Welcome to our lesson on subtracting fractions. Today, we will solve the problem 5/6 minus 2/10. To subtract fractions, they must have the same denominator. Let's see how we can solve this step by step.
Notice that the fractions have different denominators: 6 and 10. This means the parts are different sizes. We can't subtract them directly because we're comparing different-sized pieces. For example, 1/6 is larger than 1/10. We need to find a common way to represent these fractions.
To subtract these fractions, we need to find a common denominator. The best choice is the least common multiple (LCM) of the denominators. Let's list multiples of 6 and 10. For 6: 6, 12, 18, 24, 30, 36, and so on. For 10: 10, 20, 30, 40, and so on. The first common multiple is 30, so we'll use 30 as our common denominator.
Let's convert 5/6 to a fraction with denominator 30. We need to find what we multiply 6 by to get 30. Since 6 times 5 equals 30, we multiply both numerator and denominator by 5. So 5 times 5 is 25, and 6 times 5 is 30. Therefore, 5/6 equals 25/30.
Now let's convert 2/10 to a fraction with denominator 30. We need to find what we multiply 10 by to get 30. Since 10 times 3 equals 30, we multiply both numerator and denominator by 3. So 2 times 3 is 6, and 10 times 3 is 30. Therefore, 2/10 equals 6/30.
Now that both fractions have the same denominator, we can subtract. We have 25/30 minus 6/30. This equals (25 minus 6) over 30, which is 19/30. Visually, we start with 25 parts shaded and remove 6, leaving us with 19 parts shaded out of 30 total parts.
Our final answer is 19/30. Let's check if this fraction can be simplified. To simplify a fraction, we need to find common factors between the numerator and denominator. The factors of 19 are just 1 and 19 since 19 is a prime number. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The only common factor is 1, so 19/30 is already in its simplest form. Therefore, 5/6 minus 2/10 equals 19/30.