Writing & Simplifying Ratios - Pre Algebra

1. How do you write a ratio of whole numbers in simplest form?

   Divide every term by the greatest common factor of the terms.

2. What is the difference between a part-to-part ratio and a part-to-whole ratio?

   Part-to-part compares two parts of a group (boys to girls). Part-to-whole compares one part to the entire group (boys to all students).

3. What are three ways to write the ratio of 3 to 5?

   $3:5$, 3 to 5, and $\frac{3}{5}$. All three name the same comparison.

4. Simplify the ratio $2.5:10$ to whole numbers in simplest form.

   $1:4$. Divide both terms by 2.5.

5. A class has 12 boys and 15 girls. What is the ratio of boys to girls in simplest form?

   $4:5$. Divide 12 and 15 by their GCF, 3.

6. A bag holds 7 red marbles and 3 blue marbles. What is the ratio of blue marbles to all marbles?

   $3:10$. There are 10 marbles in all, and 3 of them are blue.

7. Simplify the ratio $45:60:75$.

   $3:4:5$. Divide every term by their GCF, 15.

8. A class has 12 boys and 15 girls. What is the ratio of girls to all students in simplest form?

   $5:9$. There are 27 students, and $15:27$ simplifies by dividing by 3.

9. Simplify the ratio $\frac{1}{2}:\frac{3}{4}$ to whole numbers.

   $2:3$. Multiply both terms by 4 to clear the fractions.

10. What is the ratio of 2 feet to 8 inches in simplest form?

    $3:1$. Convert to the same unit first: 24 inches to 8 inches is $24:8 = 3:1$.

11. Why does the order of the terms in a ratio matter?

    The terms follow the order the quantities are named, so $3:5$ and $5:3$ describe different comparisons.

12. Simplify the ratio $18:24$.

    $3:4$. Divide both terms by their GCF, 6.

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