Equivalent Fractions A fraction shows: #1 A fraction shows: Numerator Parts Shaded Denominator Total Parts Equivalent fractions name the same amount or the same part of a whole. You use the giant one to show equivalent fractions. Ex:

Giant One/ Simplest Form #2 Giant One/ Simplest Form The Giant One is used to reduce or simplify fractions. To find the simplest form divide the numerator and denominator by the greatest common factor.

Mixed Number 1 = = Improper Fraction #3 3 4 8 4 A mixed number has a part that is a whole number and a part that is a fraction. 1 3 = 4 Improper Fraction An improper fraction is when the numerator is greater than the denominator. 1/4 1/4 numerator 1/4 1/4 8 = 4 denominator 1/4 1/4 1/4 1/4

= 2 ) 2 5 5 2 1 2 #4 How To Change An Improper Fraction To a Mixed Number 5 = 2 Divide the numerator by the denominator. Put your remainder over the denominator. 1 2 2 denominator ) 2 5 numerator

Number To An Improper Fraction #5 How To Change A Mixed Number To An Improper Fraction 1 9 + 1) Multiply the whole number times the denominator. 2) Add your answer to the numerator. 3) Put your new number over the denominator. 4 = x 2 2

Least Common Denominator #6 Least Common Denominator TO FIND THE LCM OF 4 and 12: 1) List the multiples of both numbers 4 = 4, 8, 12, 16, 20… 12 = 12, 24, 36… 2) Find the least multiple that both numbers have in common. LCM is 12 Least Common Multiple is also known as LCD.

Comparing Fractions > #7 < > Read these symbols from left to right. < Less than > Greater than Less than or equal to Greater than or equal to **************************************************************** To compare fractions you must show your work! >

Add Fractions With The Same Denominator #8 Add Fractions With The Same Denominator -2 6 3 6 You ADD numerators + 6 1 The denominator STAYS THE SAME!

EQUIVALENT FRACTIONS OF #9

One-Third Plus Two-Fourths #10 One-Third Plus Two-Fourths Giant One horizontal 1 3 4 12 • 4 = vertical 6 12 2 4 • 3 = + 10 12 5 6

1 Add Fractions 12 4 15 5 10 2 + 3 15 22 15 #11 x 3 = x 3 = x 5 = Find a common denominator. 15 5 x 3 = 10 2 2) Add the numerators. x 5 = + 3 x 5 = 15 3) Keep the common denominator the same. 22 7 1 15 15 4) Simplify or reduce. Change improper fractions to mixed #s. 15) 22 15 7

- Subtract Fractions 5 x 4 = 20 6 x 4 = 24 1 x 3 = 3 x 3 = 8 24 17 24 #12 5 x 4 = 20 6 x 4 = 24 Always SHOW YOUR WORK! This includes the Giant One. 1 x 3 = 3 - x 3 = 8 24 17 Giant One 24

Add Mixed Numbers #13 1 5 20 11 x 4 = 24 1 6 24 x 4 = 24 5 15 x 3 = 24) 35 3 + 8 x 3 = 24 24 28 11 35 11 24 24 IMPROPER

One-Third of a Negative One-Half Piece #14 Draw one-third (horizontal) Draw negative one-half (vertical) 1 3 -1 2 What is of ? Draw a picture (overlay them). + • – = –

Multiply #15 You do NOT need common denominators  Multiply the numerators and denominators straight across. 7 4 28 Change the improper fraction to a mixed number = 2 3 6 4 4 Reduce! 6 6) 2 28 4 2 = 4 4 ÷ 24 3 6 2 ÷ 4

Multiply Mixed Number Directions #16 Multiply Mixed Number Directions You DO NOT need common denominators  1. Change the mixed numbers to improper fractions. 2. Multiply the numerators straight across. 3. Multiply the denominators straight across. 4. Simplify or reduce if possible.

Multiply Mixed Numbers #17 Multiply Mixed Numbers 35+4 4 39 39 1 + 5 = 4 7 7 28 x 35 11 IMPROPER 1 28 28) 39

5 2 17 3 3 17 3 = #18 Reciprocals 2 5 1 10 Example: X = = - - - 5 2 10 Two numbers are reciprocals if their product is one. 2 5 1 10 Example: X = = - - - 5 2 10 To find the reciprocal just flip the fraction over. Change your mixed number to an improper fraction to find the reciprocal. + 2 17 3 5 = 3 17 x 3

Divide 3  There are 12 one-fourths that fit into 3. #19 1) Draw a picture to show 3 wholes. 1 2 3 4 5 6 7 8 9 10 11 12 2) How many ’s fit into 3 wholes? There are 12 one-fourths that fit into 3.

Dividing Fractions #20 To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Example: 1 5 5 2 5 3 1 1 . X = = = - - - - - - - 6 3 6 2 4 4 . 2 .

Subtract Mixed Numbers #21 Subtract Mixed Numbers 4 2 30 = 1st: Change your mixed numbers to improper fractions. 7 7 - 1 6 13 = 7 7 2nd: Subtract numerators. 17 3rd : The denominator stays the same. 2 3 7 7 4th : Change your answer to a mixed number. 7) 17 14 3

#22 FRACTION REVIEW Add Fractions: Find a common denominator. Add the numerators, and keep the denominator the same. Subtract Fractions: Find a common denominator. Subtract the numerators, and keep the denominator the same. Multiply Fractions: Multiply the numerators and denominators straight across. Divide Fractions: Multiply the first fraction by the reciprocal of the second fraction. Mixed Numbers: Change it to an improper fractions first.

Add Fractions 12 4 15 5 -10 -2 + 3 15 2 15 #23 x 3 = x 3 = x 5 = x 5 = Find a common denominator. 4 x 3 = 15 5 x 3 = 2) Add the numerators. -10 -2 x 5 = + 3) Keep the common denominator the same. 3 x 5 = 15 2 4) Simplify or reduce. Change improper fractions to mixed #s. 15

Add & Subtract Negative Fractions #24 -2 -4 -4 -8 x 2 = x 2 = 6 12 5 10 x 2 = x 2 = 3 9 1 1 x 3 = x 1 = - + 4 x 3 = 12 10 x 1 = 10 5 -9 -8 – 1 = -8 + -1 = 12 10 -9

Multiply Negative Fractions #25 You do NOT need common denominators  Multiply the numerators and denominators straight across. -20 -5 4 Change the improper fraction to a mixed number! = 2 3 6 2 -3 Reduce! 6 6) 1 -20 -3 2 = 2 -3 ÷ 18 3 6 2 ÷ 2

Divide Negative Fractions #26 To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Example: 1 -5 -5 -5 3 1 -2 1 . X = = = - - - - - - - 6 3 6 1 2 2 . 2 .

Reciprocals #27 To write a reciprocal of a mixed number, you must change your mixed number to an improper fraction first. -42 -5 + 2 = 8 x 8 FLIP IT OVER! Then write the reciprocal of your improper fraction. -8 -42 8 42

Extras

One-Third of a One-Half Piece #Extra One-Third of a One-Half Piece Draw one-third (horizontal) Draw one-half (vertical) 1 3 1 2 What is of ? Draw a picture (overlay them).

Two numbers are reciprocals if their product is one. # Two numbers are reciprocals if their product is one. 1 2 5 10 X Example: = = - - - 5 2 10 To find the reciprocal just flip the fraction over.

Write the Reciprocal of a Mixed Number # To write a reciprocal of a mixed number, you must change your mixed number to an improper fraction first. 17 + 2 5 = 3 x 3 Then write the reciprocal of your improper fraction. 3 17 17 3