Algebra Honors (Period 6 & 7)

Chapter 1 Highlights
Variable→ symbol used to represent one or more numbers
Variable expression contains a variable
Numerical expression names a particular number
Simplifying the expression→Replacing a numerical expression by the simplest name for its value
Grouping symbols→ parentheses, brackets, fraction bar, etc used to enclose an expression that should be simplified first.
Equation→ two numerical or variable expressions that are equal. Represented by an equals sign placed between the two sides of the equation.
Open Sentences→ contain variables, such as 5x – 1 =9
or y + 2 = 2 + y

The given set of numbers that a variable represents is called the domain of the variable.
Use brackets { } to show a set of numbers. A short way to write “the set whose members are 1, 2, and 3” is {1, 2, 3}
Any value of a variable that turns an open sentence into a true sentence is a solution or root of the sentence.
The set of all solutions of an open sentence is called the solution set of the sentence.
Some equations have only one solution, and some equation have no solutions. The sentence y + 2 = 2 + y has an infinite number. The solution set is the set of all numbers. If, however, you are asked to solve of the domain {0,1,2,3}, you state that the solution set is the domain itself {0, 1, 2, 3}.

Another way to express this is

Read the above as
“y belongs to the set whose members are 0, 1, 2, 3”

Real Numbers
Natural Numbers or Counting Numbers→ 1, 2, 3, 4, 5….
Whole Numbers (Natural Numbers + 0) → 0, 1,2, 3, 4, 5 …
Integers (Natural Numbers , their opposites, + 0) → …-4, -3, -2, -1, 0, 1, 2, 3, 4, …
Rational Numbers (quotient of two integers)
So any number that is either positive, negative, or zero is called a real number.

Each number is a pair, such as 4 and -4 is called the opposite of the other number. The opposite of a is written –a.
The numerals -4(lowered minus sign) and ^-4 (raised minus sign) name the same number.
Caution –a read “the opposite of a” is NOT necessarily a negative number.
For example, if a= -2 then –a would be –(-2) = 2

Absolute value is a distance concept. It my be thought of as the distance between the graph of a number and the origin on a number line. The graphs of -4 and 4 are both 4 units from the origin.

Math 6 Honors ( Periods 1, 2, & 3)

Our Class Blog
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!

Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!

Algebra Honors (Period 6 & 7)

Our Class Blog
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!

Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!

Math 6 Honors (Period 6 and 7)

Commission and Profit 9-6

Some sales jobs pay an amount based on how much you sell. This amount is called a commission.

Like a discount, the commission can be expressed as a percent or as an amount of money.

amount of commission = percent of commission X total sales.

Using the examples from our textbook,

Maria sold $42,000 word of insurance in January. If her commission is 3% of the total sales, what was the amount of her commission in January?

amount of commission = percent X total sales
0.03 X 42,000 = 1260
Her commission was $1,260.

Profit is the difference between total income and total operating costs.

profit = total income – total costs

The percent of profit is the percent of total income that is profit

percent of profit = profit/total income
A shoe store had an income of $8600 and operating costs of $7310. What percent of the store's income was profit?

profit= income- total costs = 8600 -7310 = 1290

percent of profit = profit/total income = 1290/8600 = 0.15
So the percent of profit was 15%.

Practice finding 10%-- its easy--- just move the decimal over one place.
We practiced finding 20%. Just double what you got for 10%.



MATH AT WORK:
Caterer
A caterer provides food for parties, weddings, bar/bat mitzvahs, and other events. Caterers plan the menu, buy the ingredients, and cook the food. Often they provide seating and music as well. For each event, a caterer determines the cost per guest. The catering business requires a thorough knowledge of rations, proportions, and percents.

Algebra (Period 1)

Word Problems from Khan Academy
Check some of these out


Trains..

Math 6 Honors (Period 6 and 7)

Discount and Markup 9-5

A discount is a decrease in the price of an item. A markup is an increase in the price of an item. Both of these changes can be expressed as an amount of money or as a percent of the original price of the item. A store may announce a discount of $3 off the original price of $30 basketball, or a discount of 10%

A warm-up suit that sold for $42.50 is on sale at a 12% discount. What is the sale price?

