Here are the step-by-step solutions to complete the tables.
(1) Boys and Girls
First, we need to find the relationship (ratio) between the number of boys and girls. Looking at the third column, we see
55 boys and
44 girls.
If we divide both numbers by 11, we get:
$55 \div 11 = 5$
$44 \div 11 = 4$
So, the ratio is
5 boys for every 4 girls. We can use this rule to fill in the blanks.
*
Column 1: We have 15 boys. Since $15 \div 5 = 3$, we multiply the girl's part by 3: $4 \times 3 = \mathbf{12}$.
*
Column 2: We have 8 girls. Since $8 \div 4 = 2$, we multiply the boy's part by 2: $5 \times 2 = \mathbf{10}$.
*
Column 4: We have 20 girls. Since $20 \div 4 = 5$, we multiply the boy's part by 5: $5 \times 5 = \mathbf{25}$.
*
Column 5: We have 35 boys. Since $35 \div 5 = 7$, we multiply the girl's part by 7: $4 \times 7 = \mathbf{28}$.
*
Column 6: We have 4 girls. This matches our base ratio exactly, so there are $\mathbf{5}$ boys.
(2) Eggs and Flour
Let's look for a complete pair to find the pattern. In the last column, we have
39 eggs and
2.5 kg of flour. That calculation is a bit tricky. Let's look at the first column:
3 eggs and
0.5 kg of flour.
This tells us that for every
3 eggs, you need
0.5 kg of flour. Or simply, the number of eggs is
6 times the amount of flour ($3 \div 0.5 = 6$).
*
Column 2: We have 9 eggs. $9 \div 6 = \mathbf{1.5}$ kg.
*
Column 3: We have 1 kg of flour. $1 \times 6 = \mathbf{6}$ eggs.
*
Column 4: We have 33 eggs. $33 \div 6 = \mathbf{5.5}$ kg.
*
Column 5: We have 2 kg of flour. $2 \times 6 = \mathbf{12}$ eggs.
*
Column 7: We have 2.5 kg of flour. $2.5 \times 6 = \mathbf{15}$ eggs. *(Note: The image lists 39 eggs for 2.5kg, which seems to be a typo in the worksheet itself as it breaks the pattern established by the other numbers. Based on the consistent pattern of the rest of the table, 15 is the mathematically correct proportional answer).*
(3) Kilometers and Time
Let's check the pace using the second column:
6 km in
39 minutes.
$39 \div 6 = 6.5$ minutes per kilometer.
Let's verify with the fourth column:
15 km. $15 \times 6.5 = 97.5$ minutes.
Let's verify with the last column:
71.5 minutes. $71.5 \div 6.5 = 11$ km.
Now we can fill in the missing spots using the rule:
Time = Kilometers $\times$ 6.5.
*
Column 1: 7 km. $7 \times 6.5 = \mathbf{45.5}$ minutes.
*
Column 3: 65 minutes. $65 \div 6.5 = \mathbf{10}$ km.
*
Column 4: 15 km. $15 \times 6.5 = \mathbf{97.5}$ minutes.
*
Column 5: 26 minutes. $26 \div 6.5 = \mathbf{4}$ km.
*
Column 7: 71.5 minutes. $71.5 \div 6.5 = \mathbf{11}$ km.
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Final Answer:
(1) Number of boys / Number of girls
* Col 1: 15 /
12
* Col 2:
10 / 8
* Col 4:
25 / 20
* Col 5: 35 /
28
* Col 6:
5 / 4
(2) Number of eggs / Flower (kg)
* Col 2: 9 /
1.5
* Col 3:
6 / 1
* Col 4: 33 /
5.5
* Col 5:
12 / 2
* Col 7:
15 / 2.5
(3) Kilometers / Time (minutes)
* Col 1: 7 /
45.5
* Col 3:
10 / 65
* Col 4: 15 /
97.5
* Col 5:
4 / 26
* Col 7:
11 / 71.5
Parent Tip: Review the logic above to help your child master the concept of ratio and proportion printable worksheet.
