Final answer:
The equation 30/35=18/42 is false because after simplifying both fractions, we get 6/7 and 3/7, which are not equal. This can also be confirmed by cross-multiplying the fractions, which results in non-equal products.
Step-by-step explanation:
Comparing Two Fractions
To determine if the equation 30/35=18/42 is true or false, we need to simplify both fractions and then compare them. Firstly, both fractions can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD). For 30/35, the GCD is 5, so after dividing both the numerator and denominator by 5, we get 6/7. For 18/42, the GCD is 6, and after simplifying we get 3/7.
After simplification, it's clear that 6/7 does not equal 3/7, so the original equation 30/35=18/42 is fae. To check our work, we can also cross-multiply the original and see if the products are equal. For 30/35 and 18/42, cross-multiplying gives us 30×42 = 1260 and 35×18 = 630. Since 1260 does not equal 630, this confirms that the equation is false.