can you help with this maths question for my 9 year old?  The answer section says D but I would like to help him understand why.  Thanks.?

When dealing with mathematics, one of the tricks is to ensure that the numbers represent the same thing, like apples, SO one apple + one apples = 2 apples or one orange + one orange = two oranges, but one apple + one orange is NOT two apples or two oranges. 

To be able to add them together, we have tofind a way of making the apples and oranges the same --- call then fruit: 

so one fruit + one fruit = two fruit

In this problem we are dealing with fractions, In fractions, the denominators (the number under the short line) are like apples and oranges

1/12 is NOT the same as 1/36

How can we make these comparable?

well, 36 = 3 * 12

hence 1/2 = 3/36

so is 5/12 less than 16/36?

that's like comparing 5 lots of 3/36  which is the same as 15 lots of 1/36 to 16 lots of 1/36

or asking " is 15/36 less than 16/36?" (yes, 15 is less than 16).

do the same with the others.

3/7 = 15/35  vs 16/35 (yes, 15 is less than 16).

7/13 = 21/39 vs 22/39 (yes, 21 is less than 22).

10/11 = 30/33 vs 29/33 (no, 30 is greater than 29.

)hope this helps.... 

To compare two fractions, when the denominators are the same, the greater the numerator, the greater the fraction is.

A is true.
5/12 = (5/12) × (3/3) = 15/36 < 16/36

B is true
3/7 = (3/7) × (5/5) = 15/35 < 16/35

C is true
7/13 = (7/13) × (3/3) = 21/39 < 22/39

D is false
10/11 = (10/11) × (3/3) = 30/33 > 29/33

The answer: D 10/11 < 29/33

10/11 = 30/33 which is GREATER than 29/33

3*12=36 --3*5=15  <16/36
5*7=35 --5*3=15  <16/35
3*13=39 -- 3*7=21 <22/39
3*11=33 -- 3*10=30/33 >29/33

Answer given below

5/12 < 16/36 is the same as 5 x 36 < 12 x 16, which is the same as 180 < 192. True.
3/7 < 16/35 is the same as 3 x 35 < 7 x 16, which is the same as 105 < 112. True.
7/13 < 22/39 is the same as 7 x 39 < 13 x 39, which is the same as 273 < 507. True.
10/11 < 29/33 is the same as 10 x 33 < 11 x 29, which is the same as 330 < 319. False.

What you can do is write it as 10/11 < 29/33. Show him that  2/3 < 3/4 by this logic. Multiply both sides by 3, You will have 2 <9/4. Now again multiply by 4. You will get 8<9/ True.. Multiply by 11
10 < 29*11/33= 10 < 29/3. Multiply by 3. You get 30 <29. This is not true. You take 12 marbles. Make 3 parts and take 2 parts and count.You get 8.  Again make 4 parts and take 3 parts and count. You get 9 now.

Make the denominator of the first fraction same to the second fraction:
Like this....

A. 5/12 < 16/36 
To make them Like fractions or Same denominators, take the bigger denominator (36) then divide it to the smaller denominator (12) = 36/12 = 3
This result (3) is what you need to multiply it to 12 to make the denominators same
12 x 3 = 36
5/36 < 16/36 
The number "5" will change too because the denominator of the fraction is multiplied by 3
Multiply the numerator by 3 then that's the result
5 x 3 = 15
15/36 < 16/36, we know proved that this is true by making it like fractions.

15/36 < 16/36 = 5/12 < 16/36. This is TRUE

Do the same to the other three fractions:

B. 3/7 < 16/35
35 / 7 = 5, 5 x 7 = 35
3/35 < 16/35
3 x 5 = 15
15/35  < 16/35. This is TRUE

C. 7/13 < 22/39
39/13 = 3, 13 x 3 = 39
7/39 < 22/39
7 x 3 = 21
21/39 < 22/39. This is TRUE

D. 10/11 < 29/33
33/11 = 3, 11 x 3 = 33
10/33 < 29/33
10 x 3 = 30
30/33 < 29/33. This is FALSE, so WRONG

Why?
Because the number 30 is not SMALLER than 29 but BIGGER. So it should be....
30/33 > 29/33.

