Question

from unit 4, lesson 1
select all ratios that are equivalent to 4 : 5.
a 2 : 2.5
b 2 : 3
c 3 : 3.75
d 7 : 8
e 8 : 10
f 14 : 27.5

Explanation:

Step1: Recall equivalent ratios

Equivalent ratios can be found by multiplying or dividing both parts of the ratio by the same non - zero number. The ratio \(4:5\) can be written as a fraction \(\frac{4}{5}=0.8\). We will convert each option to a decimal to check if it is equal to \(0.8\).

Step2: Check option A

For the ratio \(2:2.5\), we calculate \(\frac{2}{2.5} = 0.8\). Since \(0.8=\frac{4}{5}\), this ratio is equivalent to \(4:5\).

Step3: Check option B

For the ratio \(2:3\), we calculate \(\frac{2}{3}\approx0.6667
eq0.8\). So this ratio is not equivalent to \(4:5\).

Step4: Check option C

For the ratio \(3:3.75\), we calculate \(\frac{3}{3.75}=0.8\). Since \(0.8 = \frac{4}{5}\), this ratio is equivalent to \(4:5\).

Step5: Check option D

For the ratio \(7:8\), we calculate \(\frac{7}{8} = 0.875
eq0.8\). So this ratio is not equivalent to \(4:5\).

Step6: Check option E

For the ratio \(8:10\), we calculate \(\frac{8}{10}=0.8\). Since \(0.8=\frac{4}{5}\), this ratio is equivalent to \(4:5\).

Step7: Check option F

For the ratio \(14:27.5\), we calculate \(\frac{14}{27.5}=\frac{140}{275}=\frac{28}{55}\approx0.509
eq0.8\). So this ratio is not equivalent to \(4:5\).

Answer:

A. \(2:2.5\), C. \(3:3.75\), E. \(8:10\)