Question7. Justify a Result Explain how you can determine $38+45 \stackrel{?}{=} 39+44$ is true or false without solving.

Studdy Solution

STEP 1

1. We are given the equation $38 + 45 \stackrel{?}{=} 39 + 44$ .
2. We need to determine if the equation is true or false without directly calculating the sums.

STEP 2

1. Analyze the structure of the equation.
2. Use properties of numbers to justify the result.

STEP 3

Analyze the structure of the equation:
The equation is $38 + 45 \stackrel{?}{=} 39 + 44$ .
Notice that on the left side, we have $38$ and $45$ , and on the right side, we have $39$ and $44$ .

STEP 4

Use properties of numbers to justify the result:
Observe that $39$ is $1$ more than $38$ , and $44$ is $1$ less than $45$ .
This means that on the right side, we have increased one number by $1$ and decreased the other by $1$ .
The sum of $39 + 44$ is effectively the same as $38 + 45$ because the increase and decrease cancel each other out.
Thus, the equation $38 + 45 = 39 + 44$ is true due to the commutative property of addition, which allows rearrangement of terms without changing the sum.
The equation $38 + 45 = 39 + 44$ is $\boxed{\text{true}}$ .

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