6.2 Division and Fractions and Division with remainder

in general if A and B are whole numbers and B is not 0, then

A divided by B is equal to a/b

generally, if A and B are whole numbers, and if A/B has whole number Q, Remainder R then

A/B = Q and R/B

division with remainder: how many groups

A/B is the largest whole number of groups that can be made when A objects are divided into groups with B objects in each group. the remainder is the number of objects left over (can't be placed in a group)

division with remainder, how many in each group: if A and B are whole numbers, and B is not zero, then

A/B is the largest whole number of objects that are in each groups when A objects are divided equally among B groups. the R is the number of objects left over (that can't be placed in a group)

for division with remainder, the connection b/w division and multiplication is different than it is for exact division: for example, 23/4 has whole number quotient 5 R3 corresponds with the contrast with exact division: 23/4 = 5.75 corresponds with

corresponds with equations that involve both X and addition

23/4=5.75 23/4= Five and 3/4 what kind of division fit to divide $23 equally among 4 people, each person should get $23/4 = 5.75 if you have 23 cups of flour, and a batch of cookies requires 4 cups of flour, then you can make 23/4= 5 and 3/4 batches of cookies. if you have 23 pencils to divide equally among 4 kids, then it doesn't make sense. why?

exact division

generally, if A and B are whole numbers, then A/B

has whole number quotient Q, remainder R, which is equivalent to A/B = Q and R/B

how does the 3rd answer 5 remainder 3 fit with divison as we have defined it

interpret division in a different manner than we have so far. for each of the two interpretations of division, there is an alternative formulation, which allows for a remainder.

when we multiply two whole numbers, when we divide two whole numbers

product is always a whole number quotient might not be a whole number

how is the notation we use with fractions related to division

same notation is used for division as well as for fractions. instead of writing the divided by symbol we sometimes write /

in chapter 3 we discussed how to turn mixed numbers into improper fractions how to turn improper fractions into mixed numbers

view mixed number as the sum of its whole number part and its fractional part view an improper fraction in terms of divisoo

when the quotient is not a whole number

we have different options for how to express the answer to the division problem

how can we make sense of fractions such as -13/5 13/-5 and -13/-5

when A and B are counting numbers, A/B = A divided by B.