [1color(red)(xx1)]+3/4)`

`color(green)(color(white)("ccccccc")->color(white)("cccc")[1color(red)(xx4/4)] + 3/4 = 7/4)`

So the total of all the `1 3/4` cups is `3xx7/4 = 21/4` cups

The amount needed to make the bread is `5 =20/4` cups

As 21 is more than 20 then yes, there is enough to make the bread