Fractions, Decimals, & Fractions, Decimals, & PercentsPercents

Users Guide to

FractionsFractions

Denominator- the number on the bottom of a fraction *Represents how many equal pieces

something is being cut into

Numerator- the number on the top *Represents the number of equal pieces

Example: two fifths 2/5Example: two fifths 2/5

Equivalent FractionsEquivalent Fractions

• Equivalent Fractions are fractions that are equal to each other.

• For instance: 1/2 = 2/4

• To find equivalent fractions, just multiply the numerator and denominator by the same number.

• Example: 1 x 2= 2

2 x 2= 4

Simplifying FractionsSimplifying Fractions

• Simplifying Fractions means to change the fractions into their simplest form

Example: 5/10 = 1/2

• You can make this change easily by looking at the factors of both the numerator and denominator.

• Factors of 5: 1, 5

• Factors of 10: 1, 2, 5, 10

Simplifying Fractions cont…Simplifying Fractions cont…

• Factors of 5: 1, 5• Factors of 10: 1, 2, 5, 10

The common factors between both numbers are one and five. Five is the Greatest. So it is the Greatest Common Factor. Most mathematicians call this the GCF.

Find out how many times the GCF goes into both the numerator and denominator.

5 goes into 5, 1 time 5 goes into 10, 2 times

therefore…. 5/10 = 1/2

Adding & Subtracting FractionsAdding & Subtracting Fractions

• When adding and subtracting fractions, you must first have the same denominators for both fractions. Example: 1/4 + 2/4

• Keep the denominator the same- add or subtract the numerators.

• 1/4 + 2/4 = ¾• (again, the denominator stays the same,

the numerators get added together.)

Common DenominatorsCommon Denominators

• Before you can add fractions, you must make the denominators the same. This is called having common denominatorscommon denominators.

• You can make common denominators by looking at the multiplesmultiples of both denominators. The smallest common multiple (least common multiple-LCM) becomes your new denominator.

ExampleExample

1/5 + 2/3 Look at the denominators and find the LCM (least common multiple)

Multiples of 5: 5, 10, 15, 20, 25, 30…

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30…

• 15 is the smallest multiple that both numbers have in common; therefore, that is the number that should be used. Although, 30 and any other common multiples will also work.

Example continuedExample continued 1/51/5 + 2/32/3

3/15 10/1510/15

++

The answer is 13/15.The answer is 13/15.

…….. Answer.. Answer

• 1/5 + 2/3 =

1/5 = 3/15

2/3 = 10/15

3/15 + 10/15 =

13/15

Multiplying FractionsMultiplying Fractions

• When multiplying fractions… or should I say when finding the product of fractions…

You simply multiply across. Step 1- Multiply the Numerators

Step 2- Multiply the DenominatorsStep 3- Simplify

*Please note that in most cases, you must simplify the fraction after multiplying.

Example continued…Example continued…

2/5 x 3/8 =

(2 x 3) / (5 x 8) = 6/40

6/40 = 3/20

2/5 x 3/8 = 3/20

DecimalsDecimals

• Think about place value and think about money

.55 means …

Fifty-five hundredths

Or

Five tenths plus five hundredths

Tenths

Hundredths

Thousandths

Ten-thousandths

Hundred- thousandths

Millionths

0.75 = ¾ = 75/100 = 75%

PercentsPercents

Percent form tells how many per every hundred.

• 50% : 50/100• Also equal to ½ or 100/200 or 200/400

Benchmark FractionsBenchmark Fractions

• These are the fractions that are the most commonly used. Memorize these benchmark fractions and their percent and decimal equivalents to make working with fractions easier.

½ 50% 0.50

1/3 33% 0.333

¼ 25% 0.25

1/5 20% 0.20

1/6 16.7% 0.167

1/8 12.5% 0.125

1/10 10% 0.10

2/3 67% 0.667

¾ 75% 0.75