Questions and Answers
A fraction represents a part of a whole and consists of a numerator and a ______.
denominator
When adding like fractions, we keep the ______ the same.
denominator
To add unlike fractions, one must first find a common ______.
denominator
When subtracting like fractions, we subtract the ______ and keep the denominator the same.
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When multiplying fractions, we multiply the ______ together.
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To divide fractions, we multiply by the ______ of the divisor.
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For multiplying fractions, after calculating the new numerator and denominator, we may need to ______ the fraction.
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In the example of adding unlike fractions, the result of ______ and ______ gives us the final fraction.
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When subtracting the fractions (2/3 and 1/4), the result is ______.
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Study Notes
Fractions
- Definition: A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).
Adding Fractions
-
Like Fractions:
- Add the numerators.
- Keep the denominator the same.
- Example: ( \frac{2}{5} + \frac{3}{5} = \frac{2 + 3}{5} = \frac{5}{5} = 1 )
-
Unlike Fractions:
- Find a common denominator (LCD).
- Convert each fraction.
- Add the numerators.
- Example: ( \frac{1}{4} + \frac{1}{6} )
- LCD = 12; ( \frac{1}{4} = \frac{3}{12}, \ \frac{1}{6} = \frac{2}{12} )
- Result: ( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} )
Subtracting Fractions
-
Like Fractions:
- Subtract the numerators.
- Keep the denominator the same.
- Example: ( \frac{5}{8} - \frac{3}{8} = \frac{5 - 3}{8} = \frac{2}{8} = \frac{1}{4} )
-
Unlike Fractions:
- Find a common denominator (LCD).
- Convert each fraction.
- Subtract the numerators.
- Example: ( \frac{2}{3} - \frac{1}{4} )
- LCD = 12; ( \frac{2}{3} = \frac{8}{12}, \ \frac{1}{4} = \frac{3}{12} )
- Result: ( \frac{8}{12} - \frac{3}{12} = \frac{5}{12} )
Multiplying Fractions
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify if necessary.
- Example: ( \frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10} )
Dividing Fractions
- Multiply by the reciprocal of the divisor.
- Example: ( \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} )
- Simplify if necessary.
Fractions Overview
- A fraction denotes a part of a whole, comprising a numerator (top part) and a denominator (bottom part).
Adding Fractions
-
Like Fractions:
- Combine the numerators while keeping the denominator unchanged.
- For example: ( \frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1 ).
-
Unlike Fractions:
- Determine the least common denominator (LCD) to convert each fraction.
- Add the adjusted numerators.
- For example:
- Calculate LCD for ( \frac{1}{4} + \frac{1}{6} ), which is 12.
- Convert: ( \frac{1}{4} = \frac{3}{12}, \ \frac{1}{6} = \frac{2}{12} ).
- Final result: ( \frac{5}{12} ).
Subtracting Fractions
-
Like Fractions:
- Subtract the numerators, maintaining the same denominator.
- Example: ( \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} ).
-
Unlike Fractions:
- Identify the least common denominator (LCD).
- Transform each fraction to the common denominator before subtracting the numerators.
- Example:
- For ( \frac{2}{3} - \frac{1}{4} ), determine LCD as 12.
- Convert: ( \frac{2}{3} = \frac{8}{12}, \ \frac{1}{4} = \frac{3}{12} ).
- Resulting in ( \frac{5}{12} ).
Multiplying Fractions
- Multiply the numerators together to form the new numerator.
- Multiply the denominators to create the new denominator.
- Simplify the result if necessary.
- Example: For ( \frac{2}{5} \times \frac{3}{4} ), calculate ( \frac{6}{20} ) which simplifies to ( \frac{3}{10} ).
Dividing Fractions
- Perform division by multiplying the first fraction by the reciprocal of the second.
- Example: ( \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} ).
- Remember to simplify the result if possible.
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Description
Test your understanding of fractions with this quiz focused on adding and subtracting both like and unlike fractions. Learn to find common denominators and apply the rules correctly through practical examples. Challenge yourself to master the fundamental concepts of fractions!