Method 1: Use the formula

amount of change = percent of change X original amount
= 12% X $42.50

therefore the discount is 0.12 X 42.50 or 5.10
The amount of discount is $5.10
The sale price is 42.50 – 5.10 = $37.40

Method 2: Since the discount is 12%, the sale price is 100% - 12% = 88%.
The sale price is 0.88 X 42.50 = $ 37.40

When you know the amount of discount you subtract to find the new price. When dealing with a markup you add to find the new price.

The price of a new car model was marked up 6% over the previous year’s model. If the previous year’s model sold for $7800, what is the cost of the new car? {and what kind of a car could that be?}
Method 1: Use the formula
amount of change = percent of change X original amount

= 6% X 7800

Therefore the markup is 0.06 X7800= $468
The new price is 7800 + 468 = $8268

Method 2: Since the markup is 6% the new price is 100% + 6% or 106% of the original price. so the new price is 1.06 X7800 = $8268

This year a pair of ice skates sells for $46 after a 15% mark up over last year’s price. What was last year’s price?

This year’s price is 100 + 15 or 115% of last year’s price. Let n present last year’s price
46 = (115/100)n

46 = 1.15n
46/.15 = 1.15n/1.115
40 = n

So last year’s price was $40.

A department store advertised eclectic shavers at a sale price of $36.
If this is a 20% discount, what was the original price?
The sale price is 100 - 20 or 80% of the original price. Let n represent the original price.
36 = (80/100)n
36 = .8n
36/.8 = .8n/.8

45 = n
The original price was $45.
Check to see that your answers are logical and reasonable.

Try these: A service station (that’s gas station, now—they no longer provide service!!) give cash customers a 5% discount on the price of gasoline. If gasoline regularly sells for $3.00 a gallon, what is the discounted price?


A store marks up the price of a $5 item to $12. What is the percent of markup?

Algebra (Period 1)

Motion Word Problems 8-5 & 10-7
rt=d problems
(rate)(time)=distance
Back in Pre-Algebra, these were fairly simple word problems:
1) If you go 60 mph for 3 hours, how far have you gone? (180 miles)
2) You've gone 100 miles in 2 hours. What was your average speed? 
(100/2 = 50 mph)
 
3)You've driven 1000 miles at an average speed of 25 mph. How long did it take you? (1000/25 = 40 hours)
 
Now the problems become more difficult. Usually they involve 2 cars, trains, planes, etc. One car is the "slow" car and the other is the "fast" car.
 
Just like the mixture problems, it helps to make a matrix and also draw a picture to help you understand the words.
 
SLOW CAR/FAST CAR LEAVE FROM SAME PLACE, IN THE SAME DIRECTION, AT DIFFERENT TIMES, WHEN WILL THE 2ND CAR CATCH UP WITH THE FIRST CAR? 
 
2 cars leave 3 hours apart. One travels 72 mph. The other travels 120 mph. The slower car leaves first. When with the faster car catch up with the slower car?
 
Use the set up forms from class... you can find more blank forms online!!

SLOW     72           t              72t  
FAST     120        t - 3        120(t - 3) 
         (fast car left 3 hours later so driving 3 less hours or t - 3)
 
At the point when the fast car catches and overtakes the slow car, what is true of the distances of the 2 cars at that exact moment???
They are equal!
WHAT IS THE EQUATION?
Set the 2 cars' distances equal:
72t = 120(t - 3)
 
72t = 120t - 360
-48t = -360
t = 7.5 hours (slow car's time on the road)
t - 3 = 7.5 - 3 = 4.5 hours (fast car's time on the road)
 
CHECK:
The 2 cars should have traveled the same distance because one car catches up with the other car:
slow: (72)(7.5) = 540
fast: (120)(4.5) = 540
 
 
SLOW CAR/FAST CAR LEAVE FROM SAME PLACE, GOING IN DIFFERENT DIRECTIONS, LEAVING AT THE SAME TIME, WHEN WILL THEY BE A CERTAIN DISTANCE APART?
 
2 cars leave going in different directions. One travels 60 mph. The other travels 50 mph. In how many hours will the cars be 605 miles apart?
 
                      CAR     (RATE)    (TIME)   =   DISTANCE
                     SLOW     50            t                  50t 
                     FAST      60            t                  60t
                      (They travel the same amount of time)
 
What is true of the distances the 2 cars travel?
Together they travel 605 miles because they are 605 miles apart.
WHAT IS THE EQUATION?
Set the 2 cars' distances as a SUM to 605.
50t + 60t = 605
110t = 605
t = 5.5 hours
So in 5 1/2 hours the 2 cars will be 605 miles apart.
 
