1. What a Fraction Represents
A fraction represents a part of a whole. It has two parts:
- The Numerator (top number) shows how many parts you have.
- The Denominator (bottom number) shows how many equal parts the whole is divided into.
This means we have 3 parts out of a whole that is divided into 4 equal parts.
Practice Problems:
1. For the fraction $\frac{5}{8}$, the numerator is ____ and the denominator is ____.
2. If a pizza is cut into 12 slices and you eat 5, what fraction of the pizza did you eat?
3. Write the fraction for the shaded part of a circle that is divided into 6 equal parts with 1 part shaded.
4. In a bag of 10 marbles, 3 are red. What fraction of the marbles are red?
2. Equivalent Fractions & Simplifying
Equivalent fractions are different fractions that name the same amount (e.g., $\frac{1}{2}$ is the same as $\frac{2}{4}$).
Simplifying a fraction means to reduce it to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).
Practice Problems: Find the equivalent fraction.
1. $\frac{1}{3} = \frac{?}{9}$
2. $\frac{3}{4} = \frac{?}{12}$
3. $\frac{2}{5} = \frac{4}{?}$
4. $\frac{5}{6} = \frac{?}{18}$
5. $\frac{7}{8} = \frac{14}{?}$
6. $\frac{1}{4} = \frac{?}{20}$
Practice Problems: Simplify the following fractions.
7. $\frac{4}{8}$
8. $\frac{6}{9}$
9. $\frac{10}{15}$
10. $\frac{12}{18}$
11. $\frac{5}{20}$
12. $\frac{14}{21}$
3. Comparing Fraction Sizes
To compare fractions, you can find a common denominator. The fraction with the larger numerator is the larger fraction.
Example: To compare $\frac{2}{3}$ and $\frac{3}{4}$, use a common denominator of 12. $\frac{2}{3} = \frac{8}{12}$ and $\frac{3}{4} = \frac{9}{12}$. Since 9 > 8, then $\frac{3}{4} > \frac{2}{3}$.
Practice Problems: Compare using <, >, or =.
1. $\frac{1}{2}$ ___ $\frac{3}{4}$
2. $\frac{2}{3}$ ___ $\frac{4}{6}$
3. $\frac{3}{5}$ ___ $\frac{1}{2}$
4. $\frac{5}{8}$ ___ $\frac{3}{4}$
5. $\frac{4}{5}$ ___ $\frac{5}{6}$
6. $\frac{7}{10}$ ___ $\frac{2}{3}$
4. Improper Fractions & Mixed Numbers
Improper Fraction: The numerator is larger than or equal to the denominator (e.g., $\frac{5}{3}$).
Mixed Number: A whole number and a fraction combined (e.g., $1\frac{2}{3}$).
Convert Mixed to Improper: (Whole Number × Denominator) + Numerator. Keep the same denominator.
Convert Improper to Mixed: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.
Practice Problems: Convert to a mixed number.
1. $\frac{7}{4}$
2. $\frac{11}{3}$
3. $\frac{9}{2}$
4. $\frac{13}{5}$
5. $\frac{16}{6}$
6. $\frac{25}{8}$
Practice Problems: Convert to an improper fraction.
7. $2\frac{1}{3}$
8. $3\frac{3}{4}$
9. $1\frac{5}{6}$
10. $4\frac{2}{5}$
11. $5\frac{1}{2}$
12. $6\frac{2}{3}$
5. Adding & Subtracting Fractions (Like Denominators)
To add or subtract fractions with the same denominator:
- Add or subtract the numerators.
- Keep the denominator the same.
- Simplify the result if possible.
Practice Problems: Add the fractions.
1. $\frac{1}{5} + \frac{2}{5} = $
2. $\frac{3}{8} + \frac{4}{8} = $
3. $\frac{2}{7} + \frac{3}{7} = $
4. $\frac{5}{12} + \frac{5}{12} = $
5. $\frac{3}{10} + \frac{6}{10} = $
6. $\frac{2}{9} + \frac{4}{9} = $
Practice Problems: Subtract the fractions.
7. $\frac{4}{5} - \frac{1}{5} = $
8. $\frac{7}{8} - \frac{3}{8} = $
9. $\frac{9}{10} - \frac{2}{10} = $
10. $\frac{5}{6} - \frac{4}{6} = $
11. $\frac{11}{12} - \frac{5}{12} = $
12. $\frac{8}{9} - \frac{2}{9} = $