Let's solve the questions one by one from the image you've uploaded.

1. Write each of these ratios in its simplest form:

(a) $3 : 12 : 17$
This ratio is already in its simplest form because there are no common factors between 3, 12, and 17 other than 1.

(b) $4 : 30 : 8$
The common factor here is 2: $4 \div 2 = 2,\quad 30 \div 2 = 15,\quad 8 \div 2 = 4$ So, the simplified ratio is $2 : 15 : 4$.

(c) $9 : 21 : 7$
The common factor is 3: $9 \div 3 = 3,\quad 21 \div 3 = 7,\quad 7 \div 3 = \text{already 7}.$ So, the simplified ratio is $3 : 7 : 1$.

(d) $11 : 99 : 9$
The common factor is 11: $11 \div 11 = 1,\quad 99 \div 11 = 9,\quad 9 \div 11 = 1.$ Thus, the simplified ratio is $1 : 9 : 1$.

(e) $7 : 21 : 3$
The common factor is 3: $7 \div 7 = 1,\quad 21 \div 7 = 3,\quad 3 \div 7 = \text{already simplified}.$ Thus, the simplest form is $1 : 3$.

(f) $12 : 15 : 4 : 5$
The greatest common divisor (GCD) here is 1, so this is already in its simplest form $12 : 15 : 4 : 5$.

2. Write in the form $1 : n$, each of the following ratios:

(a) $2 : 5$
Divide both by 2: $1 : \frac{5}{2}.$ Thus, the form is $1 : 2.5$.

(b) $8 : 40$
Divide both by 8: $1 : 5.$

(c) $5 : 7$
Divide both by 5: $1 : \frac{7}{5},\quad \text{or} \quad 1 : 1.4.$

(d) $5 : 2$
Divide both by 5: $1 : \frac{2}{5},\quad \text{or} \quad 1 : 0.4.$

(e) $10 : 37$
Divide both by 10: $1 : 3.7.$

(f) $20 : 50$
Divide both by 20: $1 : 2.5.$

3. In a class there are 18 girls and 12 boys. Write the ratio of boys to girls:

(a) In its simplest form: $\text{Ratio} = 12 : 18.$ Divide both by 6: $2 : 3.$

(b) In the form $1 : n$: $\frac{12}{18} = \frac{2}{3}.$ So, the form is $1 : 1.5$.

4. In a drink, 80 cm³ of pineapple juice is mixed with 20 cm³ of orange juice. Write the ratio of pineapple juice to orange juice:

(a) In its simplest form: $\text{Ratio} = 80 : 20.$ Divide both by 20: $4 : 1.$

(b) In the form $1 : n$: $\frac{80}{20} = 4,\quad \text{so the ratio is} \quad 1 : 0.25.$

Would you like further clarification on any of these steps?

Related Questions:

1. How do you find the simplest form of a ratio with three or more numbers?
2. What is the method to convert any ratio into the form $1 : n$?
3. Can ratios compare more than two quantities?
4. How would you handle ratios in mixed measurements, like liters and milliliters?
5. What is the real-world significance of simplifying ratios?

Tip:

When simplifying ratios, always check the greatest common divisor (GCD) of all terms in the ratio and divide by that.