Chapter 5 Sections 1 And 2 Review

Chapter 5: Section 1Comparing 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 = 52 x 5 = 103 x 5 = 15etcetera

Multiples of 10:1 x 10 = 102 x 10 = 203 x 10 = 30etcetera

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 = 22 • 3 (2 • 2 • 3) = 12

Multiples of 40 = 23 • 5 (2 • 2 • 2 • 5) =40

Multiply: 23 • 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 6a2 and 18a3:

6a2: 2 • 3 • a2

18a3: 2 • 32 • a3

2 • 32 • a3 = 2 • 3 • 3 • a3 = 9 • 2 • a3 = 18a3

18a3 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 = 23.

10 = 2 times 5.

LCM = 23 • 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 = 0.72Let the variable n equal the decimal.

100N = 72.72 Because 2 digits repeat, multiply each side by 102, 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.