Question

equivalent ratios
equivalent ratios show two sets of numbers that have the same proportions
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

1. 8:10

10:12
4:5

Explanation:

Step1: Simplify each ratio

• For \(a. 32:42\), divide both by \(2\): \(\frac{32\div2}{42\div2}=\frac{16}{21}\)
• For \(b. 1:2\), it is already in simplest form.
• For \(c. 4:3\), already in simplest form.
• For \(d. 10:4 = 25:10=50:44\), simplify \(10:4=\frac{10\div2}{4\div2}=\frac{5}{2}\), \(25:10=\frac{25\div5}{10\div5}=\frac{5}{2}\), \(50:44=\frac{50\div2}{44\div2}=\frac{25}{22}\) (not equivalent)
• For \(e. 2:6 = 12:32=3:8\), simplify \(2:6=\frac{2\div2}{6\div2}=\frac{1}{3}\), \(12:32=\frac{12\div4}{32\div4}=\frac{3}{8}\), \(3:8\) (not equivalent)
• For \(f. 3:14 = 6:21=2:7\), simplify \(3:14\) (already in simplest form), \(6:21=\frac{6\div3}{21\div3}=\frac{2}{7}\), \(2:7\) (not equivalent)
• For \(g. 22:18 = 11:9 = 100:60\), simplify \(22:18=\frac{22\div2}{18\div2}=\frac{11}{9}\), \(100:60=\frac{100\div20}{60\div20}=\frac{5}{3}\) (not equivalent)
• For \(h. 3:1 = 9:3 = 15:6\), simplify \(3:1\) (already in simplest form), \(9:3=\frac{9\div3}{3\div3}=3:1\), \(15:6=\frac{15\div3}{6\div3}=\frac{5}{2}\) (not equivalent)

Answer:

\(a. 32:42\), \(b. 1:2\), \(c. 4:3\), \(d. 10:4 = 25:10=50:44\), \(e. 2:6 = 12:32=3:8\), \(f. 3:14 = 6:21=2:7\), \(g. 22:18 = 11:9 = 100:60\), \(h. 3:1 = 9:3 = 15:6\)