Relevance: If you don’t know a product through mental
math , you can
break up one of the factors into a sum that will al low you to do
Example 6 p.43
a) Multiply 6 ٠ 14
If you don’t now what 6 times 14 is , you can break up 14 into a sum of
10 and 4, then use the distributive property.
6 ٠ 14 =6 ٠ (10+ 4) = 6 ٠ 10 + 6 ٠ 4 = 60 + 24 = 84
b) Multiply 7 ٠ 59
Specifications for a Ford Explorer 4x4 are shown in the table below. How far can
travel on a tank of gas?
4.0 L V6
21 gal ←
in 1 tank
Miles per Gal
→ Fuel economy
15 city/ 19 hwy
We are being asked to find “how far”, which is a distance.
Distance is measured in
miles. We will assume this distance is traveled in the city so we’ll use city
Dimensional analysis is used to convert units. We are
given miles per gal and gallons
per tank. We want to know how many miles can be traveled on 1 tank.
Note: if you don’t know what 15 x 21 is doing mental math,
you can do it using the
15 x 21 = 15(20+1) = 15(20) + 15(1) = 300+15=315
Example: Calculating production
The labor force of an electronics firm works two 8-hour shifts each day and
manufactures 53 TV sets each hour. Find how many sets will be manufactured in 5
We are looking for the ration s-complex-numbers.html">number of TV sets manufactured in 5
Use Dimensional Analysis. We are given TV sets manufactured per hour, and hours
worked per shift, and shifts worked per day. If you included all the pertinent
information, you should have cancelled out all the unnecessary units ( like units
cancel out like units on the bottom), and the units left should be “TV sets”,
what we want.
If you have a rectangular pattern objects, such as rows
columns, you can determine the total number of objects by
multiplying the number of rows times the number of columns (or
objects per row).
Example: Our classroom has 7 rows with 5 seats in each
Therefore our classroom can hold 7x5 = 35 people.
Area: The area of a rectangle is length X width= lw
The is the amount of area covered within the rectangle.
Note: Perimeter is the distance around the rectangle.
If length is in feet, and width is in feet,
Area = length X width means the units of the Area are feet2, or
“ square feet ”
The parking lot at the Hillside Christmas Craft Fair has 14 rows of
parking with 12 parking spaces in each row. How many cars can
fit in the parking lot?
If a times b is c, then c/b answers the question,
“c times what equals b?”
a = c/b
and c/a answers the question,
b = c/a
“c times what equals a?”
Division with 0
If a re presents any nonzero number, 0/a = 0
If a represents any nonzero number, a/0 is undefined.
0/0 is undetermined.
More Division Properties
a/1 = a
a/a = 1 (provided that a ≠ 0)
Quotient X Divisor + Remainder = Dividend Translation: The answer to the division problem times the number you divided
the remainder, should equal the number you divided into.
What about 16/3?
Quotient X Divisor + Remainder = Dividend
5 x 3 + 1 = 15+1=16 yes
A total of 216 girls tried out for a city volleyball
program. How many girls
should be put on the team roster if the following requirements must be
1)All the teams must have the same number of players.
(find a number that goes exactly into 216, so there is no remainder)
2) A reasonable number of players on a team is 7 to 10
(divide 216 players by
7 players per team, then 8, then 9, then 10). But don’t bother with 10
because we know 10 doesn’t go exactly into 216.
3) There must be an even number of teams. (The quotient
must be EVEN).
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