CHECK:
If you plug in 5.5 hours for each car to find each cars distances, they should add to 605 miles.
slow: (50)(5.5) = 275 miles traveled
fast: (60)(5.5) = 330 miles traveled
275 + 330 = 605 miles
 
SLOW CAR/FAST CAR LEAVE FROM SAME PLACE, GOING IN SAME DIRECTION, LEAVING AT THE SAME TIME, WHEN WILL THEY BE A CERTAIN DISTANCE APART?
 
2 cars leave going in the same direction. One travels 45 mph. The other travels 35 mph. In how many hours will the cars be 15 miles apart?
 
                      CAR     (RATE)    (TIME)   =   DISTANCE
                SLOW     35            t             35t 
                FAST      40            t             40t
                      (They travel the same amount of time)
 
What is true of the distances the 2 cars travel?
They are getting further and further apart as the minutes go by.
The DIFFERENCE of the 2 cars is 15 miles after a certain amount of time.
WHAT IS THE EQUATION?
40t - 35t = 15
5t = 15
t = 3 hours
So in 3 hours the 2 cars will be 15 miles apart.
 
CHECK:
If you plug in 3 hours for each car to find each cars distances, their distances should subtract to 15 miles.
slow: (35)(3) = 105 miles traveled
fast: (40)(3) = 120 miles traveled
120 - 105 = 15 miles
 
SLOW CAR/FAST CAR LEAVE FROM SAME PLACE, GOING IN DIFFERENT OR SAME DIRECTION, IN THE SAME AMOUNT OF TIME, EACH TRAVELS A  DIFFERENT DISTANCE, WHAT IS THEIR SPEED? 
One car travels 20 mph faster than the other car. One car travels 240 miles while the other travels 180 miles. Find their average speeds.
 
                      CAR     (RATE)       (TIME)   =   DISTANCE
               SLOW        r           180/r             180 
               FAST      r + 20    240/(r + 20)        240
This time you have the distance and know that the faster car is 20 mph faster than the slower car. To find the time for each car, use the fact that d/r = t so divided each car's distance by their rates.
 
WHAT IS THE EQUATION?
The times of these 2 cars is equal (left at same time and stopped at same time) so set their times equal:
180/r = 240/(r + 20)
Multiply both sides equally by the LCM:
(r)(r + 20)(180/r) = (r)(r + 20)240/(r + 20)
Cross cancel:
180(r + 20) = 240(r)
180r + 3600 = 240r
3600 = 60r
r = 60 mph (the slower car)
r + 20 = 60 + 20 = 80 mph (the faster car)
 
CHECK:
If you plug in the speeds, you should find that both cars traveled the same amount of time:
slow: (60)t = 180   t = 3 hours
fast: (80)t = 240   t = 3 hours
 
A BOAT/PLANE TRAVELS WITH THE CURRENT ON THE DEPARTING LEG OF THE JOURNEY AND TRAVELS AGAINST THE CURRENT ON THE RETURN LEG. WHAT IS THE SPEED OF THE BOAT/PLANE IN STILL WATER/AIR? 
 
A boat travels with a current of 6 mph for 3 hours and then returns home against the same current. The trip home takes 5 hours. What is the speed of the boat in still water?
 
           BOAT/PLANE        (RATE)       (TIME)   =   DISTANCE
      WITH CURRENT        r + 6           3            3(r + 6)  
      AGAINST CURRENT    r - 6           5            5(r - 6) 
r is the speed in still water and 6 is the speed of the current. The boat with need less time to go the same distance with the current than against it. 
 
WHAT IS THE EQUATION?
The distance to the boat's location and the distance home must be equal.
Set the distances equal:
3(r + 6) = 5(r - 6) 
3r + 18 = 5r - 30
48 = 2r
r = 24 mph (speed in still water)
r + 6 = 24 + 6 = 30 mph (speed with the current)
r - 6 = 24 - 6 = 18 mph (speed against the current)
 
CHECK:
If you plug in the speed with and against the current with the hours traveled, you get the distances to and home. Those distances should be equal:
3(30) = 5(18)
90 = 90

Pre Algebra (Period 2 & 4)

Volume of Prisms & Cylinders 10-7



Remember when I said that the basic formula for area is A = bh

Well, the basic formula for volume of a prism or cylinder is:

V = BH

Where capital B = the area of the base of the prism/cylinder

capital H = the height of the prism/cylinder

THE LABEL IS ALWAYS CUBED!!!


