To solve these ratio tables, we need to find the relationship between $x$ and $y$. In a ratio table, the ratio $\frac{y}{x}$ (or sometimes $\frac{x}{y}$) stays constant. We can find this constant by looking at any column where both numbers are given, and then use it to fill in the blanks.
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Let’s go one by one:
(1)
Given: when $x = 1$, $y = 2$ → so ratio is $y = 2x$
- When $x = 4$: $y = 2 × 4 = 8$
- When $x = 5$: $y = 2 × 5 = 10$
✔ matches
- When $x = 9$: $y = 2 × 9 = 18$
→ Blanks:
8,
18
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(2)
Given: when $x = 9$, $y = 1$ → so $y = \frac{1}{9}x$
Check with another: when $y = 4$, what should $x$ be? $x = 9 × 4 = 36$
When $y = 8$, $x = 9 × 8 = 72$
Also, when $x = 27$, $y = 27 ÷ 9 = 3$
→ Blanks:
3,
36,
72
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(3)
Given: when $x = 5$, $y = 25$ → so $y = 5x$
Check: if $y = 10$, then $x = 10 ÷ 5 = 2$
If $y = 50$, then $x = 50 ÷ 5 = 10$
If $x = 6$, then $y = 5 × 6 = 30$
→ Blanks:
2,
10,
30
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(4)
Look at known pairs:
When $x = 4$, $y = 8$ → so $y = 2x$
Check others:
If $y = 6$, then $x = 6 ÷ 2 = 3$
If $y = 4$, then $x = 4 ÷ 2 = 2$
If $y = 16$, then $x = 16 ÷ 2 = 8$
→ Blanks:
3,
2,
8
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(5)
Given: $x=1$, $y=5$ → $y = 5x$
So:
$x=9$ → $y=45$
$y=50$ → $x=10$
$x=8$ → $y=40$
→ Blanks:
10,
45,
40
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(6)
Given: $x=4$, $y=24$ → $y = 6x$
Check:
If $y=18$, $x=3$
If $y=60$, $x=10$
If $x=5$, $y=30$
→ Blanks:
3,
10,
30
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(7)
Given: $x=8$, $y=2$ → $y = \frac{1}{4}x$ or $x = 4y$
Check:
If $y=10$, $x=40$
If $x=56$, $y=14$
If $x=72$, $y=18$
→ Blanks:
40,
14,
18
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(8)
Given: $x=7$, $y=2$ → $y = \frac{2}{7}x$
Or better: look for multiples.
From $x=7, y=2$ → multiply both by same number.
Next: $y=6$ → that’s 3×2 → so $x=7×3=21$
Then $y=12$ → 6×2 → $x=7×6=42$
Finally, $x=63$ → 9×7 → $y=2×9=18$
→ Blanks:
21,
42,
18
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(9)
Given: $x=10$, ? ; $x=15$, ? ; $x=18$, $y=72$
Look at last pair: $x=18$, $y=72$ → $y = 4x$
Check: if $y=80$, then $x=20$
If $x=10$, $y=40$
If $x=15$, $y=60$
→ Blanks:
20,
40,
60
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(10)
Given: $x=6$, ? ; $x=20$, $y=60$ → $y = 3x$
Check: if $y=42$, $x=14$
If $x=10$, $y=30$
If $x=6$, $y=18$
→ Blanks:
18,
14,
30
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(11)
Given: $x=3$, $y=12$ → $y = 4x$
So:
$x=10$ → $y=40$
$x=4$ → $y=16$
$x=5$ → $y=20$
→ Blanks:
40,
16,
20
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(12)
Given: $x=6$, $y=4$ → $y = \frac{2}{3}x$
Or simplify: divide both by 2 → $x=3$, $y=2$ → so $y = \frac{2}{3}x$
But easier: see pattern — every time x increases by 6, y increases by 4?
Actually, ratio: $y/x = 4/6 = 2/3$
So:
$x=12$ → $y=8$
$x=18$ → $y=12$
$x=24$ → $y=16$
→ Blanks:
8,
12,
16
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Final Answer:
(1) 8, 18
(2) 3, 36, 72
(3) 2, 10, 30
(4) 3, 2, 8
(5) 10, 45, 40
(6) 3, 10, 30
(7) 40, 14, 18
(8) 21, 42, 18
(9) 20, 40, 60
(10) 18, 14, 30
(11) 40, 16, 20
(12) 8, 12, 16
Parent Tip: Review the logic above to help your child master the concept of rate tables worksheet.
