Question

Jorge wants to write 4/5 as a sum of unit fractions. What should he write?

Answer 1

Jorge can write 4/5 as a sum of unit fractions such as 1/2 + 1/4 + 1/20. By finding a common denominator and adding these unit fractions, we can confirm they equal 4/5 after simplification.

Step-by-step explanation:

Jorge wants to write 4/5 as a sum of unit fractions. A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer. There are various ways to express 4/5 as a sum of unit fractions, but one possible way is to use the Egyptian Fraction method which involves finding fractions that sum up to 4/5 without repeating any of the denominators.

An example decomposition of 4/5 into unit fractions could be:

• 1/2
• 1/4
• 1/20

To verify that these unit fractions sum to 4/5, we can use the process of adding fractions with different denominators:

1. Find a common denominator for 1/2, 1/4, and 1/20. In this case, the common denominator is 20.
2. Convert each unit fraction to have the common denominator: 1/2 becomes 10/20, 1/4 becomes 5/20, and 1/20 remains the same.
3. Add the fractions: 10/20 + 5/20 + 1/20 equals 16/20.
4. Simplify 16/20 to 4/5 to confirm they are equivalent.

This demonstrates that the sum of the unit fractions 1/2, 1/4, and 1/20 is equal to 4/5.

Answer 2

unit fractions are those where the denominator is one, so the easiest way to write 4/5 as as sum of unit fractions is by adding 1/5 four times:
1/5 + 1/5 + 1/5 + 1/5 = 4/5
that is because as the fractions share the same denominator (lower part), we only have to add the numerators (upper part)