confidential 1 today we will review “fractions”. confidential 2 let’s warm up:. 1) 0.32 + 4...

CONFIDENTIALCONFIDENTIAL 11

Today we will review Today we will review “Fractions” “Fractions”

CONFIDENTIALCONFIDENTIAL 22

Let’s Warm up:.

1) 0.32 + 4 -3.23 =1.09 2) 3.6 ÷ 2 x 5 =9

3) 2.25- 0.45 x 5 =0 4) 2.89+ 63.99 ÷ 9 =10

33 CONFIDENTIALCONFIDENTIAL

Representing FractionsRepresenting Fractions

Fraction: A number that names part of a whole or part of Fraction: A number that names part of a whole or part of a group.a group.

¼ means 1 part of 4 parts, where 4 parts is the whole or group.¼ means 1 part of 4 parts, where 4 parts is the whole or group.

Denominator: The number below the bar in a fraction.Denominator: The number below the bar in a fraction. Fraction: Fraction: 44

5 5 denominator denominator

Numerator: The number above the bar in a fraction.Numerator: The number above the bar in a fraction. Fraction: Fraction: 4 4 numerator numerator

55


Representing FractionsRepresenting Fractions

4 parts shaded4 parts shaded

7 parts in all7 parts in all

4/7 shaded4/7 shaded

Parts shaded -> Parts shaded -> 44 -> numerator -> numerator

parts in all -> 7 -> denominatorparts in all -> 7 -> denominator

2 parts shaded2 parts shaded

5 parts in all5 parts in all

2/5 shaded2/5 shaded

Parts shaded -> Parts shaded -> 22 -> numerator -> numerator

parts in all -> 5 -> denominatorparts in all -> 5 -> denominator


Your Turn!Your Turn!

Complete to write a fraction for the part that is shaded.Complete to write a fraction for the part that is shaded.

3/4

4/5


Equivalent Fractions & Simplest FormEquivalent Fractions & Simplest Form

Equivalent Fractions: Two or more fractions that name the same Equivalent Fractions: Two or more fractions that name the same number.number.

33 = = 66 Equivalent Fractions Equivalent Fractions4 84 8

Use Fraction ModelsUse Fraction Models

Equivalent Fractions for Equivalent Fractions for

Fraction Fraction piece piece usedused

Number of Number of piecespieces

Equivalent Equivalent FractionFraction

44

33

22

12

1

4

1

4

1

4

2

6

1

6

1

6

1

6

3

8

1

8

1

8

1

8

1

8

4

12

1

12

1

12

1

12

1

12

1

12

6

12

6

8

1

6

1

4

1

8

4

6

3

4

1



To find equivalent fractions multiply the numerator and denominator To find equivalent fractions multiply the numerator and denominator by 1by 1

12

6

2

2

6

312

6

3

3

4

212

6

6

6

2

1

,5

5,

4

4,

3

3,

2

2,

1

11

onsoand



Find simplest form (of 4/12)Find simplest form (of 4/12)

Step 1: Find the common factorsStep 1: Find the common factors Factors of 4: 1, 2, 4Factors of 4: 1, 2, 4 Factors of 12: 1, 2, 3, 4, 6, 12Factors of 12: 1, 2, 3, 4, 6, 12 Common factors: 2 and 4Common factors: 2 and 4

Step 2: Divide the numerator and the denominator by the greatest Step 2: Divide the numerator and the denominator by the greatest common factorcommon factor

The simplest form of 4/12 is 1/3The simplest form of 4/12 is 1/3

3

1

412

44

Divide by 4/4 to simplify. 4/4 =1, so the value of

the fraction doesn’t change.



Write each fraction in the simplest form.Write each fraction in the simplest form. 7/21 = 1/37/21 = 1/3 2/10 = 1/52/10 = 1/5


Comparing FractionsComparing Fractions

Use ModelsUse Models

4

1

8

1

4

1

8

5

4

1

4

3

4

1

8

1

8

1

8

1

8

1

8

5

4

3



Use a Number LineUse a Number Line

08

1

8

3

2

1

8

5

4

3

8

71

8

5

4

3



Use Paper and PencilUse Paper and Pencil You can write equivalent fractions with the same denominatorYou can write equivalent fractions with the same denominator Since 4 multiplied by 2 is 8, you can multiply by 1 in the form of 2/2Since 4 multiplied by 2 is 8, you can multiply by 1 in the form of 2/2

8

5

4

3 then ,

8

5

8

6 Since

8

6

24

23


Ordering FractionsOrdering Fractions

Step 1: Write each fraction as an equivalent fraction with the same Step 1: Write each fraction as an equivalent fraction with the same denominatordenominator

Step 2: Compare the numerators. Put the fractions in order from least to Step 2: Compare the numerators. Put the fractions in order from least to greatest.greatest.

