How many groups of 3/4 are in 4 1/2 How many groups of in 3/4 are in 2 2/3

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1.)There are 6.

4 1/2 = (4×2+1)/2 = 9/2

9/2 ÷ 3/4

9/2 × 4/3

9/1 × 2/3= 18/3 = 6

use this process again in question 2

Problem 1

1/2 = 2/4

The mixed number 4 & 1/2 is the same as 4 & 2/4

Then convert that mixed number to an improper fraction using the formula below

a & b/c = (a*c+b)/c

4 & 2/4 = (4*4+2)/4

4 & 2/4 = 18/4

We could reduce this, but I'll keep it unreduced so that we keep the denominator of 4.

Now think of 3/4 as "3 fourths" and 18/4 as "18 fourths".

We could easily replace "fourths" with "unit" to say 3 units and 18 units respectively.

The problem can be rephrased into this question: "how many groups of 3 units are in 18 units?"

At this point, it's probably clear that there are 6 groupings since 18/3 = 6.

It might help to set up a drawing where there are 6 circles, and inside each circle would be 3 dots. So there are 3*6 = 18 dots total.

Problem 2

3/4 = 9/12

2/3 = 8/12

2 2/3 = 2 8/12

2 & 8/12 = (2*12+8)/12 ... using the formula from earlier

2 & 8/12 = 32/12

Think of "twelfths" as a unit

So asking "how many groups of 9/12 are in 32/12" is the same as asking "how many groups of 9 units are in 32 units".

Divide the two numbers to find out

32/9 = (27+5)/9

32/9 = 27/9 + 5/9

32/9 = 3 + 5/9

32/9 = 3 & 5/9

Notice that if you were to convert the mixed number 3 & 5/9 to an improper fraction (using that formula mentioned), then you should get 32/9 back again.

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1