Final answer:
Our intuition can assist us in figuring out addition and subtraction of fractions by using principles we already know about working with whole numbers. When the denominators are the same, we add or subtract the numerators. When the denominators are different, we find a common denominator before adding or subtracting.
Step-by-step explanation:
Our intuition can assist us in figuring out addition and subtraction of fractions by relying on our understanding of whole numbers and applying the same principles to fractions. When adding fractions, we can use our intuition to recognize that if the denominators are the same, we can simply add the numerators. For example, 1/2 + 3/2 = (1 + 3)/2 = 4/2 = 2. If the denominators are different, we can use our intuition to recognize that we need a common denominator before adding. For example, 1/2 + 1/3 = (1 * 3)/(2 * 3) + (1 * 2)/(3 * 2) = 3/6 + 2/6 = 5/6.
When subtracting fractions, we can use similar intuition. If the denominators are the same, we can simply subtract the numerators. For example, 3/4 - 1/4 = (3 - 1)/4 = 2/4 = 1/2. If the denominators are different, we need a common denominator before subtracting. For example, 3/4 - 1/3 = (3 * 3)/(4 * 3) - (1 * 4)/(3 * 4) = 9/12 - 4/12 = 5/12.