Ratio Tables worksheet for practicing proportional relationships and completing missing values in ratio tables.

To solve these ratio tables, we need to find the relationship between the top row ($x$) and the bottom row ($y$). In a ratio table, this relationship is constant. This means if you multiply or divide the $x$ value by a certain number to get a new $x$, you must do the exact same thing to the $y$ value.

Let's work through each table one by one.

Table (1)
* Find the rule: Look at the first column. $x = 1$ and $y = 2$. To get from 1 to 2, we multiply by 2. Let's check if this works for the third column: $x = 5$ and $y = 10$. $5 \times 2 = 10$. The rule is multiply $x$ by 2 to get $y$.
* Fill in the blanks:
* For $x = 4$: $4 \times 2 = 8$.
* For $x = 9$: $9 \times 2 = 18$.
* Answer: 8, 18

Table (2)
* Find the rule: Look at the first column. $x = 9$ and $y = 1$. To get from 9 to 1, we divide by 9 (or multiply by $\frac{1}{9}$). Let's check the third column: $y = 4$. If we multiply $4 \times 9$, we get 36.
* Fill in the blanks:
* For $x = 27$: $27 \div 9 = 3$.
* For $y = 4$: $4 \times 9 = 36$.
* For $y = 8$: $8 \times 9 = 72$.
* Answer: 3, 36, 72

Table (3)
* Find the rule: Look at the first column. $x = 5$ and $y = 25$. To get from 5 to 25, we multiply by 5.
* Fill in the blanks:
* For $y = 10$: We need to find $x$. $10 \div 5 = 2$.
* For $y = 50$: We need to find $x$. $50 \div 5 = 10$.
* For $x = 6$: $6 \times 5 = 30$.
* Answer: 2, 10, 30

Table (4)
* Find the rule: Look at the second column. $x = 4$ and $y = 8$. To get from 4 to 8, we multiply by 2.
* Fill in the blanks:
* For $y = 6$: We need $x$. $6 \div 2 = 3$.
* For $y = 4$: We need $x$. $4 \div 2 = 2$.
* For $y = 16$: We need $x$. $16 \div 2 = 8$.
* Answer: 3, 2, 8

Table (5)
* Find the rule: Look at the first column. $x = 1$ and $y = 5$. To get from 1 to 5, we multiply by 5.
* Fill in the blanks:
* For $x = 9$: $9 \times 5 = 45$.
* For $y = 50$: We need $x$. $50 \div 5 = 10$.
* For $x = 8$: $8 \times 5 = 40$.
* Answer: 45, 10, 40

Table (6)
* Find the rule: Look at the first column. $x = 4$ and $y = 24$. To get from 4 to 24, we multiply by 6.
* Fill in the blanks:
* For $y = 18$: We need $x$. $18 \div 6 = 3$.
* For $y = 60$: We need $x$. $60 \div 6 = 10$.
* For $x = 5$: $5 \times 6 = 30$.
* Answer: 3, 10, 30

Table (7)
* Find the rule: Look at the first column. $x = 8$ and $y = 2$. To get from 8 to 2, we divide by 4.
* Fill in the blanks:
* For $y = 10$: We need $x$. $10 \times 4 = 40$.
* For $x = 56$: $56 \div 4 = 14$.
* For $x = 72$: $72 \div 4 = 18$.
* Answer: 40, 14, 18

Table (8)
* Find the rule: Look at the first column. $x = 7$ and $y = 2$. To get from 7 to 2, we multiply by $\frac{2}{7}$. Alternatively, look at the relationship between $x$ and $y$ across columns.
* Column 1: $x=7, y=2$.
* Column 2: $y=6$. This is $2 \times 3$. So $x$ must be $7 \times 3 = 21$.
* Column 3: $y=12$. This is $2 \times 6$. So $x$ must be $7 \times 6 = 42$.
* Column 4: $x=63$. This is $7 \times 9$. So $y$ must be $2 \times 9 = 18$.
* Fill in the blanks: 21, 42, 18.
* Answer: 21, 42, 18

Table (9)
* Find the rule: Look at the third column. $x = 15$ and $y = ?$. Look at the fourth column. $x = 18$ and $y = 72$.
* Let's check the ratio $y/x$. $72 / 18 = 4$.
* Let's check the first column. $x = 10$. If the ratio is 4, $y$ should be $10 \times 4 = 40$.
* Let's check the second column. $y = 80$. If the ratio is 4, $x$ should be $80 / 4 = 20$.
* Let's check the third column. $x = 15$. $y$ should be $15 \times 4 = 60$.
* Fill in the blanks:
* For $x = 10$: $10 \times 4 = 40$.
* For $y = 80$: $80 / 4 = 20$.
* For $x = 15$: $15 \times 4 = 60$.
* Answer: 20, 40, 60

Table (10)
* Find the rule: Look at the second column. $x = 20$ and $y = 60$. To get from 20 to 60, we multiply by 3.
* Fill in the blanks:
* For $x = 6$: $6 \times 3 = 18$.
* For $y = 42$: We need $x$. $42 / 3 = 14$.
* For $x = 10$: $10 \times 3 = 30$.
* Answer: 18, 14, 30

Table (11)
* Find the rule: Look at the first column. $x = 3$ and $y = 12$. To get from 3 to 12, we multiply by 4.
* Fill in the blanks:
* For $x = 10$: $10 \times 4 = 40$.
* For $x = 4$: $4 \times 4 = 16$.
* For $x = 5$: $5 \times 4 = 20$.
* Answer: 40, 16, 20

Table (12)
* Find the rule: Look at the first column. $x = 6$ and $y = 4$. The ratio is $4/6$ or $2/3$. Or simply, $y$ is $\frac{2}{3}$ of $x$.
* Alternatively, look at the pattern in $x$: 6, 12, 18, 24 (adding 6 each time).
* The pattern in $y$ should be adding 4 each time (since $6 \to 4$).
* $12 \to 8$ ($12 \times \frac{2}{3} = 8$).
* $18 \to 12$ ($18 \times \frac{2}{3} = 12$).
* $24 \to 16$ ($24 \times \frac{2}{3} = 16$).
* Fill in the blanks: 8, 12, 16.
* Answer: 8, 12, 16

Final Answer:
(1) 8, 18
(2) 3, 36, 72
(3) 2, 10, 30
(4) 3, 2, 8
(5) 45, 10, 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