Multiplying fractions with different denominators is simpler than adding or subtracting them. You don’t need to find a common denominator! Just multiply the numerators (top numbers) and denominators (bottom numbers) separately.
Example: Multiply
\frac{2}{3} and\frac{4}{5} .
- Multiply the numerator: 2 × 4=8.
- Multiply the denominator: 3 × 5=15.
So,
\frac{2}{3} \times \frac{4}{5} = \frac{8}{15} .
Steps to Multiply Fractions with Different Denominators
To multiply fractions with different or the same denominator, we can use the following steps:
- Multiply the Numerators: Take the top numbers (numerators) of both fractions and multiply them together.
\text{New Numerator} = \text{Numerator}_1 \times \text{Numerator}_2
- Multiply the Denominators: Take the bottom numbers (denominators) of both fractions and multiply them together.
\text{New Denominator} = \text{Denominator}_1 \times \text{Denominator}_2
- Write the Resulting Fraction: Place the new numerator over the new denominator to form a new fraction.
\text{Result} = \frac{\text{New Numerator}}{\text{New Denominator}}
Note: If the resulting fraction can be simplified (i.e., the numerator and denominator have a common factor), divide both by that factor to reduce the fraction to its simplest form.
Example: Multiply the fractions 1/3 and 4/5.
Solution:
- Multiply the numerators: ( 1 × 4 = 4 )
- Multiply the denominators: ( 3 × 5 = 15 )
- Write the resulting fraction: 4/15
- Simplify: 4/15 is already in simplest form.
Note: To multiply mixed fractions, simply convert them into improper fractions and use the same steps discussed above.
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