FRACTIONS, DECIMALS, AND

PERCENTSParts of the whole

LET’S WATCH THIS CLIP TO SEE HOW SOME PEOPLE CAN BE CONFUSED ON HOW FRACTIONS AND PERCENTS CAN BE USED AS EXAMPLES.

PERCENT COMES FROM THE LATIN PER CENTUM, OR “PER HUNDRED”CONSEQUENTLY, A NUMBER SUCH AS 32% CAN BE WRITTEN AS “32 PER HUNDRED” OR THE FRACTION 32/100. THIS FRACTION IS EQUIVALENT TO THE DECIMAL 0.32.PERCENT – IS A RATIO OF A NUMBER TO 100.

THE WORD “PERCENT” MEANING “PER HUNDRED” IS USED TO SHOW PARTS OF A WHOLE, THE SAME AS A FRACTION IS USED TO REPRESENT PART OF A WHOLE.IF YOU HAD A PIZZA THAT WAS CUT INTO 100 PIECES, 25% OF THE PIZZA WOULD BE 25 PIECES!

LET’S BEGIN WITH A SIMPLE CONCEPT. CONSIDER THE BLUE SQUARE BELOW. LET’S THINK OF THIS BLUE SQUARE AS ONE WHOLE SQUARE. HOW LET’S DIVIDE IT INTO 100 PIECES—EVERY PIECE JUST THE SAME SIZE AS EVERY OTHER PIECE. WE CAN EASILY SEE THAT EVERY ONE OF THE 100 PIECES IS SHADED BLUE. SO WE SAY 100% OF THE SQUARE IS SHADED BLUE. SO 100% AND 1 WHOLE ARE THE SAME THING.

SINCE PERCENT MEANS “PER HUNDRED” IT TELLS US HOW MANY FOR EACH HUNDRED, 25% MEANS 25 FOR EACH HUNDRED, OR 25 OUT OF EACH HUNDRED.HERE IS OUR ONE WHOLE SQUARE WITH A PORTION SHADED GREEN. WHAT PERCENT IS SHADED GREEN. IN PERCENT, EVERY WHOLE IS DIVIDE INTO 100 PIECES. NOW COUNT THE PIECES SHADED GREEN. THERE ARE 50 PIECES OUT OF 100 SHADED GREEN, SO 50% IS GREEN.

ONCE AGAIN OUR ONE WHOLE SQUARE HAS A PORTION SHADED, THIS TIME IT’S BLUE. WHAT PERCENT IS SHADED BLUE. REMEMBER, IN PERCENTS, EVERY QUANTITY IS DIVIDED INTO 100 PIECES. NOW COUNT THE PIECES SHADED BLUE. THERE ARE 86 PIECES OUT OF 100 SHADED BLUE, SO 86% OF THE PIECES ARE SHADED BLUE.

CAN YOU CALCULATE WHAT PERCENT OF OUR “ONE WHOLE” THAT IS SHADED RED?

THE RELATIONSHIP BETWEEN FRACTIONS

DECIMALS AND PERCENTS

All represent part of a whole

HOW DO WE GET FROM ONE FORM TO ANOTHER?

Reference Numbers

Fraction

Decimal

Percent

51/100 0.51 51%

¼ 0.25 25%

A PERCENT IS BASED ON THE NUMBER IN TERMS OF 100 OR “PER HUNDRED”.12%; 4%; 0.05%...

A fraction is based on the number into which the whole is

divided (the denominator).

The numerator (the top) is the PART, the denominator

(the bottom) is the whole.

½; ¼; ⅝…

A decimal is based on the number in terms of tenth, hundredths, thousandths, etc…0.5; 0.05; 0.005

FRACTION TO DECIMAL

Divide the denominator (the bottom of the fraction) into the numerator (the top of the fraction). Place a decimal after the number inside the division “box” and attach as many zeros as necessary to complete the division. If the quotient does not come out evenly, follow the rules for “rounding off” numbers.

numerator

denominator

DECIMAL TO PERCENT

.50 = 50%

(0.50 x 100 = 50.0) Attach the % sign

Move the decimal point two (2) places to the right (this multiplies the number by 100)

PERCENT TO DECIMAL

50% = .5050 ÷ 100 = .50

Move the decimal point two (2) places to the left (this divides the

number by 100)

PERCENT TO FRACTION

Place the number over 100 and reduce.

FRACTION TO PERCENT

Multiply the number by 100, reduce and

attach a percent (%) sign.

DECIMAL TO FRACTION

You will be using place value to do this! Count the decimal places of the decimal starting from the decimal point. If there is one decimal point, place the number over 10 and reduce. If there are two decimal places, place the number over

100, and reduce. If there are three decimal places, place the number over 1000, and

reduce…Etc.(This is really just using your knowledge of place value to

name the denominator.)

1 decimal place = tenths,2 decimal places =

hundredths,3 decimal places =

thousandths

REMEMBER THAT FRACTIONS, DECIMALS, AND PERCENTS ARE DISCUSSING PARTS OF A WHOLE, NOT HOW LARGE THE WHOLE IS.FRACTIONS, DECIMALS, AND PERCENTS ARE PART OF OUR WORLD. THEY SHOW UP CONSTANTLY WHEN YOU LEAST EXPECT THEM. DON’T LET THEM CATCH YOU OFF GUARD. LEARN TO MASTER THESE NUMBERS.

PERCENTS TO REMEMBER

PROBLEM SOLVING WITH

PERCENTSWhen solving a problem with a percent

greater than 100%, the part will be greater than the whole.

THERE ARE THREE TYPES OF PERCENT PROBLEMS: 1) FINDING A PERCENT OF A NUMBER,2) FINDING A NUMBER WHEN A PERCENT OF IT IS KNOWN, AND 3) FINDING THE PERCENT WHEN THE PART AND WHOLE ARE KNOWN

1) what is 60% of 30?

2) what number is 25% of 160?

3) 45 is what percent of 90?

SOLVING EQUATIONS CONTAINING PERCENTSMOST PERCENT PROBLEMS ARE WORD PROBLEMS AND DEAL WITH DATA. PERCENTS ARE USED TO DESCRIBE RELATIONSHIPS OR COMPARE A PART TO A WHOLE.

Sloths may seen lazy, but their extremely slow movement helps make them almost invisible to predators. Sloths sleep an average of 16.5 hours per day. What percent of the day do they sleep?

Solution

EQUATION METHOD

WHAT PERCENT OF 24 IS 16.5.

N · 24 = 16.5N = 0.6875N = 68.75%

Proportional method

Part Part

Whole Whole

24

5.16

100

n

SOLVE THE FOLLOWING PERCENT PROBLEMS

1) 27 is what percent of 30?2) 45 is 20% of what number?3) What percent of 80 is 10?4) 12 is what percent of 19?5) 18 is 15% of what number?6) 27 is what percent of 30?7) 20% of 40 is what number?8) 4 is what percent of 5?