When is it necessary to rename a mixed number when subtracting?

Answer 1

It is advisable to do so in all cases. It is particularly useful when

• the fractional part of the number being subtracted is bigger than fractional part of the number from which it is subtracted, or
  
• in the reverse situation but when the answer is negative.
  

Answer 2

Your question is a little unclear, but I'll see what I can do to answer it. If you have a subtraction problem involving mixed numbers (a whole number and a fraction jammed up together), you only have to rename the fractional part, and only if their denominators don't match up. For instance, if your problem is (and this will be hard to demonstrate here, so bear with the clunkiness of the presentation) three and three-fourths (3 3/4) minus one and one-fourth (1 1/4), you don't have to do any renaming, as you can simply subtract the whole number portions (3-1=2), subtract the fractional portions (3/4-1/4=2/4), and your answer is 2 2/4. (Since mathematicians and teachers don't like fractions like this, it can be simplified, making the correct answer 2 1/2, or two and one-half.)

If it's not that straightforward, however, then you may need to do some renaming. Let's look at 3 1/4 - 1 3/4. We could still subtract the whole numbers, but we can't subtract 1/4 - 3/4, so we have to do a little mathematical jiggery-pokery to make this work. What we can do is take one from the three, leaving two. We then change that one we took away into fourths and add them to the one-fourth. Since four fourths make a whole, and 4+1=5, that now makes our fraction 2 5/4. Now we can easily do the subtraction: 2-1=1, and 5/4-3/4=2/4, giving us an answer of 1 2/4 -- or 1 1/2 for those who require the simplest answer.

Ah, but what if the denominators don't match? We have to do a different kind of razzle-dazzle, but it will still work out fine in the end. Let's try 4 2/3 - 2 1/2. Since 2/3 is more than 1/2, we at least don't have to borrow. But we can't subtract a half from two-thirds, either. We need to change the fractions to something with the same denominator. (Fortunately, we can leave the whole numbers alone, at least this time.) We need a common multiple of 2 and 3, and if we can keep it small, everything is a lot easier. (We could use 120, since 2 and 3 both go into it, but do you really want to deal with numbers that big?) The smallest number that both 2 and 3 can divide into is 6, so we will change both fractions to sixths. Remember, when dealing with fractions, if you multiply or divide either the numerator or denominator by a number, you must do EXACTLY the same thing, with the same number, to the other one as well. In 2/3, our denominator is 3, but we want 6, so we must multiply by 2. And we must also multiply the numerator by 2, giving us a new numerator of 4, and a new equivalent fraction of 4/6. Let's do the same with 1/2, which also needs to be changed to sixths. Since 2x3=6, we must multiply both parts by 3, giving us 3/6. Now our problem is 4 4/6 - 2 3/6, and we can solve like we've been doing. 4-2=2, 4/6-3/6=1/6, and our answer is 2 1/6.

And yes, if you have a problem like this with different denominators AND the top fraction is smaller than the bottom one, you have to both convert the fractions so they have the same denominator AND borrow one from the whole number and add its fractional form to the fraction before you can do the subtracting.

Finally, if you are subtracting a mixed number from a whole number, the rules still apply. For instance, what if your problem is 5 - 3 2/7? Most people would look at this and say the answer is 2 2/7, but that's wrong. The question is really asking, what's 5 0/7 - 3 2/7? Yes, you have to borrow to make this work. When you do, you get 4 7/7 - 3 2/7, and the correct answer is 1 5/7.

I hope that helps, and isn't too overwhelming!

Answer 3

It is advisable to do so in all cases. It is particularly useful when

• the fractional part of the number being subtracted is bigger than fractional part of the number from which it is subtracted, or
  
• in the reverse situation but when the answer is negative.