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3 years ago

What is the quotient of 2 3/4 and 5 1/2?

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

Answer:

1/2

Step-by-step explanation:

This can be done several ways. Perhaps the easiest is to use the decimal equivalents:

(2 3/4)/(5 1/2) = 2.75/5.5 = 0.5

If you want to use the numbers given, the usual procedure is to convert them to improper fractions and do the division that way:

2 3/4 = (4·2 +3)/4 = 11/4

5 1/2 = (2·5 +1)/2 = 11/2

Now, the problem can be written as ...

(2 3/4) / (5 1/2) = (11/4) / (11/2)

This sort of division problem can be solved two ways:

invert and multiply (the denominator is inverted)

= (11/4) × (2/11) = (11·2)/(11·4) = 2/4 = 1/2

use a common denominator (for the two fractions)

= (11/4) / (11/2) = (11/4) / (22/4) = 11/22 = 1/2

The quotient is 1/2.

_____

Additional comments

It is helpful in many cases to just use decimal equivalents for the calculation. To do that, you need to be familiar with the equivalents of commonly used fractions. I find it is usually sufficient to know the unit fractions in each case. Then you can multiply or add to find the others.

1/9 = 0.1...(1-digit repeat), 1/8 = 0.125, 1/7 = 0.142857...(6-digit repeat), 1/6 = 0.16...(1-digit repeat), 1/5 = 0.2, 1/4 = 0.25, 1/3 = 0.3...(1-digit repeat), 1/2 = 0.5

I learned the "invert and multiply" method for dividing fractions when I was in school. The Common Core math apparently also teaches the method of matching the denominators of a compound fraction. Then the result is the ratio of numerators. (A variation not taught is that you can match the numerators and use the inverse of the ratio of denominators. Both of these methods can be validated using the "invert and multiply" method. (11/4)/(11/2) = 2/4)

"Invert and multiply" is another way of saying that division is the same as multiplication by the reciprocal. This applies everywhere, not just in fraction problems.

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Type the correct answer in each box. Use sigma notation to represent the following series for the first 10 terms. 3 + (-6) + 12

klemol [59]

Answer:

Kindly check attached picture

Step-by-step explanation:

Given the following :

First term (a) = 3

Second term = - 6

third term = 12

Fourth term = - 24

We can obtain the common ratio of the series using the relation :

(2nd term/ 1st term) = (3rd term/2nd term) = (4th term/ 3rd term) =....

(-6/3) = (12/-6) = (-24/12)

-2 = - 2 = - 2

Further explanation can be found in attached picture

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3 years ago

What form of a quadratic function would be graphed if the vertex at the same point as the y-intercept?

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2 years ago

Show work please \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$