Volume of a rectangular, square, or parallelogram prism:

V = BH

Volume = area of the base times the height of the prism

V = (bh)(H)

The lower case b and h are the base and height of the base (this is plane geometry!)


Volume of a triangular prism:

V = BH

Volume = area of the base times the height of the prism

V = (1/2 bh)(H)

The lower case b and h are the base and height of the base (this is plane geometry!)


Volume of a trapezoidal prism:

V = BH

Volume = area of the base times the height of the prism

V = [(average of the 2 bases)(h)](H)

The lower case b and h are the base and height of the base (this is plane geometry!)



Volume of a cylinder:

V = BH

Volume = area of the base times the height of the prism

V = (π r²)(H)

The lower case b and h are the base and height of the base (this is plane geometry!)

Volume of Pyramids, Cones & Spheres 10-9

To find the volume of a pyramid or cone is just as easy!!!

It's just V= 1/3 BH

That means just find the volume as if it was a prism or cone then just divide it by 3!!!


VOLUME OF A SPHERE (ball) (this one is different)
V = 4/3 π r³

Algebra (Period 1)

Khan Academy has some excellent You Tube videos to help you review basic Algebra I concepts. I suggest you watch at least some of these: :
How to :
Solve Equations using the Quadratic Equations Part 1

Solving Equations Using the Quadratic Equation Part 2

Solve Quadratic Equations by Completing the Square

Pre Algebra (Period 2 & 4)

Area & Parallelograms 10-1 & Area of Triangles & Trapezoids 10-2
AREA-
all these formulas are related to the basic concept of A = bh
Area of Parallelograms 10-1

Area of rectangles and parallelograms = (base)(height)





Now we're starting area!
Where the perimeter/circumference fenced in my puppy, the area of the yard will tell me how much sod (grass) I should buy to stop the puppy's paws from getting muddy!

Area for me is all basically the length of the base times the height of the figure

A = bh

In a parallelogram, whether it's a rectangle, rhombus, square or other parallelogram

A = bh with the height being a line perpendicular to both bases (not the slanted side!)


You have learned the area of a rectangle as A = lw, but the l = b and the w = h

You may have learned the area of a square as A = s² , but that's because the b = h


Any parallelogram can be split into 2 triangles using a diagonal.

Triangles & Trapezoids 10-2
Area of triangle = (1/2)(base)(height or altitude)


Area of trapezoid = (average of the 2 bases)(height)
Any parallelogram can be split into 2 triangles using a diagonal. Because of this, the area of a triangle is half that of a parallelogram.

A = 1/2 bh


A trapezoid has 2 bases that ARE NOT EQUAL. So which base is THE base?

If you use the smaller base, you won't have enough sod for your yard and the puppy's paws are still getting muddy.

If you use the larger base, you'll have too much sod for your yard and the extra will rot.

Sooooooooo..... you actually need to take the average of the two bases times the height

A = (average of the 2 bases)(height)

A = (b₁ + b₂)h /2

Math 6 Honors (Period 6 and 7)

Percent of Increase or Decrease 9-4

Let's say we have an iPod that originally sold for $260. It is on sale for $208. What is the amount of change? "How much did you save?"
Just subtract
260-208 = 52
$52.
What is the percent of change?
The percent of change = amount of change/original
52/260 - x/100
or just divide 52 by 260 = .2
which is 20%
REMEMBER: The denominator in the formula is ALWAYS the ORIGINAL AMOUNT.
Amount of change = percent of change X the original amount.
Find the new number when 75 is decreased by 26%
Amount of change - 26% (75
= .26(75)
=19.5
Now take the difference ( the amount of change) and subtract THAT from 75
75- 19.5 = 55.5

Remember the circle with the various parts of this formula?

Difference or amount of change
% of change X original amount

Difficult to show here so if you missed these notes make sure to ask a fellow student to see this!! IT is a great way to remember what to do!!

