What properties are these problems?
1. 17 + ___ = 33 + 17
2. (10 + 4) + 21 = (___ + 21)
3. 14 × 25 = 25 × ____
4. 8(4 × 2) = (8 × 4)____
1. To solve the equation 17 + ___ = 33 + 17, we can start by subtracting 17 from both sides of the equation to isolate the variable.
Therefore, 17 + ___ - 17 = 33 + 17 - 17. This simplifies to ___ = 33.
2. In this problem, we need to find the missing number in the expression (10 + 4) + 21 = (___ + 21). To do so, we can start by subtracting 21 from both sides of the equation.
This gives us (10 + 4) = ___ + 21 - 21, which simplifies to 14 = ___.
3. The equation 14 × 25 = 25 × ____ involves finding the missing number. To solve for it, we can divide both sides of the equation by 25.
This gives us 14 × 25 ÷ 25 = 25 × ____ ÷ 25. Simplifying this, we get 14 = ____.
4. In the equation 8(4 × 2) = (8 × 4)____, we need to find the missing number. Starting by simplifying the left side of the equation, we get 8(8) = (8 × 4)____.
Further simplifying, we have 64 = (8 × 4)____. To find the missing number, we can divide both sides by 32.
This gives us 64 ÷ 32 = _____. Simplifying this, we get ____ = 2.
To determine the properties of these problems, we need to analyze the mathematical operations and identify any patterns or relationships. Let's go through each problem one by one:
1. 17 + ___ = 33 + 17
This problem involves addition. We can solve it by finding the missing number that, when added to 17, gives us the same answer as adding 33 to 17.
To do this, we can subtract 17 from both sides of the equation:
17 + ___ - 17 = 33 + 17 - 17
This simplifies to:
___ = 33
Therefore, the missing number is 33.
The property involved here is the addition property of equality, which states that if two expressions are equal to each other (in this case, the left and right sides of the equation), then adding the same number to both sides will still keep them equal. In other words, you can add the same value to both sides of an equation without changing its truth.
2. (10 + 4) + 21 = (___ + 21)
This problem also involves addition. Similar to the previous problem, we need to find the missing number.
To find the missing number, we can subtract 21 from both sides of the equation:
(10 + 4) + 21 - 21 = ___ + 21 - 21
Simplifying gives us:
14 = ___
Thus, the missing number is 14.
In this problem, we are using the addition property of equality to show that subtracting the same value from both sides of the equation keeps it balanced and true.
3. 14 × 25 = 25 × ____
This problem involves multiplication. To find the missing number, we can divide both sides of the equation by 25:
(14 × 25) ÷ 25 = (25 × ____ ) ÷ 25
Simplifying yields:
14 = ____
Therefore, the missing number is 14.
In this case, we are using the multiplication property of equality, which states that if two expressions are equal to each other (in this case, the left and right sides of the equation), then dividing both sides by the same number will still keep them equal.
4. 8(4 × 2) = (8 × 4) ____
This problem also involves multiplication. The missing part is associated with the multiplication operation, so we need to multiply both sides by a number.
To find the missing number, we can multiply both sides of the equation by 4:
8(4 × 2) × 4 = (8 × 4) × 4
This simplifies to:
8(8) = (8 × 4) × 4
64 = ____
The missing number is 64.
In this problem, we are using the multiplication property of equality to show that multiplying the same value on both sides of the equation keeps it balanced and true.