Final answer:
To find differences between fractions, we can use number lines and equivalent fractions. By converting fractions to have a common denominator, we can easily subtract them, as seen with ½ and ⅔ becoming 2/4 and 3/4, resulting in a difference of 1/4.
Step-by-step explanation:
Finding Differences Using Number Lines and Equivalent Fractions
Understanding how to find the difference between two fractions is an essential skill in mathematics. When we look at a number line, fractions represent points between whole numbers. To find a difference, we identify the positions of two fractions and observe the distance between them. This is akin to subtracting the smaller fraction from the larger.
Let's consider how to compare fractions with different denominators using equivalent fractions. For example, if we are asked to find the difference between ½ and ⅔ (3/4), we could convert them to have a common denominator. We know that half of a whole is 0.5 and that three-quarters of a whole is 0.75. To compare these two fractions, we must express them both with the same baseline - that means finding equivalent fractions with the same denominator. The least common denominator (LCD) for 2 and 4 is 4. Thus, ½ is equivalent to 2/4, and now we can easily see that ⅔ - ½ (or 3/4 - 2/4) equals 1/4. This difference can also be visualized on a number line.
Similarly, if we must compare ⅔ (3/4) and ⅚ (5/6), we'd look for a common denominator of 12. Converting both fractions, we have 9/12 and 10/12, respectively. The difference here would be 10/12 - 9/12, resulting in 1/12.
Becoming comfortable with these concepts also helps with understanding larger mathematical ideas, such as finding the sum of fractions, which requires making denominators the same, a skill that applies to addition as well as finding differences.