State the increase or decrease. Tell what the amount of change is and the percent of change.
from:
10 to 12
increase
amount of increase: 2
% of change : 20%

4 to 3
decrease
amount of decrease:
% of change : 25%

2 to 5
increase
amount of increase: 3
% of change : 3/2 = 1.5 = 150%

12 to 6
decrease
amount of decrease: 6
% of change : 50%

6 to 12
increase
amount of increase: 6
% of change : 6/6 = 1 = 100%

Find the new number produced when the given number is increased or decrease by the given percent.

120; 20% decrease
120(.20) = 24 120 -24 = 96

30; 10% decrease
30(.10) = 3 30 -3 = 27

48: 50% increase
48(.50) = 24 48 + 24 = 72

128: decrease by 25%, then increased by 25%
What... why multiply by .25 if you can use a fraction and work smarter?
128(1/4) = 32
128 - 32 = 96
then 96 ( 1/4) = 24
96 + 24 = 120

Did you think it would be the starting number? Why wasnn't it?

Pre Algebra (Period 2 & 4)

Circles 9-6

A set of points equidistant from a center point

Radius - one endpoint on circle and one is the center (1/2 diameter)

Diameter - both endpoints on the circle and goes through the center point (twice radius)

Chord - both endpoints on the circle but not necessarily through the center

A VERY SPECIAL RELATIONSHIP WAS FOUND IN B.C.E. TIMES:
IF YOU DIVIDED THE CIRCUMFERENCE BY THE DIAMETER OF ANY SIZE CIRCLE, YOU WOULD ALWAYS GET ABOUT 3.14


Circumference = the circle fence - distance around the circle -
 
(pi)(diameter) = 2(pi)r

If you have radius, double it to get the diameter


Note: the circumference is always about triple the diameter (plus a little bit!)


Circles have 360 degrees and every circle is similar to every other circle


Central angles: vertex is the center point of a circle

Circles have 360 degrees.

So 1/4 of a circle is 90 degrees and 1/2 is 180 degrees


Review central angles with fractions, percents and degrees
We used the example from the book
Lunch (l) 25%
Recreation (r) 20%
Clothes (c) 15%
Savings (s) 40%
We need to change these percents to degrees. WE know that a circle is 360˚
so set up a proportion
% = unknown
100 360

25 = l
100 360
l = 90
so Lunch portion of the circle graph is 90˚

20 = r
100 360

Solve for r
r = 72
so the Recreation portion of the circle graph is 72˚

15 = c
100 360

Solve for c
c= 54
So the clothes portion is 54˚

40 = s
100 360

solve for s
s = 144
so the Savings portion of the cirlce graph is 144˚

Area: Circles 10-3

A = pi ∙ r²

Math 6 Honors (Period 6 and 7)

Computing with Percents 9-3
The statement 20% of 300 is 60 can be translated into the following equations
20/100(300) = 60 or 0.20 •300 = 60

EQUATION METHOD:
Notice the following relationship between the words and the symbols
20% of 300 is 60
0.20 • 300 = 60

WRITE THE PROBLEM OUT AND THEN DIRECTLY UNDER THE "IS" WRITE AN EQUAL SIGN. DIRECTLY UNDER THE WORD 'OF" WRITE A MULTIPLICATION SIGN. iF YOU ARE GIVEN A % CHANGE IT FIRST TO A DECIMAL. THEN BRING DOWN ALL THE OTHER NUMBERS GIVEN IN YOUR PROBLEM. LET x OR n REPRESENT YOUR VARIABLE... THAT IS THE "WHAT " PART OF YOUR PROBLEM.

A similar relationship occurs whenever a statement or a question involves a number that is a percent of another number

What is 8% of 75?
Let n represent the number asked for
What number is 8% of 75?
n = 0.08 • 75

solve
What percent of 40 is 6?
let n represent the percent asked for.

What percent of 40 is 6?
n% • 40 = 6
n% • 40 = 6
n% (40)/40 = 6/40
n% = 6/40
n/100 = 6/40
(100) n/100 = (100) 6/40
n=15 so 15% of 40 is 6

140 is 35 % of what number?
let n represent the number asked for
140 is 35% of what number?
140 = 0.35 • n
140 = 0.35n
140/0.35 = 0.35n/0.35 divide carefully!! Watch those decimals!!
400 = n
so 140 is 35% of 400

Always check to see if your answer is logical.

