Question

Write 7/10 as a sum of unit fractions.

a) 7/10 = 1/2 + 1/5
b) 7/10 = 1/4 + 1/4 + 1/10
c) 7/10 = 1/3 + 1/3 + 1/3
d) 7/10 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Answer 1

Option a) 7/10 = 1/2 + 1/5 is correct for expressing 7/10 as a sum of unit fractions. To verify, we find a common denominator and add the fractions, which results in the desired fraction. Intuition and understanding of fraction sizes assist in confirming the result.

Step-by-step explanation:

Writing 7/10 as a sum of unit fractions means breaking it down into fractions where the numerator is 1. Given the options, we can check each one to see if they add up to 7/10. Let's assess option a) 7/10 = 1/2 + 1/5. If we find a common denominator for 1/2 and 1/5, which is 10, we can rewrite 1/2 as 5/10 and 1/5 as 2/10. Adding these together, 5/10 + 2/10 equals 7/10. Therefore, option a) is indeed one way to express 7/10 as the sum of unit fractions.

When adding fractions, we sometimes have to use our intuition to understand the concept better. Intuitively, we understand that a half of a pie is larger than a fifth of a pie. Accordingly, the sum of these two amounts (1/2 and 1/5) will give us a portion larger than a half but smaller than a whole, which matches our fraction in question, 7/10. This intuitive approach, alongside the mathematical process of finding a common denominator, aids us in fractions addition and in verifying our answer.