Question

multiplying fractions: formative assessment
solve each problem. provide a justification for your solutions using visual representations,
numerical expressions and/or written expressions.
in chiquitas local grocery store, ( 1\frac{4}{5} ) of the total aisle space is dedicated to organic and
locally sourced items such as jams, jellies, spreads, honey, and preserves. a local
company named roberts jars of gold would like to sell their honey and preserves at
chiquitas local grocery store.

1. if roberts jars of gold stocks ( \frac{3}{4} ) of the space. how much of the organic and locally

sourced area would be available to other vendors?

1. vendors selling at chiquitas local grocery store receive three - quarters of the profits

earn from their products. the owner of roberts jars of gold anticipates in the initial
month, the products will make $1200. she wants to invest one - third of the profits into the
production of more products. how much should she anticipate investing in the
production of more products?

Explanation:

Step1: Convert the mixed number to an improper fraction

The organic and locally sourced space is \(1\frac{4}{5}\) of the total aisle space. Convert \(1\frac{4}{5}\) to an improper fraction: \(1\frac{4}{5}=\frac{1\times5 + 4}{5}=\frac{9}{5}\).

Step2: Find the remaining space

Robert's Jars of Gold stocks \(\frac{3}{4}\) of the organic and locally sourced space. The remaining space is \((1-\frac{3}{4})\) of the organic and locally sourced space.
We use the formula \(A = S\times(1 - r)\), where \(S=\frac{9}{5}\) (the total organic - locally sourced space) and \(r = \frac{3}{4}\) (the proportion stocked by Robert's Jars of Gold).

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Step3: Justification for problem 2

First, find the profits that Robert's Jars of Gold gets. Vendors receive three - quarters of the profits. The total profit is \(P = 1200\). The profit that Robert's Jars of Gold gets is \(V=\frac{3}{4}\times1200\).

$$ \frac{3}{4}\times1200=\frac{3\times1200}{4}=3\times300 = 900 $$

Then, she wants to invest one - third of her profits. Let \(I\) be the investment. Using the formula \(I=\frac{1}{3}\times V\), where \(V = 900\)

$$ I=\frac{1}{3}\times900=\frac{900}{3}=300 $$

Answer:

1. \(\frac{9}{20}\) of the organic and locally sourced area is available to other vendors.
2. She should anticipate investing \(\$300\) in the production of more products.