Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
6
© 2014 Pacific Crest
Q4. How do you generalize this calculation?
You have n people and a given amount of pizza (p). Divide the pizza by the number of people:
p/n. You can also multiply the pizza by the reciprocal of the people: p
×
(1/n). If the pizza is a
fractional amount, it still works:
=
= =
=
= =
×
×
2
1 2 1
2 pizzas, 8 people :
2
pizza per person
8
8 8 4
3
3
3 1 3
4
pizza, 2 people :
pizza per person
4
2 4 2 8
Q5. What does it mean to divide a pizza by 3 people?
If you have 2 pizzas, then that means 2/3 or 2/3 of a pizza per person
Q6
.
=
×
2
2 1
3
3 3 3
Why does
?
If we multiply both the number and denominator by 1/3
(remember that 1/3 over 1/3 equals one, due to the multiplicative
identity) then the denominator becomes 1 and the numerator
becomes 2/3
×
1/3:
×
×
×
× =
=
=
= ×
×
2 1 2 1 2 1
3 3 3 3
2
3
1
2 1
3 3
3
3 1
3
1
3 3
1
1 3
3
3
3
1
Q8. Does it matter what the numerator or the denominator becomes, especially if the
denominator is not a whole number but a fraction?
No; we still apply the same rules and perform the calculations.
Q9. When you divide by a fraction vs. a whole number, what are you actually representing
with the fraction?
Dividing by a fraction is the same as multiplying by its reciprocal (let’s use 1/2 and 2). This
makes sense if I think of dividing a pizza in two (1 pizza divided into 2 slices: 1/2). The result
is
less
than a whole pizza. If I divide that pizza by 1/2, I’m asking how many half pizzas
(1/2’s) there are in a single pizza and the answer is obviously 2: 1 ÷ 1/2 = 2. This means that
dividing by a fraction is dividing by portions: the fraction represents portions of a whole.
Q10. How do you validate the answer produced is correct for multiplication and division?
Use division to validate multiplication and vice versa.
11.
Transfer/Application
Multiply and divide fractions:
● with fractional denominators
● with mixed numbers (improper fractions)
● in problems that include zero
● with multiple sets of fractions