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# Chapter 5 Sections 1 And 2 Review

## by Middle School on Feb 02, 2010

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Chapter 5, Sections 1 and 2 Review. Comparing and ordering fractions. Finding Multiples using factor trees.

Chapter 5, Sections 1 and 2 Review. Comparing and ordering fractions. Finding Multiples using factor trees.

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## Chapter 5 Sections 1 And 2 ReviewPresentation Transcript

• Chapter 5: Section 1 Comparing and Ordering Rational Numbers (Fractions!) REVIEW
• Multiples
• A multiple of a number is the PRODUCT of that
• number and any nonzero number.
12 is a multiple of 4 24 is a multiple of 4
• Multiples of 5:
• 1 x 5 = 5
• 2 x 5 = 10
• 3 x 5 = 15
• etcetera
• Multiples of 10:
• 1 x 10 = 10
• 2 x 10 = 20
• 3 x 10 = 30
• etcetera
5, 10, 15, 20, 25, 30, etc. 10, 20, 30, 40, 50, 60, etc. What is the LEAST COMMON MULTIPLE of 5 and 10? What are the COMMON MULTIPLES of 5 and 10?
• Word Problem
• Today both the school baseball and school soccer teams had games. The baseball team plays every 6 days. The soccer team plays every 5 days. When will both teams have games on the same day again?
Finding the COMMON MULTIPLES of 5 and 6 will tell you on which days, from TODAY , that the two teams play on the SAME day .
• Find the COMMON MULTIPLES of 5 and 6.
Word Problem Multiples of 5: 5, 10, 25, 30, 35, 40…etc. Multiples of 6: 6, 12, 18, 24, 30…etc. Go no further! What is the LEAST COMMON MULTIPLE ? The next time the Baseball team and Soccer team will play on the same day is 30 days from today!
• Find the Least Common Multiple: LCM
• 3, 4:
• 4, 5:
• 3, 4, 5:
• LCM with Prime Factorization
• Find the LCM of Nasty Numbers .
• 1) Write the Prime Factorizations ( Factor Tree )
• 2) Use the greatest power of each factor.
• 3) Multiply .
Multiples of 12 = 2 2 • 3 (2 • 2 • 3) = 12 Multiples of 40 = 2 3 • 5 (2 • 2 • 2 • 5) =40 Multiply: 2 3 • 5 • 3 = 2 • 2 • 2 • 5 • 3 = 8 • 15 =120
• 9, 15:
• 12, 15, 18:
Find the Least Common Multiple: LCM
• Use Prime Factorization for Variables.
• Find the LCM for 6a 2 and 18a 3 :
• 6a 2 : 2 • 3 • a 2
• 18a 3 : 2 • 3 2 • a 3
2 • 3 2 • a 3 = 2 • 3 • 3 • a 3 = 9 • 2 • a 3 = 18a 3 18a 3 is the Least Common Multiple
• Comparing Fractions
• You can use a number line to compare fractions.
• Comparing fractions means INEQUALITIES .
4/9 and 2/9 -4/9 and -2/9 -4/9 and 2/9
• Least Common Denominator
• Fractions can have different denominators.
• 1) Rewrite the fractions with a common denominator.
• 2) Compare the numerators.
• 3) The Least Common Denominator (LCD) of two ore more fractions is the Least Common Multiple of the denominators.
• Quick Reminder on Finding Common Denominators.
• Multiply the fraction by 1 (or a fractional form of 1) to make an equivalent fractions with a usable denominator.
• A usable denominator would be the Least Common Denominator, which can be found through Prime Factorization.
• Word Problem Example
• The math team won 5/8 of its competitions and the debate team won 7/10 of its competitions. Which team won the greater fraction of competitions?
Step 1) Find the LCM of 8 and 10: 8 = 2 3 . 10 = 2 times 5. LCM = 2 3 • 5 = 2 • 2 • 2 • 5 = 8 • 5 = 40
• Word Problem Example
• The math team won 5/8 of its competitions and the debate team won 7/10 of its competitions. Which team won the greater fraction of competitions?
Step 2) Write equivalent fractions with a denominator of 40.
• Word Problem Example
• The math team won 5/8 of its competitions and the debate team won 7/10 of its competitions. Which team won the greater fraction of competitions?
Step 3) Compare the fractions. The debate team won the greater fraction of competitions.
• Ordering Fractions = Inequalities
• Do the previous three steps for ordering fractions.
• 1) Find the LCM of the denominators.
• 2) Write equivalent fractions with the LCM of the denominators.
• 3) Compare the fractions with inequalities.
• Chapter 5, Section 2: Fractions and Decimals.
• Remember Long Decimal Division?
• Convert Fractions to Decimals by Dividing the Numerator into the Denominator .
When there is no remainder to a division problem, then the quotient is called a TERMINATING DECIMAL . 5/8 = ? There may be several decimal places before you get to a remainder of zero.
• Write each fraction or mixed number as a decimal.
• ¼
• 1 7/8
• 3 3/10
• 3/5
• Repeating Decimal
• Repeating Decimal : When the same block of digits are repeated without end in the quotient.
Examples: 2/3 and 15/11, try them…
• Comparing/Ordering Fractions
• When Comparing or Ordering Fractions, it might help to convert the Fractions to Decimals.
Order from least to Greatest: 0.2, 4/5, 7/10, 0.5
• Writing Decimals as Fractions
• Reading a decimal correctly provides a way to write a fraction.
0.43 is read as “ forty-three hundredths ”, which is the same as 43/100 . Write 1.12 as a mixed number in simplest form: Write 2.32 as a mixed number in simplest form:
• Algebra and Repeating Decimals as Fractions.
• Write 0. 7272 (repeating) as a fraction in simplest form.
N = 0. 72 Let the variable n equal the decimal . 100N = 72. 72 Because 2 digits repeat, multiply each side by 10 2 , or 100. 100N = 72. 72 - N - 0.72 The subtraction property of Equality allows you to subtract an equal quantity from each side of the equation. So, subtract to eliminate 0. 72 .
• Algebra and Repeating Decimals as Fractions.
• Write 0. 7272 (repeating) as a fraction in simplest form.
100N = 72. 72 - N - 0.72 99N = 72 Divide each side by 99. 99 99 N = 72/99 Divide the numerator and denominator by the GCF, 9. N = 8/9 Simplified.