Question

you and your friend are talking about adding the fractions below:

\\\frac{3}{5} + \frac{1}{4}\\

your friends says this:

\\\frac{3}{5} + \frac{1}{4} = \frac{4}{9}\\

you disagree.

answer the questions below.

select option a or option b.

row 2

what is the best reason we need to find a common denominator when adding fractions?

option a: if the denominators are different, they represent two different sized pieces of a whole. we find common denominators so that each whole is being split into same-sized pieces.

option b: finding a common denominator makes it easier to add and subtract.

row 3

the lowest common denominator would be...

option a: 9

option b: 20

Explanation:

Explain fraction addition concept

Using the Adding Fractions and Common Denominators knowledge points:
Denominators represent the size of the fractional pieces.
To add fractions, pieces must be the same size.
Thus, we find a common denominator to split wholes into same-sized pieces.
This matches the first option in Row 2.

Determine the lowest common denominator

Using the Lowest Common Denominator knowledge point:
We need the least common multiple of the denominators \(5\) and \(4\).
Since \(5\) and \(4\) share no common factors, we multiply them:

$$ \text{LCD} = 5 \times 4 = 20 $$

This matches the second option in Row 3.

Answer:

Question 1

• Option A: If the denominators are different, they represent two different sized pieces of a whole. We find common denominators so that each whole is being split into same-sized pieces. (Correct answer)
• Option B: Finding a common denominator makes it easier to add and subtract.

Question 2

• Option A: 9
• Option B: 20 (Correct answer)