비와 비례식 단원 종합

E.1Find each unit rate. Write fractions in simplest form.

1. 1
   A snail crawls $\frac{5}{6}$ foot in $\frac{1}{6}$ minute. How many feet does it crawl per minute?
2. 2
   A machine makes $\frac{1}{3}$ pound of pasta in $\frac{1}{4}$ hour. How many pounds does it make per hour?

E.2Do the ratios form a proportion? Write yes or no.

1. 3
   $\frac{2}{1}\stackrel{?}{=}\frac{10}{5}$ 
2. 4
   $\frac{12}{27}\stackrel{?}{=}\frac{5}{9}$ 

E.3Solve each proportion.

1. 5
   $\frac{p}{2}=\frac{2}{1}$
2. 6
   $\frac{63}{k}=\frac{27}{21}$

E.4Write a proportion and solve it.

1. 7
   Jada earns $\text{\$}52.00$ for $4$ hours of babysitting. At this rate, how much does she earn for $10$ hours?
2. 8
   A printer prints $15$ pages in $3$ minutes. How many minutes will it take to print $70$ pages?

E.5Find the constant of proportionality, k, for each table.

1. 9
   $\begin{array}{ccccc}x& 2& 6& 10& 14\\ y& 1.5& 4.5& 7.5& 10.5\end{array}$
2. 10
   $\begin{array}{ccccc}x& 5& 6& 7& 8\\ y& 7.5& 9& 10.5& 12\end{array}$

E.6Write an equation in the form y = kx for each table.

1. 11
   $\begin{array}{ccccc}x& 1& 4& 7& 10\\ y& 1.5& 6& 10.5& 15\end{array}$
2. 12
   $\begin{array}{ccccc}x& 4& 7& 10& 13\\ y& 7.2& 12.6& 18& 23.4\end{array}$

E.7Is y proportional to x? Write yes or no. If yes, give the constant of proportionality, k.

1. 13
   $y=1.5x+4$
2. 14
   $y=0.75x$

E.8Write an equation, then answer the question.

1. 15
   Ben walks $2$ miles per hour. Use $d$ for miles and $t$ for hours. How far does he walk in $1.5$ hours?
2. 16
   Apples cost $\text{\$}1.00$ per pound. Use $c$ for the cost in dollars and $p$ for pounds. What do $9$ pounds cost?

E.9Use the scale to answer each question.

1. 17
   In a model, $1$ centimeter represents $5$ meters. A model building is $5.2$ centimeters tall. How tall is the real building?
2. 18
   In a model, $1$ centimeter represents $4$ meters. A model building is $5.2$ centimeters tall. How tall is the real building?

E.10E.11Answer each question.

1. 19
   A trapezoid has a area of $14$ cm². A scale drawing of it uses a scale factor of $2$. What is the area of the drawing?
2. 20
   A trapezoid has a area of $15$ ft². A scale drawing of it uses a scale factor of $3$. What is the area of the drawing?
3. 21
   $\begin{array}{ccccc}x& 2& 8& 14& 20\\ y& 3.5& 14& 24.5& 35\end{array}$
4. 22
   $\begin{array}{ccccc}x& 4& 6& 8& 10\\ y& 7.2& 10.8& 14.4& 18\end{array}$

E.1Unit Rates with Fractions

1. 1$5$ feet per minute
2. 2$1\frac{1}{3}$ pounds per hour

E.2Do the Ratios Form a Proportion?

1. 3yes
2. 4no

E.3Solve Proportions

1. 5$p=4$
2. 6$k=49$

E.4Proportion Word Problems

1. 7$\text{\$}130.00$
2. 814 minutes

E.5Constant of Proportionality from a Table

1. 9$k=0.75$
2. 10$k=1.5$

E.6Equations for Proportional Relationships

1. 11$y=1.5x$
2. 12$y=1.8x$

E.7Identify Proportional Relationships

1. 13no
2. 14yes; $k=0.75$

E.8Write & Solve Equations for Proportional Relationships

1. 15$d=2t$; $3$ miles
2. 16$c=1p$; $\text{\$}9.00$

E.9Scale Drawings

1. 1726 meters

E.9Scale Drawings (continued)

1. 1820.8 meters

E.10E.11Answer each question.

1. 19$56$ cm²
2. 20$135$ ft²
3. 21$k=1.75$
4. 22$k=1.8$