301 Moved Permanently - Free Printable

Let’s solve each proportion step by step. We’ll use cross-multiplication: if \(\frac{a}{b} = \frac{c}{d}\), then \(a \cdot d = b \cdot c\). Then we solve for the variable.

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1) \(\frac{b}{17} = \frac{5}{3}\)
Cross-multiply: \(b \cdot 3 = 17 \cdot 5\) → \(3b = 85\)
Divide by 3: \(b = \frac{85}{3}\)

✔ Answer: \(b = \frac{85}{3}\)

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2) \(\frac{2}{r} = \frac{7}{18}\)
Cross-multiply: \(2 \cdot 18 = r \cdot 7\) → \(36 = 7r\)
Divide by 7: \(r = \frac{36}{7}\)

✔ Answer: \(r = \frac{36}{7}\)

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3) \(\frac{4}{x} = -\frac{6}{18}\)
Simplify right side: \(-\frac{6}{18} = -\frac{1}{3}\)
So: \(\frac{4}{x} = -\frac{1}{3}\)
Cross-multiply: \(4 \cdot 3 = x \cdot (-1)\) → \(12 = -x\)
Multiply both sides by -1: \(x = -12\)

✔ Answer: \(x = -12\)

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4) \(-\frac{14}{12} = \frac{n}{19}\)
Cross-multiply: \(-14 \cdot 19 = 12 \cdot n\) → \(-266 = 12n\)
Divide by 12: \(n = -\frac{266}{12} = -\frac{133}{6}\) (simplified)

✔ Answer: \(n = -\frac{133}{6}\)

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5) \(\frac{a}{15} = \frac{18}{14}\)
Cross-multiply: \(a \cdot 14 = 15 \cdot 18\) → \(14a = 270\)
Divide by 14: \(a = \frac{270}{14} = \frac{135}{7}\)

✔ Answer: \(a = \frac{135}{7}\)

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6) \(\frac{10}{20} = -\frac{v}{14}\)
Simplify left: \(\frac{1}{2} = -\frac{v}{14}\)
Cross-multiply: \(1 \cdot 14 = 2 \cdot (-v)\) → \(14 = -2v\)
Divide by -2: \(v = -7\)

✔ Answer: \(v = -7\)

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7) \(-\frac{x}{18} = \frac{13}{15}\)
Cross-multiply: \(-x \cdot 15 = 18 \cdot 13\) → \(-15x = 234\)
Divide by -15: \(x = -\frac{234}{15} = -\frac{78}{5}\)

✔ Answer: \(x = -\frac{78}{5}\)

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8) \(\frac{15}{9} = -\frac{x}{8}\)
Simplify left: \(\frac{5}{3} = -\frac{x}{8}\)
Cross-multiply: \(5 \cdot 8 = 3 \cdot (-x)\) → \(40 = -3x\)
Divide by -3: \(x = -\frac{40}{3}\)

✔ Answer: \(x = -\frac{40}{3}\)

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9) \(\frac{16}{19} = \frac{4}{n}\)
Cross-multiply: \(16 \cdot n = 19 \cdot 4\) → \(16n = 76\)
Divide by 16: \(n = \frac{76}{16} = \frac{19}{4}\)

✔ Answer: \(n = \frac{19}{4}\)

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10) \(\frac{10}{7} = \frac{15}{k}\)
Cross-multiply: \(10 \cdot k = 7 \cdot 15\) → \(10k = 105\)
Divide by 10: \(k = \frac{105}{10} = \frac{21}{2}\)

✔ Answer: \(k = \frac{21}{2}\)

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11) \(\frac{19}{p} = \frac{5}{2}\)
Cross-multiply: \(19 \cdot 2 = p \cdot 5\) → \(38 = 5p\)
Divide by 5: \(p = \frac{38}{5}\)

✔ Answer: \(p = \frac{38}{5}\)

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12) \(\frac{18}{x} = \frac{12}{15}\)
Simplify right: \(\frac{12}{15} = \frac{4}{5}\)
So: \(\frac{18}{x} = \frac{4}{5}\)
Cross-multiply: \(18 \cdot 5 = x \cdot 4\) → \(90 = 4x\)
Divide by 4: \(x = \frac{90}{4} = \frac{45}{2}\)

✔ Answer: \(x = \frac{45}{2}\)

