Question

equivalent ratios show two sets of numbers that have the same proportional relationship. they are found by expanding or simplifying a ratio like a fraction.
circle the ratio that is not equivalent.
a. 32:42 4:6 60:90
b. 1:2 12:26 16:32
c. 4:3 15:10 20:15
d. 10:4 25:10 50:44
e. 2:6 12:32 3:8
f. 3:14 6:21 2:7
g. 22:18 11:9 100:60
h. 3:1 9:3 15:6
i. 8:10 10:12 4:5

Explanation:

Step1: Simplify each ratio

For ratio \(a. 32:42\), divide both by \(2\) to get \(\frac{32\div2}{42\div2}=\frac{16}{21}\).
For ratio \(b. 1:2\), it is already in simplest form.
For ratio \(c. 4:3\), it is already in simplest form.
For ratio \(d. 10:4 = 25:10 = 50:44\), simplify \(10:4=\frac{10\div2}{4\div2}=\frac{5}{2}\), \(25:10=\frac{25\div5}{10\div5}=\frac{5}{2}\), \(50:44=\frac{50\div2}{44\div2}=\frac{25}{22}\).
For ratio \(e. 2:6 = 12:32 = 3:8\), simplify \(2:6=\frac{2\div2}{6\div2}=\frac{1}{3}\), \(12:32=\frac{12\div4}{32\div4}=\frac{3}{8}\), \(3:8\) is already in simplest form.
For ratio \(f. 3:14 = 6:21 = 2:7\), simplify \(3:14\) (already in simplest form), \(6:21=\frac{6\div3}{21\div3}=\frac{2}{7}\), \(2:7\) is already in simplest form.
For ratio \(g. 22:18 = 11:9 = 100:90\), simplify \(22:18=\frac{22\div2}{18\div2}=\frac{11}{9}\), \(11:9\) is already in simplest form, \(100:90=\frac{100\div10}{90\div10}=\frac{10}{9}\).
For ratio \(h. 3:1 = 9:3\), \(3:1\) is already in simplest form, \(9:3=\frac{9\div3}{3\div3}=3:1\).
For ratio \(i. 8:10 = 10:12 = 4:5\), simplify \(8:10=\frac{8\div2}{10\div2}=\frac{4}{5}\), \(10:12=\frac{10\div2}{12\div2}=\frac{5}{6}\), \(4:5\) is already in simplest form.

Answer:

The ratios that are not equivalent are \(a. 32:42\), \(b. 1:2\), \(c. 4:3\), \(d. 10:4 = 25:10 = 50:44\), \(e. 2:6 = 12:32 = 3:8\), \(f. 3:14 = 6:21 = 2:7\), \(g. 22:18 = 11:9 = 100:90\), \(h. 3:1 = 9:3\), \(i. 8:10 = 10:12 = 4:5\) (the circled ones in the original problem are the non - equivalent ones among the given pairs).