Question

complete the following tables using equivalent rates.
each grid represents a whole. write each shaded part as a fraction and percent.

Explanation:

Step1: For Table A

We know that to find equivalent ratios, we multiply or divide both the numerator and denominator by the same non - zero number. Given $\frac{1}{5}$, to get the second fraction, if we multiply both numerator and denominator by 4, we have $\frac{1\times4}{5\times4}=\frac{4}{20}$. To get the third fraction, if we multiply both by 7, we have $\frac{1\times7}{5\times7}=\frac{7}{35}$. To get the fourth fraction, if we multiply both by 11, we have $\frac{1\times11}{5\times11}=\frac{11}{55}$.

Step2: For Table B

Let the first ratio be $\frac{1}{5}$. If we multiply both numerator and denominator by 3, we get $\frac{3}{15}$. If we multiply by 6, we get $\frac{6}{30}$. If we multiply by 9, we get $\frac{9}{45}$.

Step3: For Table C

The ratio of time to distance is $\frac{1}{0.1}=\frac{10}{1}$. So when time $t = 5$ minutes, distance $d=0.5$ miles (since $\frac{5}{d}=\frac{10}{1}$, then $10d = 5$, so $d = 0.5$). When $t = 6$ minutes, $d = 0.6$ miles (since $\frac{6}{d}=\frac{10}{1}$, then $10d=6$, so $d = 0.6$).

Step4: For Table D

The ratio of time to distance is $\frac{1.5}{90}=\frac{1}{60}$. When $t = 3$ hours, $d = 180$ miles (since $\frac{3}{d}=\frac{1}{60}$, then $d=180$). When $d = 2160$ miles, $t = 36$ hours (since $\frac{t}{2160}=\frac{1}{60}$, then $t = 36$). When $t = 6$ hours, $d = 360$ miles (since $\frac{6}{d}=\frac{1}{60}$, then $d = 360$).

Answer:

Table A: $\frac{4}{20},\frac{7}{35},\frac{11}{55}$
Table B: $\frac{3}{15},\frac{6}{30},\frac{9}{45}$
Table C: $0.5,0.6$
Table D: $180,36,360$