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Multiples

A multiple of a number is the

PRODUCT of thatnumber and any nonzero

number.

12 is a multiple of 4

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Multiples of 5:

1 x 5 = 52 x 5 = 10

3 x 5 = 15

etceteraMultiples of 10:

1 x 10 = 10

2 x 10 = 203 x 10 = 30

etcetera

5, 10, 15, 20, 25, 30, etc.

10, 20, 30, 40, 50, 60, etc.

What is the LEASTCOMMON MULTIPLE

of 5 and 10?

What are the COMMON

MULTIPLES of 5 and 10?

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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 of5 and 6 willtell you on which days, from TODAY, that the two

teams play on the SAME day.

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Find the COMMON MULTIPLES of 5 and 6.

Word Problem

Multiples of 5: 5, 10, 25, 30, 35, 40etc.

Multiples of 6: 6, 12, 18, 24, 30etc.

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!

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Find the Least Common

Multiple: LCM 3, 4:

4, 5:

3, 4, 5:

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LCM with Prime Factorization

Find the LCM ofNasty 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

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9, 15:

12, 15, 18:

Find the Least Common

Multiple: LCM

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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

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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

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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.

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Quick Reminder on Finding

Common Denominators.

Multiply the fraction by 1 (or a fractionalform of 1) to make an equivalent fractionswith a usable denominator.

A usable denominator would be the LeastCommon Denominator, which can be foundthrough Prime Factorization.

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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.

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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

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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.

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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.

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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.

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Write each fraction or mixed

number as a decimal.

1 7/8

3 3/10

3/5

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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

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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

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Writing Decimals as Fractions

Reading a decimal correctly provides a way towrite a fraction.

0.43is 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:

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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, multiplyeach side by 102, or 100.

100N = 72.72

- N - 0.72 The subtraction property ofEquality allows you to subtract an equal quantity

from each side of the equation. So, subtract to

eliminate 0.72.

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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 denominatorby the GCF, 9.

N = 8/9 Simplified.

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Assignment #33

Page 227: 15-43 odd. (15 problems).

Page 232: 27-49 odd. (12 problems).

25 Problems total.