Question

1. complete the following tables using equivalent rates.

a.

2		14	22
5	20		55

b.

2		14
5	20		55

★ c.

time (minutes)	1	5	6	10
distance (miles)	0.1	0.5	0.6	1

★ d.

time (hours)	1.5	3		6
distance (miles)	900		2700	3600

★ 8. each grid represents a whole. write each shaded part as a fraction and percent.

Explanation:

Step1: Find the rate for table A

The rate is $\frac{5}{2}=\frac{20}{8} = 2.5$.

Step2: Find the missing value for $h = 14$ in table A

Let the missing value be $x$. Using the rate $\frac{x}{14}=2.5$, so $x = 14\times2.5=35$.

Step3: Find the missing value for $e = 55$ in table A

Let the missing value be $y$. Using the rate $\frac{55}{y}=2.5$, so $y=\frac{55}{2.5}=22$.

Step4: Find the rate for table B

The rate is $\frac{5}{2}=\frac{20}{8} = 2.5$.
For $h = 14$, the earning $e=14\times2.5 = 35$. For $e = 55$, the hours $h=\frac{55}{2.5}=22$.

Step5: Find the rate for table C

The rate is $\frac{0.1}{1}=0.1$.
For time $t = 5$ minutes, distance $d=5\times0.1 = 0.5$ miles. For $t = 6$ minutes, $d = 6\times0.1=0.6$ miles. For $t = 10$ minutes, $d=10\times0.1 = 1$ mile.

Step6: Find the rate for table D

The rate is $\frac{900}{1.5}=600$.
For $t = 3$ hours, $d=3\times600 = 1800$ miles. For $d = 2700$ miles, $t=\frac{2700}{600}=4.5$ hours. For $t = 6$ hours, $d=6\times600=3600$ miles.

Answer:

Table A:

Hours ($h$)	2	8	14	22

Table B:

Hours ($h$)	2	8	14	22

Table C:

Time (minutes)	1	5	6	10

Table D:

Time (hours)	1.5	3	4.5	6