Write 10 and one-third minus three-eighths in its simplest form.
10 and one-third is a mixed number and three-eighth is a fraction. To subtract a fraction from a mixed number, we’ll need to find a common denominator. What would be the least common multiple between three and eight? Three times eight equals 24, and that means 24 is a multiple of three and eight. Three times eight equals 24. If we multiply the denominator by eight, we need to multiply the numerator by eight. One times eight equals eight. Eight times three equals 24. If we multiply the denominator on this side by three, we need to multiply the numerator by three. Three times three equals nine.
Now we have common denominators, we see that we’re trying to subtract nine twenty-fourths from 10 and eight twenty-fourths. However, we can’t subtract nine from eight. And that means we need to borrow from our whole number. Instead of having 10, we can separate that 10 into nine plus one plus eight twenty-fourths. And we wanna turn that one into a value with a denominator of 24. Twenty-four twenty-fourths is the same thing as one. Now we can add 24 plus eight, which equals 32. The denominator stays the same; it stays 24. And our whole number is now nine. Nine and thirty-two twenty-fourths is the same thing as 10 and one-third. And we’re going to subtract nine twenty-fourths. To do this we’ll subtract the numerators, 32 minus nine equals 23. The denominator doesn’t change; it’s still four. And we’re not subtracting anything from our whole number. So it stays nine. 23 is a prime number, and that means the fraction twenty-three twenty-fourths is in its simplest form: nine and twenty-three twenty-fourths.