Simplify the ratio to the lowest terms by dividing. 42:84=
The correct answer and explanation is:
The given ratio is 42:84. To simplify it, divide both terms by their greatest common divisor (GCD).
- Finding the GCD: The GCD of 42 and 84 is 42 because 42 is the largest number that divides both 42 and 84 evenly.
- Divide both terms by 42:
- 42 ÷ 42 = 1
- 84 ÷ 42 = 2
So, the ratio 42:84 simplifies to 1:2.
Explanation:
When simplifying a ratio, the goal is to express it in its lowest possible terms. This is done by dividing both numbers in the ratio by their GCD. The GCD is the largest number that divides both numbers without leaving a remainder.
In this case, 42 is a divisor of both 42 and 84, and when we divide both terms by 42, the ratio reduces to 1:2. This means that for every 1 unit of the first quantity, there are 2 units of the second quantity.
Ratios can often be simplified by factoring out common factors between the two numbers. This method ensures that the ratio is in its simplest form and is easier to work with. Simplification is especially useful in real-world applications, such as scaling recipes, adjusting quantities, or understanding proportions in fields like math, science, or even finance.
So, the simplified ratio of 42:84 is 1:2.