If you were given a 10 by 10 grid with 40 blocks shaded, how could you represent this using a fraction in simplest form?(1 point)
To represent the number of shaded blocks in a 10 by 10 grid as a fraction in simplest form, you would write the number of shaded blocks as the numerator and the total number of blocks in the grid as the denominator.
The number of shaded blocks is given as 40, and the total number of blocks in a 10 by 10 grid is 100.
Therefore, the fraction in simplest form would be 40/100.
To represent the shaded blocks on a 10 by 10 grid using a fraction in simplest form, you would need to find the ratio of the shaded blocks to the total number of blocks in the grid.
Step 1: Calculate the total number of blocks in the grid
The total number of blocks in a 10 by 10 grid is determined by multiplying the number of rows by the number of columns. In this case, it would be 10 x 10 = 100 blocks.
Step 2: Determine the number of shaded blocks
Given that there are 40 shaded blocks, we can use this number to represent the numerator of the fraction.
Step 3: Write the fraction in simplest form
To find the simplest form of this fraction, we need to reduce the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 40 and 100 is 20.
Divide both the numerator and denominator by 20:
40 ÷ 20 = 2
100 ÷ 20 = 5
Therefore, the shaded blocks on the 10 by 10 grid can be represented by the fraction 2/5 in simplest form.
To represent the shaded blocks in the 10 by 10 grid as a fraction in its simplest form, you need to find the greatest common divisor (GCD) of the number of shaded blocks and the total number of blocks in the grid.
In this case, there are 40 shaded blocks and a total of 100 blocks in the 10 by 10 grid. To find the GCD, you can start by finding the prime factors of the numerator (40) and the denominator (100):
40 = 2 × 2 × 2 × 5
100 = 2 × 2 × 5 × 5
Next, you can cancel out any common factors between the numerator and the denominator:
40/100 = (2 × 2 × 2 × 5) / (2 × 2 × 5 × 5) = (2 × 2) / (5 × 5)
Now, you can simplify the fraction by dividing both the numerator and denominator by their common factors:
(2 × 2) / (5 × 5) = 4/25
Therefore, the fraction 4/25 represents the shaded blocks in the 10 by 10 grid in its simplest form.