Question

7.rp.2 / 7.g.1 / 7.ns. 1 & 2 review
(first problem: text about a manufacturing business, table with changes, and a number line question with options a - d, some handwritten notes)
solve: ( 6 div \frac{5}{6} = )
a. ( \frac{1}{8} )
b. 5
c. ( 6\frac{5}{6} )
d. ( 7\frac{1}{5} ) (handwritten notes: ( \frac{6}{1} div \frac{5}{6} ), ( \frac{6}{1} \times \frac{6}{5} ))
( 8 div \frac{4}{5} = )
a. 10
b. ( 8\frac{4}{5} )
c. ( 6\frac{2}{5} )
d. ( \frac{1}{10} ) (handwritten notes: ( 8 div \frac{4}{5} ), ( \frac{8}{1} \times \frac{5}{4} ), 10)
solve: ( \frac{5}{8} div 5 = )
a. ( \frac{1}{8} )
b. ( \frac{8}{25} )
c. ( 3\frac{1}{8} )
d. 8
in september, louise planted a tree. every month, the tree louise planted grew 2 inches. what would the constant of proportionality of the line be?
a. ( \frac{1}{2} ) of an inch
b. 1 inch
c. 2 inches
d. 4 inches
(last problem: a line graphed on a coordinate grid shows a proportional relationship between x and y. the graph has x from 0 - 10 and y from 0 - 10, with a line through the origin. question: what is the constant of proportionality for the graph of the line? options: a. ( \frac{3}{5} ), b. ( \frac{2}{3} ), c. ( \frac{5}{3} ), d. 2)

Explanation:

Step1: Solve $6\div\frac{5}{6}$

Dividing by a fraction = multiply by reciprocal: $6\times\frac{6}{5}=\frac{36}{5}=7\frac{1}{5}$

Step2: Solve $8\div\frac{4}{5}$

Multiply by reciprocal: $8\times\frac{5}{4}=10$

Step3: Solve $\frac{5}{8}\div5$

Rewrite 5 as $\frac{5}{1}$, multiply by reciprocal: $\frac{5}{8}\times\frac{1}{5}=\frac{1}{8}$

Step4: Find tree growth constant

Growth per month = 2, so constant = 2

Step5: Find graph proportionality constant

Pick point (10,6), constant = $\frac{y}{x}=\frac{6}{10}=\frac{3}{5}$

Step6: Match number line to table

Table has changes +20, +30, +70; option B matches this scale.

Answer:

1. $6\div\frac{5}{6}$: D. $7\frac{1}{5}$
2. $8\div\frac{4}{5}$: A. 10
3. $\frac{5}{8}\div5$: A. $\frac{1}{8}$
4. Tree constant of proportionality: C. 2 inches
5. Graph constant of proportionality: A. $\frac{3}{5}$
6. Number line question: B (the second number line option)