Final answer:
To multiply fractions, multiply the numerators and denominators respectively; to divide fractions, multiply by the reciprocal of the divisor. After performing the operations, fractions should be simplified if possible.
Step-by-step explanation:
Understanding Fraction Multiplication and Division
When dealing with fraction multiplication and division, the process is straightforward. To multiply fractions, you simply multiply the numerators (top numbers) and multiply the denominators (bottom numbers). To divide fractions, you multiply by the reciprocal of the divisor (flip the second fraction upside down). Let's apply these rules to the problems at hand:
- a) Divide 3/4 by 5/6: To do this, multiply 3/4 by the reciprocal of 5/6, which is 6/5. Thus, 3/4 Ã 6/5 = 18/20, which simplifies to 9/10.
- b) Multiply 2/3 by 7/8: Multiplying the numerators 2 and 7 gives 14, and multiplying the denominators 3 and 8 gives 24, so the result is 14/24, which simplifies to 7/12.
- c) Divide 1/2 by 4/9: Multiply 1/2 by the reciprocal of 4/9, which is 9/4. Thus, 1/2 Ã 9/4 = 9/8, which is 1 1/8 in mixed number form.
- d) Multiply 5/7 by 3/10: Multiplying the numerators 5 and 3 gives 15, and multiplying the denominators 7 and 10 gives 70, so the result is 15/70, which simplifies to 3/14.
Remember to always simplify your result if possible by dividing both the numerator and denominator by their greatest common factor.