Fractions, Decimals, & Percents Users Guide to Fractions, Decimals, & Percents

Fractions 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 2/5

Equivalent 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 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… 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 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 Denominators Before you can add fractions, you must make the denominators the same. This is called having common denominators. You can make common denominators by looking at the multiples of both denominators. The smallest common multiple (least common multiple-LCM) becomes your new denominator.

Example 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 continued 1/5 + 2/3 10/15 3/15 + The answer is 13/15.

….. Answer 1/5 + 2/3 = 1/5 = 3/15 2/3 = 10/15 3/15 + 10/15 = 13/15

Multiplying 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 Denominators Step 3- Simplify *Please note that in most cases, you must simplify the fraction after multiplying.

Example continued… 2/5 x 3/8 = (2 x 3) / (5 x 8) = 6/40 6/40 = 3/20

Decimals .55 means … Tenths Hundredths Thousandths Ten-thousandths Hundred- thousandths Millionths Think about place value and think about money .55 means … Fifty-five hundredths Or Five tenths plus five hundredths

0.75 = ¾ = 75/100 = 75%

Percents Percent form tells how many per every hundred. 50% : 50/100 50% : 50/100 Also equal to ½ or 100/200 or 200/400

Benchmark 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