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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:
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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.
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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
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= 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
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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
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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.
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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! >
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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!
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EQUIVALENT FRACTIONS OF
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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
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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
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- 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
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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
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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). + • – = –
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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
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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.
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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
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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
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Divide 3 There are 12 one-fourths that fit into 3.
#19 1) Draw a picture to show 3 wholes. 2) How many ’s fit into 3 wholes? There are 12 one-fourths that fit into 3.
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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 .
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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
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#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.
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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
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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 = = 12 10 -9
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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
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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 .
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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
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Extras
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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).
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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.
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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
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