1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Look at number 17. What did I do wrong?
Gnesinka [82]
When you are checking your answers, your formula should read out as 9(2.222) - 8 = 12, which is simply filing in the x value that you calculated (it comes out to 11.998 which is correct). You wrote it out as 9(2.22) - 8 = -6, which is why your checking process was incorrect 
7 0
3 years ago
Read 2 more answers
Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with
r-ruslan [8.4K]
32 
32 x 10
hope it helps

8 0
3 years ago
Read 2 more answers
Whic one is further from zero -3 or -2
Bond [772]
-3 is further away from 0 because if you graph it on a number line, it will show that -3 is one unit further from 0 than -2.
8 0
3 years ago
Read 2 more answers
What is the sequence for 6,12,18,24
scoundrel [369]

Answer:

an =6n

Step-by-step explanation:

6,     12,      18,     24

Take the 2nd number minus the first number,  3rd minus the second, etc

12-6  =6

18-12 = 6

24-18 =6

The common difference is 6

The formula for an arithmetic sequence is

an =a1+d(n-1)

 where a1 is the first term

  d is the common difference

 n is the term number

an = 6+6(n-1)

 Distributing

     = 6+6n-6

     = 6n

7 0
3 years ago
On average during the summer, a 30,000 cubic foot house costs $7 per day to cool, while a 25,000 cubic foot house costs $6.50 pe
Ber [7]

The house with 30000 cubic foot costs less to cool per cubic foot than the house with 25000 cubic foot.

Step-by-step explanation:

The cost of cooling 30000 cubic foot house = $7

Cost per cubic foot = 7/30000

=$0.00023

The cost of cooling 25000 cubic foot house= $6.50

Cost per cubic foot=6.50/25000

= $0.00026

The house with 30000 cubic foot costs less to cool per cubic foot than the house with 25000 cubic foot.

3 0
3 years ago
Other questions:
  • Gary took 7 hours
    10·1 answer
  • What is the question to b(x)=3x-1.
    8·2 answers
  • Here is an inequality for the graph that one of your
    12·1 answer
  • 70000000000 x 7700000
    12·1 answer
  • 29. New grass seeds grow rapidly. A grass seed has grown to 0.3 millimeters tall. Tomorrow it will be 0.9 millimeters
    6·1 answer
  • Multiplies to -294 but adds to 7
    14·1 answer
  • Find the value of h(-67) for the function below. h(x) = -49x − 125
    9·2 answers
  • Pls pls pls help me I will mark you brainest
    14·1 answer
  • Which ordered pairs is a solution to -5x + 3y &gt; 12?
    8·1 answer
  • Anyone know asap pls
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!