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13) \(\frac{13}{n} = \frac{6}{19}\)
Cross-multiply: \(13 \cdot 19 = n \cdot 6\) → \(247 = 6n\)
Divide by 6: \(n = \frac{247}{6}\)

✔ Answer: \(n = \frac{247}{6}\)

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14) \(\frac{12}{7} = -\frac{r}{12}\)
Cross-multiply: \(12 \cdot 12 = 7 \cdot (-r)\) → \(144 = -7r\)
Divide by -7: \(r = -\frac{144}{7}\)

✔ Answer: \(r = -\frac{144}{7}\)

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15) \(\frac{12}{16} = \frac{16}{m}\)
Simplify left: \(\frac{3}{4} = \frac{16}{m}\)
Cross-multiply: \(3 \cdot m = 4 \cdot 16\) → \(3m = 64\)
Divide by 3: \(m = \frac{64}{3}\)

✔ Answer: \(m = \frac{64}{3}\)

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16) \(-\frac{12}{n} = -\frac{16}{2}\)
Simplify right: \(-\frac{16}{2} = -8\)
So: \(-\frac{12}{n} = -8\)
Multiply both sides by -1: \(\frac{12}{n} = 8\)
Then: \(12 = 8n\) → \(n = \frac{12}{8} = \frac{3}{2}\)

✔ Answer: \(n = \frac{3}{2}\)

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17) \(\frac{2}{7} = \frac{16}{x}\)
Cross-multiply: \(2 \cdot x = 7 \cdot 16\) → \(2x = 112\)
Divide by 2: \(x = 56\)

✔ Answer: \(x = 56\)

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18) \(-\frac{b}{6} = \frac{16}{11}\)
Cross-multiply: \(-b \cdot 11 = 6 \cdot 16\) → \(-11b = 96\)
Divide by -11: \(b = -\frac{96}{11}\)

✔ Answer: \(b = -\frac{96}{11}\)

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19) \(\frac{17}{12v} = \frac{12}{18}\)
Simplify right: \(\frac{12}{18} = \frac{2}{3}\)
So: \(\frac{17}{12v} = \frac{2}{3}\)
Cross-multiply: \(17 \cdot 3 = 12v \cdot 2\) → \(51 = 24v\)
Divide by 24: \(v = \frac{51}{24} = \frac{17}{8}\)

✔ Answer: \(v = \frac{17}{8}\)

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20) \(\frac{x}{17} = \frac{16}{12}\)
Simplify right: \(\frac{16}{12} = \frac{4}{3}\)
So: \(\frac{x}{17} = \frac{4}{3}\)
Cross-multiply: \(x \cdot 3 = 17 \cdot 4\) → \(3x = 68\)
Divide by 3: \(x = \frac{68}{3}\)

✔ Answer: \(x = \frac{68}{3}\)

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21) \(-\frac{n}{13} = \frac{12}{7}\)
Cross-multiply: \(-n \cdot 7 = 13 \cdot 12\) → \(-7n = 156\)
Divide by -7: \(n = -\frac{156}{7}\)

✔ Answer: \(n = -\frac{156}{7}\)

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22) \(-\frac{13}{17} = \frac{15}{a}\)
Cross-multiply: \(-13 \cdot a = 17 \cdot 15\) → \(-13a = 255\)
Divide by -13: \(a = -\frac{255}{13}\)

✔ Answer: \(a = -\frac{255}{13}\)

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Final Answer:
1) \(b = \frac{85}{3}\)
2) \(r = \frac{36}{7}\)
3) \(x = -12\)
4) \(n = -\frac{133}{6}\)
5) \(a = \frac{135}{7}\)
6) \(v = -7\)
7) \(x = -\frac{78}{5}\)
8) \(x = -\frac{40}{3}\)
9) \(n = \frac{19}{4}\)
10) \(k = \frac{21}{2}\)
11) \(p = \frac{38}{5}\)
12) \(x = \frac{45}{2}\)
13) \(n = \frac{247}{6}\)
14) \(r = -\frac{144}{7}\)
15) \(m = \frac{64}{3}\)
16) \(n = \frac{3}{2}\)
17) \(x = 56\)
18) \(b = -\frac{96}{11}\)
19) \(v = \frac{17}{8}\)
20) \(x = \frac{68}{3}\)
21) \(n = -\frac{156}{7}\)
22) \(a = -\frac{255}{13}\)