Leah has two same size rectangles divided into the same number of equal parts.One rectangle has 1/3 of the parts shaded,and the other has 2/5 of the parts shaded.What is the least number of parts into which both rectangles could be divided?
15
15
To find the least number of parts into which both rectangles could be divided, we first need to find the least common multiple (LCM) of the denominators of the fractions.
The denominators are 3 and 5. To find the LCM of 3 and 5, we can list the multiples of each number until we find a common multiple.
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
The first common multiple we see is 15. Therefore, the least number of parts into which both rectangles could be divided is 15.
Now let's calculate the number of shaded parts in each rectangle:
- In the first rectangle, 1/3 of the parts are shaded. So (1/3) * 15 = 5 parts are shaded.
- In the second rectangle, 2/5 of the parts are shaded. So (2/5) * 15 = 6 parts are shaded.
Hence, the least number of parts into which both rectangles could be divided is 15, and the first rectangle has 5 shaded parts while the second rectangle has 6 shaded parts.