Basic Mathematics for College Students

Find the area of a triangle.

As the figures below show, a triangle has three sides. The length of the base of the

triangle can be represented by the letter band the height by the letter h. The height of

a triangle is always perpendicular (makes a square corner) to the base. This is shown

by using the symbol.

Recall that the area of a figure is the amount of surface that it encloses. The area

of a triangle can be found by using the following formula.

Height

Base

b

h Height h

Base

b

5

226 Chapter 3 Fractions and Mixed Numbers

Form The key phrase ofsuggests that we are to find a part of the 435 possible

votes using multiplication.

We translate the words of the problem to numbers and symbols.

is equal to of



SolveTo find the product, we will express 435 as a fraction and then use the rule

for multiplying two fractions.

Write 435 as a fraction:

To prepare to simplify, write 435 in prime-factored

form: 3  5 29.

Any whole number divided by 1 is equal to that number.

StateIt would take 290 votes in the House to override a veto.

CheckWe can estimate to check the result. We will use 440 to approximate the

number of House members voting. Since of 440 is 220, and since is a greater part

than we would expect the number of votes needed to be more

than220. The result of 290 seems reasonable.

1

2 ,

2

3

1

2

 290

Multiply the remaining factors in the numerator:

2  1  5  29 290.

Multiply the remaining factors in the denominator:

1  1 1.



290

1

Remove the common factor of 3 from

 (^) the numerator and denominator.

2  3

1

 5  29

3

1

 1



2  3  5  29

3  1

Multiply the numerators.

 (^) Multiply the denominators.

2  435

3  1

435 ^4351.

2

3

 435 

2

3



435

1

 435

2

3

The number of

votes needed in

the House to

override a veto

the number

of House

members

that vote.

2

3

The number of

votes needed in

the House to

override a veto

2

3

435

~3 145

~^5 ~ 29