Because of the commutative property of multiplication, it is true that 3/4 × 4=4×3/4
. However, these expressions can be calculated in different ways even though the solutions will be the same.
Below, show two different ways of solving this problem.
First, show how 3/4×4
can be solved using repeated addition
To solve 3/4 × 4 using repeated addition, we can start by recognizing that 3/4 means we have 3 out of 4 equal parts of something. In this case, let's say we have a rectangle divided into 4 equal columns, and we shade in 3 of those columns.
[ , , , ] (3 shaded columns out of 4)
Next, we want to find the total number of shaded columns if we have 4 equal groups of 3 shaded columns. To do this, we can add 3 shaded columns to themselves 4 times.
[ , , , ]
[ , , , ]
[ , , , ]
Counting the shaded columns, we have a total of 12 shaded columns. So, 3/4 × 4 = 12.
Now, let's show how 4 × 3/4 can be solved using repeated addition.
To solve 4 × 3/4 using repeated addition, we can start by recognizing that 3/4 means we have 3 out of 4 equal parts of something. In this case, let's say we have a rectangle divided into 4 equal rows, and we shade in 3 of those rows.
[-------------]
[-------------]
[-------------] (3 shaded rows out of 4)
[ ]
Now, we want to find the total number of shaded rows if we have 4 equal groups of 3 shaded rows. To do this, we can add 3 shaded rows to themselves 4 times.
[-------------]
[-------------]
[-------------]
[-------------]
[-------------]
Counting the shaded rows, we have a total of 12 shaded rows. So, 4 × 3/4 = 12.
By using repeated addition in both cases, we have shown that 3/4 × 4 = 4 × 3/4, and the solutions in both cases are 12.