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Chapter 2 Study Guides

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  • 1. Mixed Number
    • A mixed number has a part that is a whole number and a part that is a fraction.
    = 1 3 4 #1 An improper fraction is when the numerator is greater than the denominator. Improper Fraction 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 8 4 = numerator denominator
  • 2. How To Change An Improper Fraction To A Mixed Number = 5 2 2 ) 5 numerator denominator 2 1 Divide the numerator by the denominator. Put your remainder over the denominator. 2 #2
  • 3. How To Change A Mixed Number To An Improper Fraction
    • 1) Multiply the whole number times the denominator.
    • 2) Add your answer to the numerator.
    • 3) Put your new number
    • over the denominator.
    4 1 2 x + = 9 2 #3
  • 4. Decimals Terminating Decimal Is a decimal that stops. The decimal terminates if you reach a remainder of zero when you divide. Repeating Decimal Is a decimal that shows a pattern of repeating digits. #4
  • 5. Decimal Place Value ___ , ___ ___ ___ ___ ___ ___ ___ Thousands Hundreds Tens Ones Ten ths Hundred ths Thousand ths Ten Thousand ths 2 4 3 1 6 Read as 243 and 16 hundredths #5 Decimals are read as “ and ”
  • 6. To A Fraction : Read the decimal using the correct place value. How you say it determines the fraction. 0.2 TO CHANGE A DECIMAL #6 Two tenths
  • 7. To a Decimal : Divide the numerator by the denominator. #7 TO CHANGE A FRACTION 3 4 3 4 0 . 7 2 8 2 0 0 5 20 0
  • 8. #8 Writing Repeating Decimals as Fractions
  • 9. Equivalent Fractions Equivalent fractions name the same amount or the same part of a whole. You use the giant one to show equivalent fractions. Example: #9 A fraction shows: Parts Shaded Total Parts Numerator Denominator
  • 10. Least Common Denominator
    • TO FIND THE LCM OF 4 and 12:
    2) Find the least multiple that both numbers have in common. 1) List the multiples of both numbers 4 = 4, 8, 12, 16, 20… 12 = 12, 24, 36… LCM is 12 #10 Least Common Multiple is also known as LCD.
  • 11. < Less than > Greater than Less than or equal to Greater than or equal to Read these symbols from left to right. **************************************************************** C o m p a r i n g F r a c t i o n s #11 To compare fractions you must show your work ! >
  • 12. Steps for Rounding Find the number. Circle it. Look next door. 4 or less just ignore. 5 or more add one more. Example : Round 5.328 to nearest hundredth . Circle the 2 in the hundredths place. Look next door at the 8. It is 5 or more so add 1 more to the hundredths place. 5.328 rounds to 5.33 # 12
  • 13. Add Decimals Add 3.41 + 2.5 1 Step 1: Line up the decimals 3.41 + 2.5 Step 2: If needed, put zeros in as place holders Step 3: Add decimals Step 4: Bring decimal down . 0 #13 9 5
  • 14. Subtract Decimals Subtract 3.58 – 1.6 8 Step 1: Line up the decimals 3.58 - 1.6 Step 2: If needed, put zeros in as place holders Step 3: Subtract decimals Step 4: Bring decimal down . 0 #14 2 1 9 1
  • 15. -2 6 3 6 1 + You ADD numerators The denominator STAYS THE SAME ! Add Fractions With The Same Denominator #15 6
  • 16. Giant One/ Simplest Form The Giant One is used to reduce or simplify fractions . #16 To find the simplest form divide the numerator and denominator by the greatest common factor.
  • 17. Draw one-third (horizontal) Draw negative one-half (vertical) 1 3 -1 2 What is of ? Draw a picture (overlay them). #17 One-Third of a Negative One-Half Piece + • – = –
  • 18. Multiply 4 3 7 2 = 28 6 6 ) 28 4 24 4 = 2 3 4 You do NOT need common denominators  Multiply the numerators and denominators straight across. #18 Change the improper fraction to a mixed number 4 6 ÷ ÷ 2 2 Reduce! 4 4 6
  • 19. Multiplying Decimals Steps for Multiplying Decimals Step 1: Write the problem vertically. Step 2: Ignore the decimal point(s) and multiply. Step 3: Determine where the decimal point goes in the product. Place the decimal point in the answer by counting how many places the decimal point has moved. #19
  • 20. Divide 3  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. 1 2 3 4 5 6 7 8 9 10 11 12 #20
  • 21. Reciprocals = Example: - - X 2 2 5 5 - = 1 10 10 To find the reciprocal just flip the fraction over. #21 Two numbers are reciprocals if their product is one. Change your mixed number to an improper fraction to find the reciprocal. 5 2 3 x + = 17 3 3 17
  • 22. Dividing Fractions Example: 5 - 6 - 2 - . . 3 = - 5 6 X - 3 2 = 1 2 - 5 4 = 1 - 1 4 . To divide fractions, multiply the first fraction by the reciprocal of the second fraction. #22
  • 23. NO decimal point in the divisor. Divide 0.27  3 3 0. 27 . 0 0 0 2 7 9 27 0 #23 Divisor Dividend Step 2: Move the decimal point in the dividend straight up into the quotient Step 3: Divide as usual Step 1: Write the problem in the long division format TRICK: D ead M onkeys S mell B ad !
  • 24. Divide Decimals Step 2: Move the decimal point in the divisor to the far right of the divisor Step 5: Divide as usual Step 1: Write the problem in the traditional long division Divide 0.42  0.6 0 6 0 4 2 . 0 0 0 4 2 7 42 0 Step 3: Move the decimal point the SAME NUMBER of places in the dividend Step 4: Move the decimal point in the dividend straight up into the quotient . . . . #24 Dividend  Divisor Yes, decimal point in the divisor.
  • 25. EQUIVALENT FRACTIONS OF #25
  • 26. One-Third Plus Two-Fourths #26 horizontal vertical 1 3 2 4 • 4 • 4 Giant One • 3 • 3 4 12 6 12 10 12 + 5 6 = =
  • 27. Add Fractions 4 5 -2 3 + 15 15 x 5 = x 3 = x 5 = x 3 = -10 12 2 15
    • Find a common denominator .
    2) Add the numerators. 3) Keep the common denominator the same. #27 4) Simplify or reduce. Change improper fractions to mixed #s.
  • 28. Subtract Fractions 5 6 1 8 - 24 24 x 3 = x 4 = x 3 = x 4 = 3 20 17 24 Always SHOW YOUR WORK ! This includes the Giant One. #28 Giant One
  • 29. Add Mixed Numbers 5 6 5 8 + 24 24 x 3 = x 4 = x 3 = x 4 = 15 20 35 24 24 3 24 ) 35 1 11 11 24 24 1 28 11 24 #29 IMPROPER
  • 30. Subtract Mixed Numbers
    • 1 st : Change your mixed numbers to improper fractions .
    2 7 6 7 - 7 7 13 30 17 7 4 1 = = 2 nd : Subtract numerators. 3 rd : The denominator stays the same. 4 th : Change your answer to a mixed number. 7 ) 17 2 14 3 7 3 #30
  • 31. Multiply Mixed Numbers 1 4 = 4 7 x 35 35 + 4 5 + 39 7 39 28 28 ) 39 1 11 28 #31 IMPROPER
  • 32. 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 fraction first.
    #32

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