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.

equal to

step-by-step explanation:

27

step-by-step explanation: