45/21 times 49/9 divided by 42/3?

Question

45/21 times 49/9 divided by 3/42
and

20/36 times 24/5 divided by 54/9

please help and thanks for your time please explain

Answer 1

(45/21*49/9)/42/3= (45*49*3)/(21*9*42)=5/6
(20/36*24/5)/54/9=(20*24*9)/(36*5*54)=4/9

(a/b)/(c/d)=(a*d)/(b*c)

Answer 2

Processing:
a) Inverting the division (third fraction)
b) Multiplying numerating for numerator and denominator for denominator. After, to divide one for the other, simplifying each term or in the final result one, as you prefer.
45/21 times 49/9 divided by 3/42 =
45/21 times 49/9 times 42/3 =
(45 x 49 x 42) : (21 x 9 x 3) = 5/6
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20/36 times 24/5 divided by 54/9 =
20/36 times 24/5 times 9/54 =
(20 x 24 x 9) : (36 x 5 x 54) = 4/9
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Answer 3

45/ 21 x 49/9 div 42/3=
45/21 x 49/9 x 3/42= (look for common factors in order to cancel)
(5 x 9 x 7 x 7 x 3)/ (3 x 7 x 9 x 3 x 2 x 7)= cancel top to bottom of fraction because 9/9=1, 7/7=1 (twice!) 3/3=1
this leaves 5/(3 x 2)=

5/6 (that is the final answer)


next problem... set up and look for all cancellation possibilities... different set up this time

20/36 x 24/5 div 54/9= (first invert 54/9 to 9/54 then set up multiplication)

20 x 24 x 9 =5 x 4 x 6 x 4 x 9
_________ = ____________= (5/5=1,4/4=1,6/6=1,9/9=1)
36 x 5 x 54 = 4 x 9 x 5 x9 x6

leaving 4/9 done!

Answer 4

For the first one, you multiply the two fractions
45/21*49/9 Simplify by cross reducing
5/3*7/1=35/3

Divide your answer by 42/3, but when you divide fractions, you multiply by the reciprocal which is 3/42
35/3*3/42 cross reduce
5/1*1/6=5/6

For the second one, you already know what 45/21*49/9 is from the previous problem, so now we multiply it by the reciprocal of 3/42
35/3*42/3 cross reduce
35/1*14/3=490/3=163 1/3

For the last problem you multiply your first two numbers
20/36*24/5 cross reduce
4/6*4/1=16/6=8/3

Now multiply 8/3 by the reciprocal of 54/9
8/3*9/54 Cross reduce
4/1*3/27=12/27=4/9

Answer 5

There are two ways to do this kind of problem. The brute-force way is just to do all the multiplying and dividing, then try to simplify. This usually results in ridiculously large numbers before simplification. For instance, the first one would be 92610/567 before you simplified it.

A better way is to simplify it as you go. 45 and 21 are both divisible by 3, so divide them by 3 and your first fraction is 15/7. When you multiply it by 49/9, you get 15*49/9*7.

Now you can simplify some more. 49 and 7 are both divisible by 7, so go ahead and divide them both by 7, and you get 15*7/9. 15 and 9 are divisible by 3, so divide them and you get 5*7/3. That's as much as you can simplify for now, so now you bring in the third fraction.

To divide by a fraction, you "invert and multiply". That means that to divide by 3/42, you multiply by 42/3. That will give 5*7*42/3*3. Now we simplify again. 42 is divisible by 3, so you can factor that out and get 5*7*14/3. That's as far as you can simplify it, so you go ahead and multiply out the numerator and get 490/3.

Now for the second one. Start with 20/36. Those numbers are both divisible by 4, so you can simplify it to 5/9. Then multiply it by 24/5. That gives 5*24/9*5. Obviously you can get rid of the 5's, leaving 24/9. 24 and 9 are divisible by 3, so you can simplify that to 8/3.

Finally, divide by 54/9. That means multiply by 9/54, giving 8*9/3*54. Now 8 and 54 are both divisible by 2, so simplify it to 4*9/3*27. Then 27 is divisible by 9, so you can simplify it again to 4/3*3. That's as far as you can simplify it, so you go ahead and multiply out the denominator to get 4/9.

I hope that made sense. It's easier to explain when you write the equations out by hand than when you try to type them.

Answer 6

45/21*49/9 / 3/42
Answer = 0.019064415889812715209540606366003

20/21*24/5 / 54/9
Answer = 0.0094062316284538506760728982951205

Answer 7

45/21 times 49/9. you multiply the top two terms and then the bottom two.
2205/189 simplify to 11 and 2/3
as an improper fraction, it is 35/3. when you divide fractions, you keep the first fraction as is. change the dicision sign to multiplication. then reciprocate the second fraction which means switching the top and bottom terms.
35/3 divided by 54/9. first, 54/9 equals six so it is:
35/3 divided by six. six is hte same as 6/1.
so keep the first fraction, change the sign, flip the second fraction:
35/3 times 1/6.
multiply the two fractions.
35/18

Answer 8

45/21 times 49/9 divided by 3/42
= (45/21) * (49/9 )/ ( 3/42)
= [(3*3*5)/(7*3)] * [(7*7)/(3*3)] over [3/(7*2*3)]
= [(3*3*5)*(7*7)] /[(7*3)*(3*3)] over [3/(7*2*3)]
= [(5)*(7)] /[(3)] over [3/(7*2*3)]
= [(5)*(7)] /[(3)] * [(7*2*3)/3]
= [(5)*(7)] * (7*2*3)/(3*3)
= 5*7*7*2/3 = 490/3

20/36 times 24/5 divided by 54/9
=(5*4)/(9*4) times (6*4)/5 div (9*6)/9
=(5/9) times (6*4)/5 div 6
= (5/9) *(6*4)/5 div 6
= (5*6*4)/(5*9) div 6
= (6*4)/(9) div 6
= (6*4)/(9*6)
=4/9

(It'd be easier if we could write down it on paper!!!)

Answer 9

45/21 times 49/9=45/21*49/9
...........................=(45*49)/(21*9)
...........................=(9*5*7*7)/(7*3*9)
deleting common nos.
...........................=5*7/3=35/3
now divide by 42/3
means multiply by 3/42
ans1=(35/3)*(3/42)
........=35/42
(dividing by 7)
ans1=5/6

2>ans2=20/36*24/5*9/54
............=(20*24*9)/(36*5*54)
............=24/54 (since20*9=36*5)
dividing by 6
ans2=4/9

Answer 10

490/3

4/9

Calculator? Remember to flip 3/42 and 54/9 when dividing, and multiply by their reciprocals instead.