decimals year 8 homework

[ytrewq]

how do I add or take away decimals if the demoninator is completely different. The sum by son has for homework is 34/48 +23/25 + 14/81. We can't find a common demominator and have been told not to convert them to decimals. Thanks

[748rhydhir]

if a common denominator cannot easily be found then ,in this case the common denominator will be;
48*25*81=97200
hope this helps

[Tom Braider]

34/48=17/24 so that would make the answer 54/48600 (instead of 71/97200) and then you can convert 54/48600 to 27/24300 which equals 900

[Rev. Green]

It is always safe just to multiply the denominators together i.e. 48 * 25 * 81 = 97200

If you want to find the smallest common denominator, first find the prime factors of each number. These are the prime numbers which have to be multiplied together to give each denominator. Sometimes you need to repeat some.

So 48 = 2 " 2 " 2 * 2 * 3
25 = 5 * 5
81 = 3 * 3 * 3 * 3

Now you need to take each factor 2, 3, and 5 the maximum number of times it appears for any denominator.

So you take 2 four times (from the factors of 48),
you take 5 twice (from the factors of 25)
3 appears once (as a factor of 48) and four times (as a factor of 81) so you take the larger of these - four times.

Multiply all these together
2 * 2 * 2 * 2 * 3 * 3 * 3 * 3 * 5 * 5 = 32400

So 32400 is the smallest common denominator.

[Mrs Y]

I think the previous posters have forgotten that if you multiply out the denominators to make them common, then you also have to multiply the numerators.

In this case, 34/48 will become 17/24 (as already stated), which will then multiply out to 34425/48600; 23/25 will become 44712/48600, and 14/81 will become 8400/48600.

Added together, this gives a total of 87537/48600, which can be factorised down into 1 and 12979/16200. It can't be factorised any further, as 12979 is a prime number.

Hope that helps!

[ytrewq]

Thanks for all your answers - homework finished hey!!

[mibn2cweus]

"12979" <"?

[Mrs Y]

Eh?

[mibn2cweus]

Mrs Y, I appears you may have trans-positioned a few digits in your answer.

Estimate:
a quick first look reveals the addition of three fractions smaller than one so the answer will be less than 3 but >23/25 (the largest fraction).

scaling 34/48 + 23/25 + 14/81 to
tenths: ~7/10 + ~9/10 + ~2/10 = ~18/10 =
~1.8 plus or minus ~10%


Solve:
34/48 + 23/25 + 14/81 minimise each fraction optional:
17/24 + 23/25 + 14/81

scale to common denominator:
17/24 x [25, 81] = 17/24 x 2025/2025 = 34425/48600
23/25 x [24, 81] = 23/25 x 1944/1944 = 44712/48600
14/81 x [24, 25] = 14/81 x 600/600 = 8400/48600

add numerators and divide by common denominator:
(34425 + 44712 + 8400)/48600 =
87537/48600 minimise [3 gosinta]

29179/16200

equals 1.80117283951 close to original estimate

[Mrs Y]

I think you may have mis-read my answer, as it's exactly the same as yours (i.e. right).

29179/16200 is the same as 1 and 12979/16200; my answer merely changed it from being a top-heavy fraction.

[mibn2cweus]

Duh! Thanks for clearing that up for me.

[derrynoose]

As a former teacher of mathematics I can't see the point in setting such a brute of a question to any child. So much more could have been gained by setting a number of simpler fractions where the required processes still have to be gone through. The difference is that the learner would gain confidence and encouragement through his/her repeated success.