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### Course: Math (NSDC) - English > Unit 8

Lesson 4: Evaluating expressions# Example: Evaluating expressions with 2 variables

Evaluating Expressions with Two Variables. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- how many sign are there that mean to multiply.(13 votes)
- (5)(4) - parentheses

5*4 - the asterisk

5·4 - the center dot

5x4 - the classic primary school symbol for multiplication

5y - a number and a variable together signifies multiplication

As you get further along in math, you will use mostly the first one and the last one.(21 votes)

- where did you you get the parentheses(7 votes)
- The parenthesis were added to show that 10 and -4 are multiplied together. The "why aren't we using the multiplication sign?" video probably explains this better, but basically "10 x -4" can be confusing because the letter x is often used for variable. So, to avoid confusion, you can write "10(-4)" instead of "10 x -4" to show that 10 and -4 should be multiplied. Hope that helps.(8 votes)

- For some reason, I'm having a hard time with fractions being multiplied. How do I handle fractions in all this?

Example: 3/7_r_ + 5/8_s_ when*r_ = 14 and _s*= 8

From this, I SOMEHOW pulled 69.5 when the answer was 11. How do I work with fractions, here? Haha!(6 votes)- If it helps, I'll go through that problem for you.

We're going to evaluate`3/7r + 5/8s when r = 14 and s = 8`

.

So then`3/7r + 5/8s`

becomes`3/7(14) + 5/8(8)`

To do 3/7 times 14, we can write straight 14 as the fraction 14/1. Then an easy way to write two fractions to multiply them is`numerator • numerator/ denominator • denominator`

.

So`3/7 • 14/1`

becomes`42/7`

(3 • 14 = 42 and 7 • 1 = 7)

To do the same to the second fraction, we'll multiply`5/8 • 8/1`

. This makes`40/8`

(5 • 8 = 40 and 8 • 1 = 8)

The problem is now simplified to`42/7 + 40/8`

. This can be simplified further to`6 + 5`

(7 can go into 42 6 times evenly and 8 can go into 40 5 times evenly.)

And your answer:`6 + 5 =`

**11**

I have no idea how you got 69.5, but I tend to do the same thing so I won't judge :). Hopefully this example can help you with fractions in the future.(10 votes)

- Can someone explain how to multiply a fraction by a whole number? I came across this in a quiz.

It said: Evaluatie 1/4c + 3d when c=6 and d=7

when i multiply 1/4 with 6 I get 1 whole number and 2/4... How do I put that in a normal number, and not a fraction?

In the quiz 1/4 times 6 equals 1.5 - i don't get how…

Is 2/4 just a half?(7 votes)- You get 1/4 out of 6, which number x times 4 will make 6? 1.5, + d is 7 so 3x7 = 21, 21 + 1.5 = 22.5(3 votes)

- I find Khan Academy very helpful. I appreciate what Sal is doing.

Is there a reason why you repeat the same thing multiple times?

"10 times....10 times..."

"Minus 8....Minus 8"(6 votes)- Sal repeats himself while he takes the times to write what he's saying.(2 votes)

- How would do you convert a fraction to a decimal(4 votes)
- It is a straightforward process-divide the numerator by the denominator after the decimal point. We can do that by adding zeroes to the number until the remainder is zero. This Khan Academy video will show a worked example-https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-decimals-to-fractions/v/converting-fractions-to-decimals-example)(3 votes)

- How can you do that if some of the integers are decimals or fractions(4 votes)
- why does 7 have to get multiplied by 10 and then squared(1 vote)
- 7 does not get multiplied by 10, here is the example in steps....

a^2 + 10b - 8 = ? a = 7 b = -4

Rewrite

7^2 + 10 x -4 - 8 = ?

7^2 is the same thing as 7 x 7, so this equals 49

10 x -4 = -40,

Now you can solve it.

49 + -40 - 8 = ?

49 + -40 = 9

9 - 8 = 1

Remember that exponents come first before x or -.(7 votes)

- Where can you practice these tips?(3 votes)
- How do you multiply fractions by a whole number?(3 votes)
- i dont really know but i know u can watch a video on it :)(1 vote)

## Video transcript

We're asked to evaluate
the expression a squared plus 10b minus 8 when a is
equal to 7 and b is equal to 4. So to evaluate the
expression, we really just have to substitute a with 7 and
substitute b with negative 4 because they're saying evaluate
it when a is equal to 7 and b is equal to negative 4. So let's do that. So a everywhere we see
an a in the expression, we should put a 7 there. So instead of a squared, we
should write 7 squared plus-- I'll do it in that same
color-- plus 10 times b. But instead of a b
there, we are now going to substitute it with
b is equal to negative 4. So 10 times negative 4 instead
of the b right over there. And then we have the minus 8. And now we just have
to evaluate this thing. 7 squared is 49. And then 10 times negative 4. Remember, order of
operations, multiplication comes before addition. So we have to multiply this. 10 times negative
4 is negative 40. So it's negative 40. And then we have minus
8 back over here. And so we get 49
plus negative 40, which is really the same
thing as 49 minus 40 is going to be 9. And then we're going to
subtract 8 from that. And so we get 1. 49 minus 40 is 9 minus 8 is 1. And we are done. We've evaluated the expression
when a is equal to 7 and b is equal to negative 4.