Final answer:
To simplify a complex fraction, we cancel out quantities that are equal in the numerator and denominator. For instance, 1 meter over 100 centimeters simplifies to 1 since they represent the same length. By performing equivalent operations on both sides, the value of the expression is preserved, keeping the equality intact.
Step-by-step explanation:
The question asks us to find an expression equivalent to a given complex fraction. Let's simplify the complex fraction step-by-step while maintaining the equality. Firstly, we note that a fraction with the same quantity in the numerator and denominator equals 1. Applying this rule, we can simplify parts of the complex fraction.
For example, if we have 1 meter in the numerator and 100 centimeters, which is equivalent to 1 meter, in the denominator, they would cancel out and leave us with 1:
We then cancel equivalent terms in the numerator and denominator:
- 0.00675 (0.15)m
- --------------- = 4.5 m
- 0.00300 (0.10)m
When we cross multiply both sides of an equation, it helps us find the value of the expression with the appropriate unit:
- ----- 7.88 cm3
- Right numerator x Left denominator = Left numerator x Right denominator
We must perform the same operation on both sides of an equation to maintain the equality. Also, understanding fractions and their relationship to multiplication and division is essential: dividing by a number is the same as multiplying by its reciprocal.