1. Introduction to fractions: A fraction is a numerical representation of a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number) separated by a horizontal line or diagonal slash.

2. Understanding the numerator: This number represents how many parts you have of the whole.

3. Understanding the denominator: This number indicates the total number of equal parts into which the whole is divided.

4. Simplifying fractions: To simplify a fraction, find the greatest common divisor (GCD) between the numerator and denominator and then divide both numbers by the GCD.

5. Adding fractions with common denominators: Add the numerators together, then place this sum over the common denominator.

6. Adding fractions with different denominators: Find a common denominator, convert both fractions into equivalent forms with this new denominator, then add as above.

7. Subtracting fractions: Follow a similar process as for addition – ensure that you have a common denominator before proceeding and then subtract the numerators.

8. Multiplying fractions: Multiply the numerators and multiply the denominators, then write these product results as your new numerator and new denominator respectively.

9. Dividing fractions: Turn the second fraction upside down (creating its reciprocal), convert division into multiplication, and follow step 8 as if you are multiplying two fractions together.

10. Mixed numbers: A mixed number is a combination of whole numbers and fractions that represent values greater than one e.g., “3 ½”. To convert it into an improper fraction (where numerator > denominator), multiply the whole number by the denominator, add it to the current numerator, and leave the denominator unchanged.

11. Converting decimals to fractions: Write down your decimal number over its place value (tenths, hundredths etc.), then reduce to its simplest form if necessary.

12. Comparing fractions: If comparing two fractions with the same form (i.e., having the same denominator), simply compare their numerators. If the denominators are different, find the least common multiple (LCM) to create equivalent fractions and then compare.

13. Visualizing fractions: Use graphical representations such as number lines, pie charts, and fraction strips as an effective way to understand and explain fractions better.

By following these 13 steps, you can gain a strong foundation in understanding fractions and apply them in various mathematical operations and real-life situations. Keep practicing problems to become more comfortable with this fundamental mathematical concept.