So the answer for that problem is D. 10/11 < 29/33

The answer is D.  10/11 is equal to 30/33, which is 1/33 greater than 29/33, not less.

To compare two fractions, the denominators have to be the same.Any number divided by itself equals 1,  so to make the denominators in the two fractions in D the same, you have to multiply 10/11 by 3/3, which will give you 30/33,which has the same denominator, 33, as the other fraction, 29/33. Now you can see that 30/33 is 1/33 greater than 29/33.  Since < means "less than", the expression in D is false.

30/33 is NOT less than 29/33, 
so it's FALSE!

Let's take the first inequality as an example:
5/12 < 16/36.
Now cross multiply the left numerator times the right denominator 5*36 = 180 keep this on the left side and the left denominator and the right numerator  12*16=192 keep this on the right side.
Now compare 180 from the left answer is less than 192 from the right. So the first one is true.
Do this for each inequality to see which one is false.
I hope this helps!
Cipherman

the answer is D because 10/11 is the same thing as 30/33 and the other fraction is 29/33. Now that we have fractions with the same denominator. Now all we need to do is look at the numerators and compare. So 30 is actually greater than 29.

Because in A. B. and C. when we multiply the left hand of the inequality by,  actually, by 3/3=1 we maintain the left hands value because p/q*1=p/q, q<>0.

But, in D, we multiply 10/11 * 3/3 = 30/33 which is not < 29/33 because 30>29.

others have explained the solution.

i shall show you the tricks to decide quickly


5/12 < 16/36

cross multiply

5*12 ; 12*16

60 ; 192 you know that 60<192


similarly
10/11 ; 29/33
10*33 ; 29*11

330 ; 319

 so 330 > 319 so, what is indicated is false

First of all, make the fraction equal :

A. 5/12 = 15/36 
B. 3/7 = 15/35
C. 7/13 = 21/39
D. 10/11 = 30/33 

Now compare the top numbers & you will see answer D. 30 is lesser than 29 which is wrong.

Find the LCM of denominator of all terms and equalize the denominators and then compare resultant fractions in each of A , B , C , D equations.
In first 3 equations first term is smaller than the second term !
But , ...
The first term in  last D equation is greater than the secord term ., i.e.
10/11 is greater than 29/33 ,  therefore D is wrong !

A. 0.4166<0.444
B. 0.42857< 0.457
C. 0.5384<0.56
D. 0.909090< 0.8787

D is false.

Here's what you say to your son. A,B,C and D are 4 inequalities. This is what you do with each inequality. Make sure the denominators are the same for each
fraction in the inequality. In A, for example, if we divide 36 by 12 we get 3 and 
when we multiply both the numerator and denominator of the fraction on the left
side by 3 we get 15/36. Now it's obvious that 15/36 is less than 16/36. We do the same for B and C and it's obvious that 5*3 is less than 16 and 3*7 is less than 22. Now we come to D. 33/11 = 3 and (3/3)(10/11) = 30/33 , not less than
(29/33). So inequality D is false.

To compare fractions the denominators (the number at the bottom) must be the same.

So for A, multiply the fraction on the left by 3/3, i.e. multiply the top and bottom by three, which gives 15/36, which is less than 16/36 (by 1/36 or 1 thirty-sixth).

Do the same for the other fraction. You should be manipulating the fraction on the left to make the denominator the same as the one on the right.

The left-hand fractions should be (do them yourselves):
B - 15/35
C - 21/39
D - 30/33
Then it's clear that only D is false.

5/12 = 15/36...(multiplying by 3)

so, 15/36 < 16/36...true

3/7 = 15/35...(multiplying by 5)

15/35 < 16/35...true

7/13 = 21/39...(multiplying by 3)

21/39 < 22/39...true

10/11 = 30/33...(multiplying by 3)

30/33 < 29/33...not true, but 30/33 > 29/33

:)>