Ratio and Proportion Worksheets - Math Monks - Free Printable

To determine if the \( x \) and \( y \) values are proportional, we need to check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \). If the ratio is the same for all pairs, then \( x \) and \( y \) are proportional. Let's solve each problem step by step.

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1)

\[
\begin{array}{c|cccc}
x & 4 & 19 & 22 & 18 \\
\hline
y & 32 & 76 & 88 & 72 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (4, 32) \): \( \frac{32}{4} = 8 \)
- For \( (19, 76) \): \( \frac{76}{19} = 4 \)
- For \( (22, 88) \): \( \frac{88}{22} = 4 \)
- For \( (18, 72) \): \( \frac{72}{18} = 4 \)

The ratios are not constant (\( 8, 4, 4, 4 \)). Therefore, \( x \) and \( y \) are not proportional.

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2)

\[
\begin{array}{c|cccc}
x & 3 & 6 & 9 & 12 \\
\hline
y & 12 & 24 & 36 & 48 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (3, 12) \): \( \frac{12}{3} = 4 \)
- For \( (6, 24) \): \( \frac{24}{6} = 4 \)
- For \( (9, 36) \): \( \frac{36}{9} = 4 \)
- For \( (12, 48) \): \( \frac{48}{12} = 4 \)

The ratios are constant (\( 4, 4, 4, 4 \)). Therefore, \( x \) and \( y \) are proportional.

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3)

\[
\begin{array}{c|cccc}
x & -6 & -4 & -5 & -8 \\
\hline
y & -48 & -32 & 40 & 64 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (-6, -48) \): \( \frac{-48}{-6} = 8 \)
- For \( (-4, -32) \): \( \frac{-32}{-4} = 8 \)
- For \( (-5, 40) \): \( \frac{40}{-5} = -8 \)
- For \( (-8, 64) \): \( \frac{64}{-8} = -8 \)

The ratios are not constant (\( 8, 8, -8, -8 \)). Therefore, \( x \) and \( y \) are not proportional.

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4)

\[
\begin{array}{c|cccc}
x & -54 & 18 & -27 & 45 \\
\hline
y & 6 & -2 & 3 & -5 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (-54, 6) \): \( \frac{6}{-54} = -\frac{1}{9} \)
- For \( (18, -2) \): \( \frac{-2}{18} = -\frac{1}{9} \)
- For \( (-27, 3) \): \( \frac{3}{-27} = -\frac{1}{9} \)
- For \( (45, -5) \): \( \frac{-5}{45} = -\frac{1}{9} \)

The ratios are constant (\( -\frac{1}{9}, -\frac{1}{9}, -\frac{1}{9}, -\frac{1}{9} \)). Therefore, \( x \) and \( y \) are proportional.

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5)

\[
\begin{array}{c|cccc}
x & 18 & 15 & 14 & 12 \\
\hline
y & 90 & 75 & 70 & 60 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (18, 90) \): \( \frac{90}{18} = 5 \)
- For \( (15, 75) \): \( \frac{75}{15} = 5 \)
- For \( (14, 70) \): \( \frac{70}{14} = 5 \)
- For \( (12, 60) \): \( \frac{60}{12} = 5 \)

The ratios are constant (\( 5, 5, 5, 5 \)). Therefore, \( x \) and \( y \) are proportional.

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6)

\[
\begin{array}{c|cccc}
x & 9 & 3 & 2 & 6 \\
\hline
y & 0 & 6 & 10 & 3 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (9, 0) \): \( \frac{0}{9} = 0 \)
- For \( (3, 6) \): \( \frac{6}{3} = 2 \)
- For \( (2, 10) \): \( \frac{10}{2} = 5 \)
- For \( (6, 3) \): \( \frac{3}{6} = \frac{1}{2} \)

The ratios are not constant (\( 0, 2, 5, \frac{1}{2} \)). Therefore, \( x \) and \( y \) are not proportional.

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7)

\[
\begin{array}{c|cccc}
x & 4 & 2 & 3 & 9 \\
\hline
y & 20 & 10 & 15 & 45 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (4, 20) \): \( \frac{20}{4} = 5 \)
- For \( (2, 10) \): \( \frac{10}{2} = 5 \)
- For \( (3, 15) \): \( \frac{15}{3} = 5 \)
- For \( (9, 45) \): \( \frac{45}{9} = 5 \)

The ratios are constant (\( 5, 5, 5, 5 \)). Therefore, \( x \) and \( y \) are proportional.

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8)

\[
\begin{array}{c|cccc}
x & 10 & 16 & 20 & 26 \\
\hline
y & 5 & 8 & 10 & 13 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (10, 5) \): \( \frac{5}{10} = \frac{1}{2} \)
- For \( (16, 8) \): \( \frac{8}{16} = \frac{1}{2} \)
- For \( (20, 10) \): \( \frac{10}{20} = \frac{1}{2} \)
- For \( (26, 13) \): \( \frac{13}{26} = \frac{1}{2} \)

The ratios are constant (\( \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2} \)). Therefore, \( x \) and \( y \) are proportional.

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9)

\[
\begin{array}{c|cccc}
x & 5 & 10 & 15 & 20 \\
\hline
y & 2 & 4 & 6 & 8 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (5, 2) \): \( \frac{2}{5} \)
- For \( (10, 4) \): \( \frac{4}{10} = \frac{2}{5} \)
- For \( (15, 6) \): \( \frac{6}{15} = \frac{2}{5} \)
- For \( (20, 8) \): \( \frac{8}{20} = \frac{2}{5} \)

The ratios are constant (\( \frac{2}{5}, \frac{2}{5}, \frac{2}{5}, \frac{2}{5} \)). Therefore, \( x \) and \( y \) are proportional.

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10)

\[
\begin{array}{c|cccc}
x & -4 & -2 & 6 & 2 \\
\hline
y & -14 & -7 & 21 & 7 \\
\end{array}
\]

- Calculate \( \frac{y}{x} \) for each pair:
- For \( (-4, -14) \): \( \frac{-14}{-4} = \frac{7}{2} \)
- For \( (-2, -7) \): \( \frac{-7}{-2} = \frac{7}{2} \)
- For \( (6, 21) \): \( \frac{21}{6} = \frac{7}{2} \)
- For \( (2, 7) \): \( \frac{7}{2} = \frac{7}{2} \)

The ratios are constant (\( \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2} \)). Therefore, \( x \) and \( y \) are proportional.

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Final Answers:

\[
\boxed{
\begin{array}{cccccc}
1) & \text{Not proportional} & 2) & \text{Proportional} & 3) & \text{Not proportional} \\
4) & \text{Proportional} & 5) & \text{Proportional} & 6) & \text{Not proportional} \\
7) & \text{Proportional} & 8) & \text{Proportional} & 9) & \text{Proportional} \\
10) & \text{Proportional} & & & &
\end{array}
}
\]