Answer: The smallest number of equally sized pieces each fraction bar can be broken into is 24.
Explanation:
To model the difference of 5/8 and 1/3 using fraction bars, Oman needs to represent each fraction using the same number of equally sized pieces. The smallest number of equally sized pieces each fraction bar can be broken into is 24.
To see why this is the case, we need to find the least common multiple (LCM) of the denominators of 5/8 and 1/3, which is the smallest number that both denominators can evenly divide into. The denominator of 5/8 is 8 and the denominator of 1/3 is 3. The multiples of 8 are 8, 16, 24, 32, 40, 48, and so on. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on.
The smallest number that appears in both lists is 24, so we can break each fraction bar into 24 equally sized pieces. To model 5/8, Oman will need to shade in 15 out of the 24 pieces, and to model 1/3, Oman will need to shade in 8 out of the 24 pieces.
Oman can then subtract the shaded portion of the 1/3 fraction bar from the shaded portion of the 5/8 fraction bar to find the difference between the two fractions. The resulting fraction bar will have 7 out of the 24 pieces shaded, which represents the difference of 5/8 - 1/3.