Multiplying Fractions
Learn how to multiply fractions by multiplying numerators and denominators, and understand what it means to take a fraction of a fraction.
Definition
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Worked Examples
Calculate
Multiply the numerators
→ New numerator:
Multiply the denominators
→ New denominator:
Write the result
→
Simplify by dividing by GCF (2)
→
Answer:
Common Mistakes
Adding numerators and denominators instead of multiplying
Why it's wrong: Students confuse fraction multiplication with addition rules. Addition needs common denominators, but multiplication does not.
Correct: Always multiply: numerator times numerator, denominator times denominator. , not .
Finding common denominators before multiplying
Why it's wrong: This extra step comes from fraction addition. For multiplication, you don't need common denominators.
Correct: Just multiply straight across! No need to find common denominators when multiplying fractions.
Forgetting to simplify the final answer
Why it's wrong: The product of two fractions often needs to be reduced to lowest terms.
Correct: Always check if your answer can be simplified. Better yet, cross-cancel before multiplying to make the final answer easier.
Cross-canceling incorrectly (canceling horizontally)
Why it's wrong: Cross-canceling only works diagonally between a numerator and the opposite denominator.
Correct: You can only cancel a numerator with the other fraction's denominator, not with its own denominator.
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History
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Practice Problems
15 problemsWhat is ?
Why It Matters
- Cooking: If a recipe calls for cup of flour and you want to make half the recipe, you need cup
- Sales and Discounts: A shirt is off, and you have a coupon for off the sale price
- Time: If of the class finished a test, and of those got an A, what fraction got an A?
- Area: Finding the area of a rectangle with fractional dimensions
Real World Applications
Cooking and Recipes
When you scale a recipe up or down, you multiply fractions to find the new ingredient amounts.
Example:
If a cookie recipe needs cup butter and you make half the batch: cup butter.
A smoothie recipe calls for cup of yogurt. You want to make of the recipe.
How much yogurt do you need?
Step 1: Write the mathematical expression
Calculate:
Area Calculations
Finding the area of rectangles with fractional dimensions requires multiplying fractions.
Example:
A garden plot is meter wide and meter long. Area = square meter.
A picture frame is foot wide and foot tall.
What is the area of the picture frame?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1To multiply fractions, multiply numerators together and denominators together:
- 2The word 'of' in fraction problems usually means multiply
- 3Cross-canceling (simplifying before multiplying) makes calculations easier
- 4A whole number can be written as a fraction with denominator 1
- 5Always simplify your final answer to lowest terms
Frequently Asked Questions
Glossary
- Numerator
- The top number of a fraction, showing how many parts you have
- Denominator
- The bottom number of a fraction, showing how many equal parts the whole is divided into
- Cross-cancel
- Simplifying before multiplying by dividing a numerator and the opposite denominator by their common factor
- Product
- The result of multiplying two or more numbers
- Simplify
- Reduce a fraction to its lowest terms by dividing numerator and denominator by their GCF