Solved on Jan 18, 2024

Find the value of $\frac{a+2bc}{3a}$ when $a=4, b=-5, c=-7$ .

STEP 1

Assumptions
1. The value of $a$ is 4.
2. The value of $b$ is -5.
3. The value of $c$ is -7.
4. We are to evaluate the expression $\frac{a+2bc}{3a}$ with the given values of $a$ , $b$ , and $c$ .

STEP 2

First, we substitute the given values of $a$ , $b$ , and $c$ into the expression.
$\frac{a+2bc}{3a} = \frac{4+2(-5)(-7)}{3 \cdot 4}$

STEP 3

Next, we calculate the product $2bc$ .
$2bc = 2 \cdot (-5) \cdot (-7)$

STEP 4

Perform the multiplication to find the value of $2bc$ .
$2bc = 2 \cdot (-5) \cdot (-7) = 70$

STEP 5

Now, we plug the value of $2bc$ back into the expression.
$\frac{4+2(-5)(-7)}{3 \cdot 4} = \frac{4+70}{3 \cdot 4}$

STEP 6

Add the numbers in the numerator.
$\frac{4+70}{3 \cdot 4} = \frac{74}{3 \cdot 4}$

STEP 7

Multiply the numbers in the denominator.
$\frac{74}{3 \cdot 4} = \frac{74}{12}$

STEP 8

Now, we simplify the fraction by dividing the numerator by the denominator.
$\frac{74}{12} = 6 \frac{2}{12}$

STEP 9

Reduce the fractional part of the mixed number by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$6 \frac{2}{12} = 6 \frac{1}{6}$
The value of the expression when $a=4, b=-5$ , and $c=-7$ is $6 \frac{1}{6}$ .

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Find the value of $\frac{a+2bc}{3a}$ when $a=4, b=-5, c=-7$ .

STEP 1

Assumptions
1. The value of $a$ is 4.
2. The value of $b$ is -5.
3. The value of $c$ is -7.
4. We are to evaluate the expression $\frac{a+2bc}{3a}$ with the given values of $a$ , $b$ , and $c$ .

STEP 2

First, we substitute the given values of $a$ , $b$ , and $c$ into the expression.
$\frac{a+2bc}{3a} = \frac{4+2(-5)(-7)}{3 \cdot 4}$

STEP 3

Next, we calculate the product $2bc$ .
$2bc = 2 \cdot (-5) \cdot (-7)$

STEP 4

Perform the multiplication to find the value of $2bc$ .
$2bc = 2 \cdot (-5) \cdot (-7) = 70$

STEP 5

Now, we plug the value of $2bc$ back into the expression.
$\frac{4+2(-5)(-7)}{3 \cdot 4} = \frac{4+70}{3 \cdot 4}$

STEP 6

Add the numbers in the numerator.
$\frac{4+70}{3 \cdot 4} = \frac{74}{3 \cdot 4}$

STEP 7

Multiply the numbers in the denominator.
$\frac{74}{3 \cdot 4} = \frac{74}{12}$

STEP 8

Now, we simplify the fraction by dividing the numerator by the denominator.
$\frac{74}{12} = 6 \frac{2}{12}$

STEP 9

Reduce the fractional part of the mixed number by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$6 \frac{2}{12} = 6 \frac{1}{6}$
The value of the expression when $a=4, b=-5$ , and $c=-7$ is $6 \frac{1}{6}$ .

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Find the value of a+2bc3a\frac{a+2bc}{3a}3aa+2bc​ when a=4,b=−5,c=−7a=4, b=-5, c=-7a=4,b=−5,c=−7.

STEP 1

Assumptions1. The value of a a a is 4.2. The value of b b b is -5.3. The value of c c c is -7.4. We are to evaluate the expression a+2bc3a \frac{a+2bc}{3a} 3aa+2bc​ with the given values of a a a, b b b, and c c c.

STEP 2

First, we substitute the given values of a a a, b b b, and c c c into the expression.a+2bc3a=4+2(−5)(−7)3⋅4 \frac{a+2bc}{3a} = \frac{4+2(-5)(-7)}{3 \cdot 4} 3aa+2bc​=3⋅44+2(−5)(−7)​

STEP 3

Next, we calculate the product 2bc 2bc 2bc.2bc=2⋅(−5)⋅(−7) 2bc = 2 \cdot (-5) \cdot (-7) 2bc=2⋅(−5)⋅(−7)

STEP 4

Perform the multiplication to find the value of 2bc 2bc 2bc.2bc=2⋅(−5)⋅(−7)=70 2bc = 2 \cdot (-5) \cdot (-7) = 70 2bc=2⋅(−5)⋅(−7)=70

STEP 5

Now, we plug the value of 2bc 2bc 2bc back into the expression.4+2(−5)(−7)3⋅4=4+703⋅4 \frac{4+2(-5)(-7)}{3 \cdot 4} = \frac{4+70}{3 \cdot 4} 3⋅44+2(−5)(−7)​=3⋅44+70​

STEP 6

Add the numbers in the numerator.4+703⋅4=743⋅4 \frac{4+70}{3 \cdot 4} = \frac{74}{3 \cdot 4} 3⋅44+70​=3⋅474​

STEP 7

Multiply the numbers in the denominator.743⋅4=7412 \frac{74}{3 \cdot 4} = \frac{74}{12} 3⋅474​=1274​

STEP 8

Now, we simplify the fraction by dividing the numerator by the denominator.7412=6212 \frac{74}{12} = 6 \frac{2}{12} 1274​=6122​

STEP 9

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Find the value of $\frac{a+2bc}{3a}$ when $a=4, b=-5, c=-7$ .

Assumptions
1. The value of $a$ is 4.
2. The value of $b$ is -5.
3. The value of $c$ is -7.
4. We are to evaluate the expression $\frac{a+2bc}{3a}$ with the given values of $a$ , $b$ , and $c$ .

First, we substitute the given values of $a$ , $b$ , and $c$ into the expression.
$\frac{a+2bc}{3a} = \frac{4+2(-5)(-7)}{3 \cdot 4}$

Next, we calculate the product $2bc$ .
$2bc = 2 \cdot (-5) \cdot (-7)$

Perform the multiplication to find the value of $2bc$ .
$2bc = 2 \cdot (-5) \cdot (-7) = 70$

Now, we plug the value of $2bc$ back into the expression.
$\frac{4+2(-5)(-7)}{3 \cdot 4} = \frac{4+70}{3 \cdot 4}$

Add the numbers in the numerator.
$\frac{4+70}{3 \cdot 4} = \frac{74}{3 \cdot 4}$

Multiply the numbers in the denominator.
$\frac{74}{3 \cdot 4} = \frac{74}{12}$

Now, we simplify the fraction by dividing the numerator by the denominator.
$\frac{74}{12} = 6 \frac{2}{12}$