# 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?

Aug 26, 2017

$\text{yes}$

#### Explanation:

$\text{calculate the total amount of flour they have}$

$\Rightarrow 3 \times 1 \frac{3}{4}$

$\text{change "1 3/4" to an "color(blue)"improper fraction}$

$= \frac{3}{1} \times \frac{7}{4} = \frac{7 \times 3}{1 \times 4} = \frac{21}{4} = 5 \frac{1}{4}$

$\text{they have the required 5 cups with "1/4" left over}$

Aug 26, 2017

Yes there is enough flour to make the bread.

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

#### Explanation:

$\textcolor{b l u e}{\text{Three very important facts}}$

$\textcolor{b r o w n}{\text{Fact 1: }}$

A structure of a fraction consists of

$\textcolor{w h i t e}{\text{bbbbbb.")("count")/("size indicator of what you are counting}}$

$\textcolor{w h i t e}{\text{ccccccccccc")("count")/("size indicator")->("numerator")/("denominator}}$

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$\textcolor{b r o w n}{\text{Fact 2: }}$

You can not $\underline{\text{directly compare}}$ counts (numerators) unless the size indicators (denominators) are the same.

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$\textcolor{b r o w n}{\text{Fact 3: }}$

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.
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$\textcolor{b l u e}{\text{Answering the question}}$

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

Converting 5 into quarters:

$\textcolor{g r e e n}{5 \textcolor{red}{\times 1} \textcolor{w h i t e}{\text{cccc") ->color(white)("c} \bigvee v} 5 \textcolor{red}{\times \frac{4}{4}} = \frac{20}{4}}$

Converting $1 \frac{3}{4}$ into all quarters:

$\textcolor{g r e e n}{1 \frac{3}{4} \textcolor{w h i t e}{\text{cccc")->color(white)("cccc}} \left[1 \textcolor{red}{\times 1}\right] + \frac{3}{4}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ccccccc")->color(white)("cccc}} \left[1 \textcolor{red}{\times \frac{4}{4}}\right] + \frac{3}{4} = \frac{7}{4}}$

So the total of all the $1 \frac{3}{4}$ cups is $3 \times \frac{7}{4} = \frac{21}{4}$ cups

The amount needed to make the bread is $5 = \frac{20}{4}$ cups

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