Evaluate Each Expression

Evaluate each expression is very simple concept in math. When you substitute a particular value for each variable and then act the operations called evaluating expression. The mathematical expression is algebraic, it involves a finite sequence of variables and numbers and then algebraic operations. Evaluation is simplifying the expression.

Algebraic operations are:

Addition

subtraction

multiplication

division

raising to a power

Extracting a root.

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Evaluating algebraic expressions are using PEMDAS method.

Rules for PEMDAS method:

1. First it performs operations inside the parenthesis.

2. Second exponents

3. Third multiplication and division from left to right

4. Finally addition and subtraction from left to right

Evaluate each expression for x=-5 and y=8

2x4-x2+y2

Solution:

Given expression is 2x4-x2+y2

Substitute x and y values in given expression

So,

=2(-5)4-(-5)2+ (8)2

=2(625)-(25) +64

=1250-25+64

=1314-25

=1289

Therefore answer is 1289

Evaluate the expression x3-x2y+9 for x=3, y=9

Solution:

Given expression x3-x2y+9

Plugging the x and y values in given expression

=33-329+9

=27-9*9+9

=27-81+9

=36-81

=-45

Therefore answer is -45

example problems for evaluating the expressions:

Evaluate each expression using PEMDAS method

3 * (9 + 12) - 62 `-:` 2 + 8

Solution:

Remember the PEMDAS rules

First parenthesis: (9+12) = (21)

3*21-62`-:` 2+8

Then exponents: 62 = 6 *6 = 36

3*21-36`-:` 2+8

Then multiplication and division: 3 * 21 = 63 and 36`-:` 2 = 18

63-18+8

Then addition: 63+8=71

71-18

Finally subtract the term

53

Therefore the answer is 53

Evaluate each expression for a = –2, b = 3, c = –4, and d = 4.

bc3 – ad

Solution:

= (3) (–4)3 – (–2) (4)

using PEMDAS exponent rule (-4)3=-4*-4*-4 = -64

= (3) (–64) – (–8)

then multiply the numbers 3*(-64) = -192

= –192 + 8

Add the numbers

= –184

(b + d)2

Solution:

= ((3) + (4))2

Add the inside numbers 3+4=7

= (7)2

using exponent rule 72=7*7=49

= 49

so, the answer is 49

a2b

Solution:

= (–2)2(3)

= (4) (3)

= 12

a – cd

Solution:

= (–2) – (–4)(4)

= (-2)-(-16)

= (-2) +16

= 16-2

= 14

b2 + d2

Solution:

= (3)2 + (4)2

= 9+16

= 25

Evaluate each expression For x = –3.

3x2 – 12x + 4

Solution:

= 3(–2)2 – 12(–2) + 4

= 3(4) + 24 + 4

= 12+24+4

=40

x4 + 3x3 – x2 + 6

Solution:

= (–3)4 + 3(–3)3 – (–3)2 + 6

= 81 + 3(–27) – (9) + 6

= 81 – 81 – 9 + 6

= –3

Solving Proportions

We will be solving proportions for x, by using our property that says the cross products of a proportion are equal to each other. If you remember the cross product we find them by multiplying a numerator one ratio time the denominator of the other. So just by looking over one proportion problems we will get the idea how exactly it is solved.

Say, x/15=21/45 here we will do the cross multiplication as 45 times x = 15 times 21 that is 45x= 315, now divide 45 both sides and we get x= 7. And this makes sense, 7 over 15 and 21/45 are equal fractions which is basically what proportions are.

One more question, 17/20=x/25. Here 17 times 25 equals to 20 times x. 425=20x, again dividing both the sides by 20 and we get the solution as x= 21.25. These types are nothing but theproportion solver.

We can learn this method only by practicing more by solving proportion examples. Thus the proportion examples are as follows, solving the proportion let us start with x/15=6/10. So here we have two ratios which are equal to each other. We need to find the value of x which will make the whole fraction proportionate to another.

We are going to find what this x number is going to represent so then this ratio in fact is equal to another ratio.  Using the cross product method will be used to solve this problem. we multiply two numbers which are diagonal from each other.10 times x=15 times 6.we get 10x=90, kindly remember there is no sign between the number and the variable it means they both have to multiply that here in this question will be 10 times x as 10 x. now by dividing 10 no both the sides,

we get the value of x as 9. Make sure if our solution is correct, simplify the problem by putting the value of x into the fraction, we will find the both fractions are proportionate to each other.

Let us take one more example, 3/15= y/50. Now again we have to solve this for the variable known as y. to do this we are going to find cross products. So 15 times y equals to 3 times 50, will be written as 15y=150, now dividing both the sides by 15 we get the value for y. and the value of y is 10.thus our final answer is y=10. And we can check that by plugging the value of y and simplifying shows that the fractions are in proportion.