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
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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
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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
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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
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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 ”
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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
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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
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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
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.
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< 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 ! >
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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
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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
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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
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-2 6 3 6 1 + You ADD numerators The denominator STAYS THE SAME ! Add Fractions With The Same Denominator #15 6
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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.
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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 + • – = –
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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
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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
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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
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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
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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
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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 !
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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.