Refer to the following figure.
An illustration shows a 5 column by 3 row grid. The left three columns are outlined, forming a square. The first and second rows of the outlined area, or a total of 6 units, are shaded.
What fraction of the total boxes is inside the thicker, orange outline?
What fraction of the boxes inside the thicker, orange outline is shaded?
What fraction of the total boxes is shaded? How can you use the answers to questions 1 and 2 to find out? Is there another way you could find out?
Choosing different numbers, make a similar diagram that shows a fraction of a fraction. Multiply the fractions to find the relationship between the shaded boxes and the total number of boxes.
1. To find the fraction of the total boxes that is inside the thicker, orange outline, we need to count the number of boxes inside the outline and divide it by the total number of boxes.
Inside the outlined area, there are 3 columns and 2 rows, so there are 3 x 2 = 6 boxes inside the outline.
The total number of boxes in the grid is 5 columns x 3 rows = 15 boxes.
Therefore, the fraction of the total boxes inside the thicker, orange outline is 6/15.
2. To find the fraction of the boxes inside the thicker, orange outline that is shaded, we need to count the number of shaded boxes inside the outline and divide it by the total number of boxes inside the outline.
Inside the outlined area, there are 6 shaded boxes.
Therefore, the fraction of the boxes inside the thicker, orange outline that is shaded is 6/6, which simplifies to 1.
3. To find the fraction of the total boxes that is shaded, we divide the number of shaded boxes by the total number of boxes.
From question 2, we know that the fraction of shaded boxes inside the outlined area is 6/6.
Using the answer from question 1, we know that the fraction of total boxes inside the outlined area is 6/15.
To find the fraction of the total boxes that is shaded, we can multiply the fractions from questions 1 and 2:
(6/15) x (6/6) = 36/90
This fraction can be simplified to 2/5.
Therefore, 2/5 of the total boxes are shaded.
To find out the relationship between the shaded boxes and the total number of boxes, we can multiply the fractions from questions 1 and 2:
(6/15) x (6/6) = 36/90
This fraction represents the ratio of shaded boxes to the total number of boxes.
To create a similar diagram that shows a fraction of a fraction, let's say 1/4 of the shaded boxes are actually shaded with a different color.
In the original diagram, there were 6 shaded boxes out of 15 total boxes.
If we shade 1/4 of the original shaded boxes with a different color, that would be (1/4) x 6 = 6/4 = 1.5 shaded boxes.
So, the new diagram would have 1.5 shaded boxes out of 15 total boxes.
To find the relationship between the shaded boxes and the total number of boxes, we can multiply the fractions:
(1.5/15) x (6/15) = 9/225 = 1/25.
Therefore, the relationship between the shaded boxes and the total number of boxes in this new diagram is 1/25.