Fraction Review Foldable | Math = Love - Free Printable

The image you provided is a summary of the basic operations with fractions: Reducing, Multiplying, Adding & Subtracting, and Dividing. Below, I will explain each section in detail:

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1. Reducing Fractions

- Definition: A fraction is fully reduced when the only number that divides evenly into both the numerator and the denominator is 1.
- Process: Divide both the numerator and the denominator by their greatest common divisor (GCD) until no further simplification is possible.

#### Example:
\[
\frac{120}{112} \div 2 = \frac{60}{56} \div 2 = \frac{30}{28} \div 2 = \frac{15}{14}
\]
\[
\frac{42}{56} \div 7 = \frac{21}{28} \div 7 = \frac{3}{4}
\]

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2. Multiplying Fractions

- Key Point: You can multiply fractions with any denominators.
- Steps:
1. Multiply the numerators.
2. Multiply the denominators.
3. Simplify the resulting fraction, if possible.

#### Example:
\[
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
\]

For instance:
\[
\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}
\]

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3. Adding & Subtracting Fractions

- Key Point: You can only add or subtract fractions if they have the same denominator.
- Steps:
1. Rewrite the fractions as equivalent fractions with the same denominator.
2. Add or subtract the numerators.
3. The denominator stays the same.
4. Simplify the resulting fraction, if possible.

#### Example:
To add \(\frac{1}{2}\) and \(\frac{1}{3}\):
1. Find a common denominator (LCM of 2 and 3 is 6).
2. Rewrite the fractions:
\[
\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
\]
3. Add the numerators:
\[
\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}
\]

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4. Dividing Fractions

- Key Point: You can divide fractions by rewriting the division as a multiplication problem.
- Steps:
1. Keep the first fraction the same.
2. Change the division sign to multiplication.
3. Flip (take the reciprocal) of the second fraction.
4. Follow the rules for multiplying fractions.

#### Example:
To divide \(\frac{2}{3}\) by \(\frac{4}{5}\):
1. Keep the first fraction: \(\frac{2}{3}\).
2. Change division to multiplication: \(\frac{2}{3} \times \).
3. Flip the second fraction: \(\frac{4}{5}\) becomes \(\frac{5}{4}\).
4. Multiply:
\[
\frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}
\]
5. Simplify:
\[
\frac{10}{12} = \frac{5}{6}
\]

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Summary of Rules

1. Reducing: Divide numerator and denominator by their GCD.
2. Multiplying: Multiply numerators and denominators, then simplify.
3. Adding & Subtracting: Ensure same denominators, add/subtract numerators, keep denominator, simplify.
4. Dividing: Rewrite as multiplication by flipping the second fraction, then multiply and simplify.

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Final Answer:

\[
\boxed{\text{See detailed explanations above.}}
\]