Example: Order ½, ¼, and 3/8 from least to greatestExample: Order ½, ¼, and 3/8 from least to greatest Step1: Write equivalent fractions with the same denominator. Change them all Step1: Write equivalent fractions with the same denominator. Change them all

to eights.to eights.

Compare the numerators. 4 is the greatest and 2 is the leastCompare the numerators. 4 is the greatest and 2 is the least Order from least to greatest is ¼, 3/8, 1/2Order from least to greatest is ¼, 3/8, 1/2

8

38

2

24

21

4

18

4

42

41

2

1



Write >, <, or =. ¼ __ ¾ <Write >, <, or =. ¼ __ ¾ <

Order from least to greatest. ¼, 1/8, ½.Order from least to greatest. ¼, 1/8, ½. ¼ = 2/8, 1/8, ½ = 4/8¼ = 2/8, 1/8, ½ = 4/8 1/8, ¼, ½1/8, ¼, ½


Mixed NumbersMixed Numbers

Mixed Number: A number named by a whole number and a Mixed Number: A number named by a whole number and a fraction.fraction.

A mixed number is greater than 1A mixed number is greater than 1

2

12

4

31


Improper FractionsImproper Fractions

Improper Fraction: A fraction with a numerator that is Improper Fraction: A fraction with a numerator that is greater than or equal to the denominator.greater than or equal to the denominator.

Rename a mixed number Rename a mixed number Example: Write 1 ¼ as an improper fractionExample: Write 1 ¼ as an improper fraction Step 1: Rename the whole number as a fraction.Step 1: Rename the whole number as a fraction. 1 = 4/41 = 4/4

Step 2: Add the fractions.Step 2: Add the fractions. 4/4 + ¼ = 5/44/4 + ¼ = 5/4

A whole number is a number without a fraction.


Improper FractionsImproper Fractions

Rename a Fraction Rename a Fraction Example: Write 7/4 as an improper fractionExample: Write 7/4 as an improper fraction Step 1: Rename the whole number as a fraction.Step 1: Rename the whole number as a fraction. 4/4 = 1 whole4/4 = 1 whole

7/4 - 4/4 = ¾7/4 - 4/4 = ¾

1 ¾1 ¾



Rename each as a mixed number, improper fraction, or Rename each as a mixed number, improper fraction, or fraction in simplest form.fraction in simplest form.

8/7 = 1 1/78/7 = 1 1/7 1 1/3 = 4/31 1/3 = 4/3


Fractions, decimals, percentsFractions, decimals, percents

Percent means per hundred; It Percent means per hundred; It is another way of naming part is another way of naming part of a whole.of a whole.

The grid shows that 25 out of The grid shows that 25 out of 100 squares are blue.100 squares are blue.

25% of the grid is blue25% of the grid is blue

As a fraction, 25 out of 100 = As a fraction, 25 out of 100 = 25/100 = ¼25/100 = ¼

As a decimal; 25 out of 100 = As a decimal; 25 out of 100 = 25 hundredths = 0.2525 hundredths = 0.25

25% = 25/100 = 0.2525% = 25/100 = 0.25


Add with like denominatorsAdd with like denominators

Step 1: Add the numeratorsStep 1: Add the numerators

Step 2: Use the common denominatorStep 2: Use the common denominator

Step 3: Write the sum in simplest formStep 3: Write the sum in simplest form Example: Find: 1/8 + 1/8 + 1/8Example: Find: 1/8 + 1/8 + 1/8

11/8 + /8 + 11/8 + /8 + 11/8 = 3/8/8 = 3/8

1/8 + 1/8 + 1/8 = 3/1/8 + 1/8 + 1/8 = 3/88

The Greatest Common Factor of 3 and 8 is 1, so 3/8 is already in The Greatest Common Factor of 3 and 8 is 1, so 3/8 is already in simplest formsimplest form



Add. Write each sum in simplest form.Add. Write each sum in simplest form.

