301 Moved Permanently - Free Printable

Let’s solve each proportion step by step. We’ll use cross-multiplication — that means if you have:

> a/b = c/d

Then you multiply:
a × d = b × c

We’ll do this for every problem.

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1) b/17 = 5/3
Cross-multiply:
b × 3 = 17 × 5
3b = 85
b = 85 ÷ 3 → b = 85/3 or 28⅓

But let’s keep it as fraction unless told otherwise.
✔ b = 85/3

Wait — maybe we should check if it reduces? 85 and 3 share no common factors, so yes.

Actually, let me double-check:
17 × 5 = 85, divided by 3 → correct.

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2) 2/r = 7/18
Cross-multiply:
2 × 18 = r × 7
36 = 7r
r = 36 ÷ 7 → r = 36/7 or 5⅐

✔ r = 36/7

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3) 4/x = -6/18
First simplify right side: -6/18 = -1/3
So: 4/x = -1/3
Cross-multiply:
4 × 3 = x × (-1)
12 = -x
x = -12

✔ x = -12

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4) -14/12 = n/19
Simplify left: -14/12 = -7/6
So: -7/6 = n/19
Cross-multiply:
-7 × 19 = 6 × n
-133 = 6n
n = -133 ÷ 6 → n = -133/6

✔ n = -133/6

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5) a/15 = 18/14
Simplify 18/14 = 9/7
So: a/15 = 9/7
Cross-multiply:
a × 7 = 15 × 9
7a = 135
a = 135 ÷ 7 → a = 135/7

✔ a = 135/7

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6) 10/20 = -v/14
Simplify left: 10/20 = 1/2
So: 1/2 = -v/14
Cross-multiply:
1 × 14 = 2 × (-v)
14 = -2v
v = 14 ÷ (-2) = -7

✔ v = -7

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7) -x/18 = 13/15
Multiply both sides by -1 first? Or just cross-multiply directly.

Cross-multiply:
(-x) × 15 = 18 × 13
-15x = 234
x = 234 ÷ (-15) = -234/15

Simplify: divide numerator and denominator by 3 → -78/5

✔ x = -78/5

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8) 15/9 = -x/8
Simplify 15/9 = 5/3
So: 5/3 = -x/8
Cross-multiply:
5 × 8 = 3 × (-x)
40 = -3x
x = 40 ÷ (-3) = -40/3

✔ x = -40/3

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9) 16/19 = 4/n
Cross-multiply:
16 × n = 19 × 4
16n = 76
n = 76 ÷ 16 = 19/4 (divide num and den by 4)

✔ n = 19/4

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10) 10/7 = 15/k
Cross-multiply:
10 × k = 7 × 15
10k = 105
k = 105 ÷ 10 = 21/2

✔ k = 21/2

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11) 19/p = 5/2
Cross-multiply:
19 × 2 = p × 5
38 = 5p
p = 38 ÷ 5 = 38/5

✔ p = 38/5

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12) 18/x = 12/15
Simplify 12/15 = 4/5
So: 18/x = 4/5
Cross-multiply:
18 × 5 = x × 4
90 = 4x
x = 90 ÷ 4 = 45/2

✔ x = 45/2

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13) 13/n = 6/19
Cross-multiply:
13 × 19 = n × 6
247 = 6n
n = 247 ÷ 6 → doesn’t reduce → n = 247/6

✔ n = 247/6

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14) 12/7 = -r/12
Cross-multiply:
12 × 12 = 7 × (-r)
144 = -7r
r = 144 ÷ (-7) = -144/7

✔ r = -144/7

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15) 12/16 = 16/m
Simplify 12/16 = 3/4
So: 3/4 = 16/m
Cross-multiply:
3 × m = 4 × 16
3m = 64
m = 64 ÷ 3 = 64/3

✔ m = 64/3

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16) -12/n = -16/2
Simplify right: -16/2 = -8
So: -12/n = -8
Multiply both sides by n: -12 = -8n
Divide by -8: n = (-12)/(-8) = 12/8 = 3/2

✔ n = 3/2

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17) 2/7 = 16/x
Cross-multiply:
2 × x = 7 × 16
2x = 112
x = 56

✔ x = 56

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18) -b/6 = 16/11
Cross-multiply:
(-b) × 11 = 6 × 16
-11b = 96
b = 96 ÷ (-11) = -96/11

✔ b = -96/11

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19) 17/(12v) = 12/18
Simplify right: 12/18 = 2/3
So: 17/(12v) = 2/3
Cross-multiply:
17 × 3 = 12v × 2
51 = 24v
v = 51 ÷ 24 = 17/8 (divide by 3)

✔ v = 17/8

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20) x/17 = 16/12
Simplify 16/12 = 4/3
So: x/17 = 4/3
Cross-multiply:
x × 3 = 17 × 4
3x = 68
x = 68 ÷ 3 = 68/3

✔ x = 68/3

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21) -n/13 = 12/7
Cross-multiply:
(-n) × 7 = 13 × 12
-7n = 156
n = 156 ÷ (-7) = -156/7

✔ n = -156/7

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22) -13/17 = 15/a
Cross-multiply:
(-13) × a = 17 × 15
-13a = 255
a = 255 ÷ (-13) = -255/13

Check if reducible? 255 ÷ 13 = 19.6… not integer. 13×19=247, 255-247=8 → so no.

✔ a = -255/13

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Now, compiling all answers clearly:

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