Use the number line to show that 2 X (3 + 2) =
2 × 3 + 2 × 2.
To represent the expression 2 X (3 + 2), we start by showing the number 2 on the number line.
The number 2 is represented as a point on the number line.
Next, we represent the expression (3 + 2) by counting 3 units to the right from the number 2.
This brings us to the number 5 on the number line.
Finally, we multiply 2 by the number 5.
The result is shown by counting 2 units to the right from the number 5 on the number line.
We arrive at the number 10 on the number line.
Therefore, 2 X (3 + 2) = 10.
Now let's represent the expression 2 × 3 + 2 × 2 on the number line.
We start by showing the number 2 on the number line.
Next, we represent 2 × 3 by counting 3 units to the right from the number 2.
This brings us to the number 6 on the number line.
Then, we represent 2 × 2 by counting 2 more units to the right from the number 6.
This brings us to the number 10 on the number line, which is the same as the result we obtained for 2 X (3 + 2).
Therefore, using the number line, we can visually see that 2 X (3 + 2) is equal to 2 × 3 + 2 × 2.
To use the number line to show that 2 × (3 + 2) = 2 × 3 + 2 × 2, we can break down each side of the equation step by step.
Step 1: Start with the expression 2 × (3 + 2) on the left side of the equation.
Step 2: To simplify the expression, we first need to evaluate the addition inside the parentheses, which gives us 2 × 5.
Step 3: Multiplying 2 by 5, we get 10.
Step 4: Now, let's move on to the right side of the equation: 2 × 3 + 2 × 2.
Step 5: Multiplying 2 by 3, we get 6.
Step 6: Multiplying 2 by 2, we get 4.
Step 7: Adding 6 and 4, we get 10.
Step 8: We can see that 10 is equal to 10, which verifies that the left side of the equation (2 × (3 + 2)) is equal to the right side of the equation (2 × 3 + 2 × 2) using the number line.
To show that 2 × (3 + 2) is equal to 2 × 3 + 2 × 2 using the number line, we can visualize this equation step by step.
Step 1: Start by drawing a number line and marking the point for 3.
--------3--------
Step 2: Now, add 2 units to the right of 3 on the number line to represent (3 + 2).
--------3-----2----
Step 3: Next, multiply the entire sum by 2. To do this on the number line, make a copy of the sum (3 + 2) and position it next to the original sum, indicating multiplication by 2.
--------3-----2---- + --------3-----2----
Step 4: Add 2 copies of 3 to the second sum. This represents 2 × (3 + 2).
--------3-----2---- + --------3-----2----
3 3
Step 5: Finally, simplify the equation by counting the total number of units on each side of the equation.
On the left side, we have a total of 5 units (3 + 2).
On the right side, we have 2 copies of 3 (2 × 3) and 2 copies of 2 (2 × 2), which also equals 5 units.
Therefore, we can visually see that 2 × (3 + 2) is indeed equal to 2 × 3 + 2 × 2 on the number line.