Distribute.
A\times(B + C)
RESULT
Each row has B + C = B+C
rectangles, and there are A
rows.
Counting by color:
Number of orange rectangles: A \times B = A * B
Number of blue rectangles: A \times C = A* C
Total number of rectangles: A * B + A * C = RESULT
Counting by row:
Number of rows: A
Number of rectangles in a row: B + C = B + C
Total number of rectangles: A \times B + C = RESULT
Both ways of counting result in the same number, and this is known as the distributive property.
(A \times B) + (A \times C) = A\times(B + C)
Using the picture below as a guide, what number could replace SYMBOL
?
A\times(B + C) = ( SYM_A \times SYM_B ) + ( SYM_A \times SYM_C )
There are A
rows, and each row has B + C = B+C
rectangles.
MISSING
Counting by color:
Number of orange rectangles: A \times B = A * B
Number of blue rectangles: A \times C = A* C
Total number of rectangles: A * B + A * C = RESULT
Counting by row:
Number of rows: A
Number of rectangles in a row: B + C = B + C
Total number of rectangles: A \times B + C = RESULT
Both ways of counting result in the same number, and this is known as the distributive property.
(A \times B) + (A \times C) = A\times(B + C)
Thus the symbol SYMBOL
could be replaced with MISSING
.