Question

cool down
lesson 12: percentages and tape diagrams
cool down: small and large
complete the statement with a situation and a unit of your choice. then answer the question and draw a diagram.
a small holds 75% as much as a large

1. if the small holds 36 units, how much does the large hold?
2. draw a diagram to illustrate your answer.

Explanation:

Step1: Set up the equation

Let the amount the large holds be \(x\). We know that \(36 = 0.75x\) (since \(75\%=0.75\)).

Step2: Solve for \(x\)

Divide both sides of the equation by \(0.75\). So \(x=\frac{36}{0.75}\).
Calculate \(\frac{36}{0.75}=\frac{36\times4}{0.75\times4}=\frac{144}{3} = 48\).

Answer:

1. The large holds \(48\) units.
2. For the diagram: Draw a long rectangle (representing the large) and divide it into 4 equal - sized smaller rectangles (since \(75\%=\frac{3}{4}\)). Then draw a shorter rectangle (representing the small) which has the length of 3 of those smaller rectangles. Label the small rectangle as \(36\) units. If each of the 4 equal - sized parts of the large rectangle is \(y\) units, then \(3y = 36\), so \(y = 12\), and the total length of the large rectangle (which is \(4y\)) is \(48\) units.