Question

Consider the sum ( 1/4 + 1/4 ). We have ( 1/4 + 1/4 = 2/4 = 1/2 ). Notice that the sum, when written in simplest form, has a smaller denominator than either of the two tions we originally added. Find two tions in simplest form with different denominators such that the sum of the tions written in the simplest form has a smaller denominator than either of the two tions.

a) ( 1/3 + 1/4 )
b) ( 2/5 + 1/6 )
c) ( 3/7 + 1/8 )
d) ( 4/9 + 1/10 )

Answer 1

By finding common denominators and simplifying, we determine that adding 4/9 and 1/10 results in a sum with a smaller denominator in simplest form, which is 7/18. This makes option d) the correct answer to the student's question.

Step-by-step explanation:

To answer the question, we'll need to find the sums of the given fractions and then simplify them to see if the resulting denominator is smaller than either of the original denominators.

Option a)

Adding 1/3 and 1/4 requires a common denominator, which is 12 in this case. So we rewrite the fractions as 4/12 and 3/12, respectively. Adding these together gives 7/12, which does not have a smaller denominator than the original fractions.

Option b)

Next, adding 2/5 and 1/6 requires a common denominator of 30. The fractions become 12/30 and 5/30, which sum to 17/30. This also does not have a smaller denominator.

Option c)

Addition of 3/7 and 1/8 involves finding a common denominator of 56. We get 24/56 and 7/56, and their sum is 31/56, which again, does not have a smaller denominator than the original fractions.

Option d)

Finally, adding 4/9 and 1/10 leads us to a common denominator of 90. This gives us 40/90 and 9/90, and together they sum to 49/90. Simplified, this is 7/18, which has a smaller denominator than either of the original fractions. Therefore, option d) meets the requirement.