QuestionEvaluate $9 \times(40+5)$ in two different methods.

Studdy Solution

STEP 1

Assumptions1. We are using the standard order of operations, also known as BIDMAS or PEMAS, where parentheses (or brackets) take precedence over multiplication and addition. . We can evaluate the expression in two ways by following the order of operations strictly, or by using the distributive property of multiplication over addition.

STEP 2

First, let's evaluate the expression by strictly following the order of operations. According to the order of operations, we should perform operations inside parentheses first.
$9 \times (40+5)$

STEP 3

Perform the addition inside the parentheses.
$9 \times45$

STEP 4

Now, perform the multiplication.
$9 \times45 =405$

STEP 5

Now, let's evaluate the same expression using the distributive property of multiplication over addition. The distributive property states that $a \times (b + c) = a \times b + a \times c$ . $9 \times (40+5)$

STEP 6

Apply the distributive property.
$9 \times40 +9 \times5$

STEP 7

Perform the multiplication operations.
$360 +45$

STEP 8

Perform the addition operation.
$360 +45 =405$ Both methods yield the same result, $405$ . Therefore, we can conclude that the expression $\times (40+5)$ evaluates to $405$ regardless of the method used.

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QuestionEvaluate $9 \times(40+5)$ in two different methods.

Studdy Solution

STEP 1

STEP 2

First, let's evaluate the expression by strictly following the order of operations. According to the order of operations, we should perform operations inside parentheses first.
$9 \times (40+5)$

STEP 3

Perform the addition inside the parentheses.
$9 \times45$

STEP 4

Now, perform the multiplication.
$9 \times45 =405$

STEP 5

Now, let's evaluate the same expression using the distributive property of multiplication over addition. The distributive property states that $a \times (b + c) = a \times b + a \times c$ . $9 \times (40+5)$

STEP 6

Apply the distributive property.
$9 \times40 +9 \times5$

STEP 7

Perform the multiplication operations.
$360 +45$

STEP 8

Perform the addition operation.
$360 +45 =405$ Both methods yield the same result, $405$ . Therefore, we can conclude that the expression $\times (40+5)$ evaluates to $405$ regardless of the method used.

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QuestionEvaluate 9×(40+5)9 \times(40+5)9×(40+5) in two different methods.

Studdy Solution

STEP 1

STEP 2

First, let's evaluate the expression by strictly following the order of operations. According to the order of operations, we should perform operations inside parentheses first.9×(40+5)9 \times (40+5)9×(40+5)

STEP 3

Perform the addition inside the parentheses.9×459 \times459×45

STEP 4

Now, perform the multiplication.9×45=4059 \times45 =4059×45=405

STEP 5

Now, let's evaluate the same expression using the distributive property of multiplication over addition. The distributive property states that a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times ca×(b+c)=a×b+a×c.9×(40+5)9 \times (40+5)9×(40+5)

STEP 6

Apply the distributive property.9×40+9×59 \times40 +9 \times59×40+9×5

STEP 7

Perform the multiplication operations.360+45360 +45360+45

STEP 8

Perform the addition operation.360+45=405360 +45 =405360+45=405Both methods yield the same result, 405405405. Therefore, we can conclude that the expression ×(40+5) \times (40+5)×(40+5) evaluates to 405405405 regardless of the method used.

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QuestionEvaluate $9 \times(40+5)$ in two different methods.

First, let's evaluate the expression by strictly following the order of operations. According to the order of operations, we should perform operations inside parentheses first.
$9 \times (40+5)$

Perform the addition inside the parentheses.
$9 \times45$

Now, perform the multiplication.
$9 \times45 =405$

Now, let's evaluate the same expression using the distributive property of multiplication over addition. The distributive property states that $a \times (b + c) = a \times b + a \times c$ . $9 \times (40+5)$

Apply the distributive property.
$9 \times40 +9 \times5$

Perform the multiplication operations.
$360 +45$

Perform the addition operation.
$360 +45 =405$ Both methods yield the same result, $405$ . Therefore, we can conclude that the expression $\times (40+5)$ evaluates to $405$ regardless of the method used.