Carl shades a row in the multiplication table. The products in the row are all even. The ones digits in the products repeat 0, 4, 8, 2, 6. What row does Carl shade?
the row for 4
To find the row that Carl shades in the multiplication table, you need to take a closer look at the ones digits in the products.
The pattern of the ones digits repeating 0, 4, 8, 2, 6 corresponds to the multiples of 2.
The multiples of 2 from 0 to 9 are: 0, 2, 4, 6, 8.
From this pattern, we can conclude that Carl shades the row of multiples of 2, which is the second row in the multiplication table.
To determine the row that Carl shades in the multiplication table, we can analyze the pattern of the ones digits in the products.
In the multiplication table, the ones digit of any product is obtained by multiplying the ones digits of the multiplicands. Let's observe the pattern of the ones digits in the given sequence: 0, 4, 8, 2, 6.
We can start by noting that the ones digit of any even number will be 0, 2, 4, 6, or 8. Since the sequence given only includes the digits 0, 2, 4, 6, and 8, we can conclude that the row shaded by Carl consists of even numbers only.
Let's examine the pattern more closely. If we observe the products generated by multiplying the numbers in the first column of that row with numbers in the first row, we can find a clear pattern:
1 x 0 = 0
1 x 1 = 1
1 x 2 = 2
1 x 3 = 3
1 x 4 = 4
...
1 x 9 = 9
As we can see, the ones digits repeat in a cycle of length 4: 0, 1, 2, 3. Since Carl's shaded row has a repeating pattern of the ones digits 0, 4, 8, 2, 6, we can conclude that the numbers in Carl's shaded row are obtained by performing multiplication using the numbers of the row labeled '4' in the multiplication table.
Therefore, Carl shades the row labeled '4' in the multiplication table.