1/10 + 1/10 = 2/10 = 1/51/10 + 1/10 = 2/10 = 1/5


Subtract with like denominatorsSubtract with like denominators

Step 1: Subtract the numeratorsStep 1: Subtract the numerators

Step 2: Use the common denominatorStep 2: Use the common denominator

Step 3: Write the difference in simplest formStep 3: Write the difference in simplest form Example: Find ¾ - ¼Example: Find ¾ - ¼ ¾ - ¼ = ¾ - ¼ = 22/4 /4 ¾ - ¼ = 2/¾ - ¼ = 2/44 2 ÷ 22 ÷ 2 = ½ = ½

4 ÷ 44 ÷ 4

Divide the numerator and the denominator by the Greatest

Common Factor



Subtract. Write the difference in simplest form.Subtract. Write the difference in simplest form. 7/10 – 5/10 = 2/10 = 1/57/10 – 5/10 = 2/10 = 1/5


Add with unlike denominatorsAdd with unlike denominators

Step 1: Find equivalent fractions with a common denominatorStep 1: Find equivalent fractions with a common denominator

Step 2: Add the numerators. Write the sum above the common Step 2: Add the numerators. Write the sum above the common denominatordenominator

Step 3: Write the sum in the simplest formStep 3: Write the sum in the simplest form

10

3

10

1

10

210

2

25

2110

1

5

1 Find



Add. Write in simplest form.Add. Write in simplest form. 7/8 + ¼ = 7/8 + 2/8 = 9/8 = 1 1/87/8 + ¼ = 7/8 + 2/8 = 9/8 = 1 1/8


Subtract with unlike denominatorsSubtract with unlike denominators

Step 1: Find equivalent fractions with a common denominatorStep 1: Find equivalent fractions with a common denominator

Step 2: Subtract the numerators. Write the sum above the Step 2: Subtract the numerators. Write the sum above the common denominatorcommon denominator

Step 3: Write the sum in the simplest formStep 3: Write the sum in the simplest form

2

1

3

3

6

36

3

6

1

6

46

4

23

226

1

3

2 Find



Subtract. Write the difference in simplest form.Subtract. Write the difference in simplest form. 7/8 – 3/8 = 4/8 = 1/27/8 – 3/8 = 4/8 = 1/2


Multiplication of proper fraction Multiplication of proper fraction & whole number& whole number

Step 1: Multiply the numerator with the whole numberStep 1: Multiply the numerator with the whole number

Step 2: Simplify the fractionStep 2: Simplify the fraction Find ½ x 4Find ½ x 4 1 x 4 = 41 x 4 = 4 4/44/4 11



Multiply 1/3 x 7 = 7/3 = 2 1/3Multiply 1/3 x 7 = 7/3 = 2 1/3


Let us take a break!Let us take a break!


GameGame

Click meClick me

Let us see how fast you are on this one!


AssessmentAssessment

1.1. Write a fraction for the part that is shaded.Write a fraction for the part that is shaded.1/41/4

2.2. Write the fraction 9/54 in the simplest form.Write the fraction 9/54 in the simplest form.1/61/6

3.3. Order from least to greatest 1/8, 2/4, 5/8Order from least to greatest 1/8, 2/4, 5/81/8, 2/4, 5/81/8, 2/4, 5/8

4.4. Rename as a improper fraction, or fraction in simplest form.Rename as a improper fraction, or fraction in simplest form. 2 2/3 = 8/32 2/3 = 8/3

5.5. Write equivalent decimal and percent for the fraction 30/100Write equivalent decimal and percent for the fraction 30/1000.30; 30%0.30; 30%


AssessmentAssessment

6.6. Add 1/7 + 3/7 = 4/7Add 1/7 + 3/7 = 4/7

7.7. Subtract 5/6 – 4/6 = 1/6Subtract 5/6 – 4/6 = 1/6

8.8. Add 1/6 + 1/3 = 3/6 = 1/2Add 1/6 + 1/3 = 3/6 = 1/2

9.9. Subtract 2/4 – 1/8= 3/8Subtract 2/4 – 1/8= 3/8

10.10. Multiply 3/5 x 4= 12/5 = 2 2/5Multiply 3/5 x 4= 12/5 = 2 2/5


Good Job!Good Job!

You have learned a lot today!!!You have learned a lot today!!!

confidential 1 today we will review “fractions”. confidential 2 let’s warm up:. 1) 0.32 + 4...

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