We are given the problem 7/10 minus 1/6. These fractions have different denominators, which means we cannot subtract them directly. To visualize this, we can represent 7/10 as a bar divided into 10 equal parts with 7 parts shaded, and 1/6 as a bar divided into 6 equal parts with 1 part shaded.
To subtract fractions with different denominators, we need to find a common denominator. The best choice is the least common multiple, or LCM. Let's find the LCM of 10 and 6 by listing their multiples. The multiples of 10 are 10, 20, 30, 40, 50, and so on. The multiples of 6 are 6, 12, 18, 24, 30, 36, and so on. We can see that 30 is the smallest number that appears in both lists, so the LCM of 10 and 6 is 30.
Now we convert both fractions to equivalent fractions with the common denominator of 30. For 7/10, we multiply both the numerator and denominator by 3, giving us 21/30. For 1/6, we multiply both the numerator and denominator by 5, giving us 5/30. We can visualize these equivalent fractions using bars divided into 30 parts. The first bar has 21 parts shaded, and the second bar has 5 parts shaded.
Now that both fractions have the same denominator, we can subtract them by subtracting the numerators. Our problem is 21/30 minus 5/30. We subtract the numerators: 21 minus 5 equals 16. The denominator stays the same, so our result is 16/30. Visually, we start with a bar representing 21/30, remove 5 parts, and are left with 16 parts out of 30.
Our result is 16/30, but this fraction can be simplified. To simplify a fraction, we find the greatest common divisor, or GCD, of the numerator and denominator. The factors of 16 are 1, 2, 4, 8, and 16. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The greatest common factor is 2. We divide both the numerator and denominator by 2: 16 divided by 2 is 8, and 30 divided by 2 is 15. So 16/30 simplifies to 8/15. This is our final answer: 7/10 minus 1/6 equals 8/15. We can visualize this as a bar divided into 15 parts with 8 parts shaded.