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**Decimals and Fractions**

Unit 4.4 Pages

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**Find the greatest common factor for these sets**

Warm Up Problems 15, 24 = 30, 60 = 12,16,24 = Find the greatest common factor for these sets 3 30 4

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**Decimals and Fractions**

Objective: Students will be able to convert numbers in decimals, into fractions, and then back again. These may include mixed numbers, and placing them on a number line.

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Definitions: Mixed Number: A number that can claim both whole numbers bigger than 0, and a part of a whole. Repeating Decimal: is a number that never ends because a zero is brought down from the dividend.

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**Decimals can be written as Fractions or as Mixed Numbers**

Decimals can be written as Fractions or as Mixed Numbers. We can also plot these numbers on a number line to help show us how large or small they are. .23 1.7 1 2 3 .23 100 7 10 1 The 3 is in the hundredths place so we use the 100 as the denominator. The 7 is in the tenths place so we use 10 as the denominator.

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**#1) Write the decimal below as a fraction or mixed number**

#1) Write the decimal below as a fraction or mixed number. Then plot it on the number line below. 0.15 1 2 3 .15 100 The 5 is in the hundredths place so we use the 100 as the denominator.

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**#2) Write the decimal below as a fraction or mixed number**

#2) Write the decimal below as a fraction or mixed number. Then plot it on the number line below. 1.25 1 2 3 25 100 The 5 is in the hundredths place so we use the 100 as the denominator. 1

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**#3) Write the decimal below as a fraction or mixed number**

#3) Write the decimal below as a fraction or mixed number. Then plot it on the number line below. 0.43 1 2 3 The 3 is in the hundredths place so we use the 100 as the denominator. 43 100

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**2.6 2 6 1 2 3 10 #4) Write the decimal below as a fraction.**

Then plot it on the number line below. 2.6 1 2 3 6 10 The 6 is in the tenths place so we use 10 as the denominator. 2

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**Fractions can be converted (or changed) into Decimals**

Fractions can be converted (or changed) into Decimals. We use the fraction bar to divide until it factors out, or if it continues to repeat. .75 = ___% 4 3.00 -28 20 3/4 Divided By 1 2 3 .75 The 5 is in the hundreths place so we use 100 as the denominator.

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**#5) Write the following fraction or mixed number as a decimal.**

2/5 .40 =___% 5 2.00 -2 0 Divided By 1 2 3 .40 The 4 is in the tenths Place so we use 10 as the denominator.

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**#7) Write the following fraction or mixed number as a decimal.**

.122 =___% 8 1.00 - 8 20 -18 1/8 Divided By 1 2 3 .12 The 2 is in the hundreths Place so we use 100 as the denominator.

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**Write the following fraction or mixed number as a decimal.**

.666 3 2.00 -1 8 20 When a number keeps repeating we place a bar over it. 2 2 2/3 Divided By 1 2 3 The 2 is on the Left of the decimal so place that 2 as a whole number on the left in the answer. 2.66

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**#6) Write the following fraction or mixed number as a decimal.**

.875 =___% -6 4 6 0 -5 6 4 0 2 7/8 Divided By 1 2 3 The 2 is on the Left of the decimal so place that 2 as a whole number on the left in the answer. 2.66

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Now that we know how to make every fraction a decimal, and every decimal a fraction we can look at fractions and try to estimate how big or small they are.

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**Close to 1 Close to 0 Close to ½ Let’s practice estimating decimals:**

Use the worksheet below to practice. Close to 0 Close to ½ Close to 1

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Homework (4.4) page 177 Due: Friday 12-27

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**Convert these fractions into decimals to the nearest hundredth.**

Warm Up Problems 4/25= 3/20= 2/5 = Convert these fractions into decimals to the nearest hundredth. .16 .15 .40

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**Introduce how to order simple fractions using**

Fraction cards (J sets 1-5) register tape 4.4 grading warm up.

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**If I give you a piece of register tape**

If I give you a piece of register tape. How would we plot all our fractions to see which ones are larger, and which ones are smaller? Where would the 0, ½ and 1 be placed? How can we show that these are equal? Would we want to show any other points besides the 1, ½ and 1?

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**Now that we know how to convert decimals we can place them for least to greatest on a number line.**

% % 0.50, 0.37, 1/5 .20 = ____% 5 1.00 -1 0 00 1/5 .20 0.50 1 2 3 0.37

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**#9) Order the fractions and decimals from least to greatest.**

% % 2/3, .78, .21 . =___% 2 3. 2/3 .66 1 2 3 0.21 0.78

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**#10) Order the fractions and decimals from least to greatest.**

5/16, 0.67, 1/6 . 16 5. . 6 1.0 1 2 3 1/6 5/16 0.67

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**#11) Order the fractions and decimals from least to greatest.**

0.52, 1/9, 0.3 . 9 1. 1 2 3 1/9 0.3 0.52

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Homework (4.4) page 177 Due: Monday (15 questions)

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0.24 2 3/5 Write each decimal as a fraction. Write as a decimal. 6/25 2.6 Order from Least to Greatest Order from Least to Greatest 2/3, 5/12, 4/9, 1/ .49 , ½, .82 5/12, 4/9, 2/3

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