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vlada-n [284]
3 years ago
9

How do compare ratios then simplify to find the answer

Mathematics
1 answer:
gogolik [260]3 years ago
3 0

"Compare ratios" covers a lot of territory. If all you want to do is find which one is larger, you can subtract or divide.

(a/b) - (c/d) > 0 . . . . means a/b is larger

(a/b) / (c/d) > 1 . . . . means a/b is larger

These operations with fractions are done using the methods of arithmetic with fractions that you have been taught.

____

"Simplify" when applied to ratios usually means common factors are removed from each of the terms.

For example, the ratio 2:12 is a ratio of even numbers, so we know both numbers have a factor of 2. (2 is a factor common to both numbers.) When we divide them both by 2, we have the reduced ratio 1:6. That is, 2:12 simplifies to become 1:6.

(It is helpful to have a good working knowledge of multiplication tables when you approach problems in simplifying ratios.)

= = = = = = = = = =

In "quick and dirty" terms, you can do the subtraction ...

\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}

That is, you really only need to find out if (ad) > (bc) to determine if (a/b) > (c/d). A similar result is obtained when you consider division ...

\displaystyle\frac{\left(\frac{a}{b}\right)}{\left(\frac{c}{d}\right)}=\frac{a}{b}\cdot\frac{d}{c}=\frac{ad}{bc}

This will be greater than 1 if (ad) > (bc), signifying that (a/b) > (c/d).

_____

Here's an example with numbers.

... Compare 6/7 to 43/50.

... The relationship of interest will be revealed by the products 6·50 = 300 and 7·43 = 301.

... Since 300 < 301, these tell us 6/7 < 43/50.

_____

We say the above methods are "quick and dirty" because the results may need to be simplified when you're done.

For example, subtracting 1/6 from 1/2 gives

... 1/2 - 1/6 = (1·6 - 2·1)/(2·6) = 4/12

Here, numerator and denominator have a common factor of 4. Removing that gives 4/12 = 1/3.

Even if you do this by the method of common denominators, you still need to reduce the result.

... 1/2 - 1/6 = 3/6 - 1/6 = (3-1)/6 = 2/6

This must be reduced to 1/3 by removing a common factor of 2 from numerator and denominator.

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If angle c=60° , b=5 ,a=4 then find the value of the c ?​
Lyrx [107]

Answer:

c=sqrt21

Step-by-step explanation:

angle c is the angle between a and b, so use the cos law

c^2=a^2+b^2-2*a*b*cosC

c^2= 16+25-2*4*5*1/2

c^2=21

c=sqrt21

5 0
2 years ago
How many terms are in the expression shown below?
stich3 [128]

Answer:

3 terms. All of the numbers are considered terms.

Step-by-step explanation:

If it asked for variables, it would be 2.

4 0
3 years ago
5 1/6 + 7 1/3 helpppppppp fasssssssssttttttt
natali 33 [55]

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Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A sign language club made $627. 50 from selling popcorn at a festival. The popcorn cost the club $95. 0. Which expression repres
solmaris [256]

The expression representing the amount of money that was raised for each member of the club is \dfrac{627.50 - 95.0}{m} (in dollars)

<h3>How to interpret the division? </h3>

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus, a \div b = a divided in b equal parts.

Also, we can write: a \div b = a \times \dfrac{1}{b}

(it is since a = a \times 1 so a/b = 1 \times (a/b) = (1/b) \times a )

<h3>How to find the profit earned?</h3>

Profit earned is the extra money which we make after deducing the cost price of the process we're doing.

So, we get:

Profit earned = Total amount earned - Amount spent initially for preparation to earn

P = Selling price (S.P.) = Cost price (C.P.)

For the given case, we're given that:

  • Amount made by the sign language club by selling popcorn at a festival = $627.50
  • The cost price for the popcorn to the club = $95.0

The money raised = Amount made by selling popcorn - amount costed to the club for getting popcorn

Money raised = $627.50 - $95.0

If it is given that: m = number of members in the considered club, then:

Money each member of the considered club will get = Money raised divided in equal m parts = \dfrac{627.50 - 95.0}{m} (in dollars)

(we don't write symbols like of currency generally, and understand it from context.)

Thus, the expression representing the amount of money that was raised for each member of the club is \dfrac{627.50 - 95.0}{m} (in dollars)

Learn more about division here:

brainly.com/question/26411682

8 0
2 years ago
The curved surface area of a cylinder is 880cm2 and its volume is 770cm3.Find its diameter and height.
natima [27]

Answer:

The height of cylinder is: h = 80.07 cm

The diameter of cylinder is: d = 3.5 cm

Step-by-step explanation:

Curved surface area of cylinder = 880 cm^2

Volume of cylinder = 770 cm^3

We need to find its diameter and height.

The formula used are:

Curved\: surface\: area=2\pi rh\\Volume=\pi r^2h

If we divide volume by curved surface, we can find radius

\frac{Volume}{Curved\: surface\: area}=\frac{\pi r^2h}{2\pi rh}  \\\frac{770}{880}=\frac{r}{2}\\0.875=  \frac{r}{2}\\=> r= 0.875\times 2\\r=1.75

So, we get radius r = 1.75

Now, we can find height using curve surface area formula:

Curved\: surface\: area=2\pi rh\\880=2(3.14)(1.75)h\\h=\frac{880}{10.99}\\h=80.07 \:cm

So, the height of cylinder is: h=80.07 cm

Now finding diameter using formula: d=2r

Putting value of r in above formula:

d=2r\\d=2(1.75)\\d=3.5\:cm\\

So, the diameter of cylinder is: d = 3.5 cm

5 0
3 years ago
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