Perform the indicated operation and, if possible, simplify. Please show all of your work. (8/15)(-5/14)(5)?
To make it easier, let's multiply the first two fractions first. 8·······-5 --····x----- 15····14 Cross cancel by dividing out the common factors for each diagonal. Between 8 and 14, the common factor is 2. The common factor between 5 and 15 is 5. Divide these out. The fractions should now look like this: 4····-1 -- x---- 3····7 Now multiply straight across. Don't forget the negative sign on the 1. -4 --- 21 Now, multiply the fraction by 5. -4·····5 --- x --- 21····1 The answer is -20 ----- 21 Cross canceling can be a bit tricky. If you're having trouble, just multiply straight across, then reduce. If you're still having trouble, use this web page: http://www.purplemath.com/modules/fracti... Hope this helps!
Multiply or divide as indicated. Leave your answer with no factors in the denominator?
========= When you write things on a single line be sure to include parentheses to indicate the correct order of operations. I assume you mean p^-4q^5r^6/(p^-3qr^-2) only because the correct interpretation of what you actually typed is a totally trivial problem. But I can't tell for sure whether you expect me to solve what you really typed or the altered interpretation that would make it more interesting. I'll provide a solution to the more interesting problem, ignoring what you typed. ======= Use the rule that m^(-n) = 1/m^n. That will help you turn the division into a multiplication problems. p^-4q^5r^6/(p^-3qr^-2) = p^-4q^5r^6p^3q^-1r^2 Use the commutative property of multiplication to group like terms. The use the property that n^m * n^p = n^(m+p). p^-4q^5r^6p^3q^-1r^2 = p^(-4+3)q^(5-1)r(6+2) = p^(-1) * q^4* r^8 Since the question mentions a denominator I assume you want the final answer to be left in the form of a division problem, or fraction. p^(-1) * q^4* r^8 = q^4 * r^8 / p
Why do we divide first, multiply next, then add and lastly subtract, what goes wrong when we don't follow this rule?
This is not a question of discovery. It is a question of convention.Mathematics is a language, and, in this language, the sentence[math]1+2\times 3[/math]means“find the product of [math]2[/math] and [math]3[/math], and add [math]1[/math] to this value”.If you, instead, intended to convey the sentence“find the sum of [math]1[/math] and [math]2[/math], and multiply this value by [math]3[/math]”then the mathematics language allows you to write this as[math](1+2)\times 3.[/math]Nobody discovered this fact — rather, this is how the mathematical language was devised. As for any other language, people need to follow the rules of this language in order for everyone to understand each other when communicating with it. After all, we say ‘my car is red’ rather than ‘my red is car’ for the same reasons.
Why do we need to multiply 5/18 to convert km/hr into m/s?
The problem here, as far as I see it, is because someone gave you a number to convert and they didn’t teach you the dimensional analysis tools you needed for it. So let’s get this out of the way, you aren’t really multiplying by 5/18. Effectively you are, but that number came from combining together two conversions. The first is converting km/hr to km/sec. in order to do that, you multiply by 1hr/3600sec. This is because 3600sec = 1hr. This conversion cancels the hour Unit while keeping the velocity the same. After that, you multiply by 1000m/1km. That converts your km unit to meters, once again keeping the velocity the same.Whoever told you to multiply by 5/18 combined the two conversions into 1000/3600 with weird units like meter hour/km second, it’s kinda silly. Then, they reduced the fraction 1000/3600 to 5/18. By doing this, they made the math simpler to calculate by completely divorcing it from the tools you needed for conceptual understanding. Which sucks. Sorry.
Calculus help...? Solving equations for indicated variables?
7a. Multiply both sides by abc: xbc + acy + abz = abc Factor out an a in each term that has one: xbc + a(cy) + a(bz) = a(bc) Get them all on the same side of the equation, and away from everything else: xbc = a(bc) - a(cy) - a(bz) Combine the terms on the right: xbc = a(bc - cy - bz) Divide both sides by (bc - yc - zb) to isolate a: xbc/(bc - yc - zb) = a 7b. Distribute the 2 inside the parentheses: V = 2ab + 2bc + 2ca Get everything without an a on the other side of the equation: V - 2bc = 2ab + 2ca Factor out an a on the right: V - 2bc = a(2b + 2c) Divide both sides by (2b + 2c); (V - 2bc)/(2b + 2c) = a; if you factor out a 2 in the denominator, it will look the same as the given answer. d. Factor out a P from both terms on the right: A = P(1 + nr) Divide both sides by (1 + nr); P = A/(1 + nr).
How do I solve this equation for the indicated variable?
(a+3)/b = (a-3)/b + (b+3)/a Start by moving (a-3)/b to the left side of the equals sign: (a+3)/b - (a-3)/b = (b+3)/a Since both terms on the left have the same denominator, they can be combined into a single fraction: ((a+3) - (a-3))/b = (b+3)/a (a+3-a+3)/b = (b+3)/a 6/b = (b+3)/a Now cross-multiply, by multiplying the numerator of the left with the denominator of the right, and setting that equal to the product of the denominator of the left and the numerator of the right: 6a = b(b+3) Now divide both sides by 6 to solve for a: a = b(b+3)/6 You were close, just off by a minus sign. Check your work, you may have done everything right and just accidentally wrote a minus sign in one step.
How do I find the indicated product and quotient?
assuming that the bottom says y^2 - 7y + 10... this is a complex fraction, otherwise a big fraction with the numerator and denominator both being a fraction themselves. so, how to start? solve like any other complex fraction! instead of thinking this as division...think it as multiplying the reciprocal. also since this fraction isnt equal to anything, you dont solve for y. (1 / (25 - y^2)) / ((6 - 3y) / (y^2 - 7y + 10)) (1 / (25 - y^2)) * ((y^2 - 7y + 10) / (6 - 3y)) now factor each expression that can be factored to see if anything cancels out. (1 / -(y + 5)(y - 5)) * (((y - 5)(y - 2)) / (-3(y - 2))) so the (y - 5) cancels, along with (y - 2) and the negatives in the denominators, leaving you with... (1 / (y + 5)) * (1 / 3) combine the two for the final answer of (1 / (3y + 15)) or (1 / 3(y + 5)), whatever floats your boat. hope that helped! : )
Divide 4 1/5 by 3 1/7. Write in the simplest form.?
You need a common denominator when adding or subtracting. When you are multiplying or dividing you do NOT need a common denominator. (21/5)(7/22) Multiply the numbers on the top together (that will be the numerator), and multiply the numbers on the bottom together (that will be the denominator) = (21*7)/(5*22) = 147/110 = 1 & 37/110