PROPORTION METHOD

In these types of percent problems you are always know three parts of the following proportion

n/1oo = a/b
or better yet
n/100 = is/ of

The n represents the %

Read the problems carefully and you can easily determine which is the "is" and which represents the 'of"
For example:
What percent of 40 is 6?
What percent -- from the problem above indicates that we DO NOT know the n
of 40-- hmm... then 40 must be the 'of' and
similarly is 6 means that 6 represents the 'is'

n/100 = 6/40 solve as a proportion
and you get n= 15 but since it asked us to state the 5 your answer is 15%

140 is 35 % of what number?
In this problem I notice 35% right away so that is the n!!
Then I read the problem again and notice 140 is... hmmm.. THat says 140 must be the is

35/100 = 140/ x I do not know the 'of'

Solve again
x = 400

Math 6 Honors (Period 6 and 7)

Percent and Fractions 9-1

The word “percent” is derived from the Latin “per centum” meaning “per hundred” or “out of one hundred” so 28% means 28 out of 100

A percent is a ratio that compares a number to 100. Therefore you can write a percent as a fraction with a denominator of 100, so 28% is also 28/100

Our book’s example is as follows;
During basketball season, Alice made 17 out of 25 free throws, while Nina made 7 out of 10. To see who did better, we compare the fractions representing each girl’s successful free throws. 17/25 or 7/10
We have calculated this type of problem before.. this time when we compare fractions use the common denominator 100, even if 100 is not the LCD of the fractions.
17/25 = 68/100 and
7/10 = 70/100

Since Alice makes 68 free throws per 100 and Nina makes 70 per hundred, Nina is the better free throw shooter.
the ratio of a number to 100 is called a percent. We write percents by using the symbol %
so
17/25 =68% and
7/10= 70%

Rule
To express the fraction a/b
as a percent, solve the equation

a/b = n/100

for the variable n and write n%


Express 17/40 as a percent
n/100 = 17/40 multiply both sides by 100 100 ( n/100) = 17(100)/40
n = 17(100)/40 n = 85/2 n= 42½

Therefore, 17/40 = 42 1/2 %


Rule
To express n% as a fraction, write the fraction

n/100 in lowest terms


Express 7 ½ % as a fraction in lowest terms

7 ½ % = 7.5% = 7.5/100 How do we get rid of the decimal?
multiply the numerator and the denominator by 10
7.5(10)/100(10) simplify
Similarly, you could change a mixed numebr into an improper fraction
5 3/8% becomes 43/8 % and to change that to a fraction simple divide by 100
That looks messy but if you remember that to divide by 100 you are actually multiplying by 1/100
(43/8) (1/100) = 43/800 and you are finished with your calculations!! EASY!!

Since a percent is the ratio of a number to 100, we can have percents that are greater than or equal to 100%

1 = 100/100 = 100%

165/100 = 165 %

Write 250% as a mixed number in simple form

250% = 250/100

250/100 = 2 50/100 = 2 1/2

The town of Wonderful spends 42% of its budget on education. What percent is used for other purposes?
the whole budget is represented by 100%. Therefore, the part used for other purposes is

100 - 42 or 58%

Percents and Decimals 9-2

By looking at the following examples, you will be able to see a general relationship between decimals and percents

57% = 57/100
0.79 = 79/100 = 79%
113% = 113/100 = 1 13/100
0.06 = 6/100 = 6%

Rules

To express a percent as a decimal, move the decimal point two places to the left and remove the percent sign

57% = 0.57
113% = 1.13

To express a decimal as a percent, move the decimal point two places to the right and add a percent sign

0.79 = 79%
0.06 = 6%


In 9-1 you learned one method of changing a fraction into a percent. Here is an alternative method

Rule
To express a fraction as a percent, first express the fraction as a decimal
and then as a percent

Express 7/8 as a percent

Divide 7 by 8
7/8 = 0.875 = 87.5%

Express 1/3 as a percent
divide 1 by 3
0.33333….. it’s a repeating decimal
express the decimal as a percent 0.333… = 33 1/3%
so, to the nearest tenth of a percent = 33.3% but it is much more accurate to keep the 1/3 and write 33 1/3%