w1 - lesson 3: fractions and mixed numbers 7 - week 1...3. 4 6, 6 9, and 8 12 are all equivalent...

$: W1 - Lesson 3: Fractions and Mixed Numbers 7 - Week 1...3. 4 6, 6 9, and 8 12 are all equivalent fractions of 2 3. Multiplying or dividing the numerator and denominator by the same$
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Mathematics Grade7W1-Lesson3: FractionsandMixed

Numbers

ImportantConceptsofGrade7Mathematics

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Mathematics Grade 7Version 6Preview/Review W1 - Lesson 3ISBN 1-894894-75-8

Publisher: Alberta Distance Learning CentreWritten by: Sandy Reviewed by: Barb Philips

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W1 - Lesson 1 ........................................................................Divisibility RulesW1 - Lesson 2 ...................................................................... Decimal NumbersW1 - Lesson 3 .....................................................................................FractionsW1 - Lesson 4 ................ Improper Fractions, Mixed Numbers,Percents, andDecimalsW1 - Lesson 5 .................................Integers, Number Lines, and SequencingW1 - Quiz

W2 - Lesson 1 ..................... Table of Values and Graphing Linear EquationsW2 - Lesson 2 ...............................Modeling Expressions, Equations, and thePreservation of EqualityW2 - Lesson 3 ..................................................Algebra and Linear EquationsW2 - Lesson 4 .....................................................................................StatisticsW2 - Lesson 5 .............................. Circle Graphs and Calculating ProbabilityW2 - Quiz

W3 - Lesson 1 .........................................................................................CirclesW3 - Lesson 2 ...................................... Area of Triangles and ParallelogramsW3 - Lesson 3 ............................................................................Line Segments W3 - Lesson 4 ..................................Parts and Plotting on a Cartesian PlaneW3 - Lesson 5 .........................................................................TransformationsW3 - Quiz

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ImportantConceptsofGrade7Mathematics

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Preview/Review Conceptsfor

Grade Seven Mathematics

W1 – Lesson 3:

Fractions and Mixed Numbers

Developed by Alberta Distance Learning Centre ....................................................................................................... 1

Preview/Review Concepts W1 - Lesson 3 MathematicsGrade7

W1 – Lesson 3: Fractions

Warm-up:

• Icanusepatternblockstomodelfractions.

Fraction Tiles

How many?

1. are in ? _______ 2. are in ? _______

3. are in ? _______ 4. are in ? _______

5. are in ? _______

Based on the relationships above,

1. If = 1. = _______

2. If = 1. = _______

3. If = 1. = _______

4. If = 1. = _______

Preview/Review Concepts W1 - Lesson 3MathematicsGrade7

....................................................................................................... Developed by Alberta Distance Learning Centre2

Now, try some really fun shapes.

1. If + = 1, what is ? _______

2. If + = 1, what is + ? _______

3. If + = 1, what is + ? _______

4. If + = 1, what is ? _______

5. If - = 1, what is + ? _______



Review:

• Iunderstandfractionbasics.

Practice

Example 1: What fraction of the pie has been removed?

One of eight pieces has been removed; therefore, 18

has been removed.

Example 2: What fraction of the eggs is left in the carton?

Ten of twelve eggs are still in the carton; therefore 1012

or 56

is left in the carton.

3 numerator or dividend vinculum 7 denominator or divisor

properfraction: a fraction in which the numerator is lessthan the denominator Example: 2

3

mixednumber: the sum of a whole number and a proper fraction

Example: 647

improperfraction: a fraction in which the numerator is greaterthan the denominator Example: 7

2

vinculum: the line between the numerator and the denominator, showing that the two numbers are connected



Equivalent Fractions

Example: Write three equivalent fractions for 23

.

46

, 69

, and 812

are all equivalent fractions of 23

.

Multiplying or dividing the numerator and denominator by the same number can generate an unlimited number of equivalent fractions.

Practice

Fill in the blanks to complete the equivalent fractions.

a. 23 15= b.

17 21=

c. 4 18= d. 5 10

12=

e. 7

11 33= f.

618 9

=

g. 8

20 5= h.

33 199

=

i. 2 4

10= j. 3 21

28=

Fractions that represent the same amount are called equivalent fractions.

2 4 2 6 2 8 3 6 3 9 3 12

X 2

X 2

X 3

X 3

X 4

X 4



Reducing Fractions to Simplest Form

Example: Write the fractions in lowest terms.

a. 9 and 12 are both divisible by 3.

The simplest form of 912

is 34

.

b. 712

Because 7 and 12 do not have any numbers by which they are both divisible, the fraction is already in its simplest form.

Practice

Express each fraction in lowest terms.

a. 2 4= b. 4

12=

c. 6 9= d. 5

15=

e. 7 21

= f. 10 18

=

g. 8 24

= h. 50 100

=

i. 312

= j. 5 25

=

A fraction in simplest form is the fraction that cannot be divided to �nd an equivalent fraction.

9 312 4

3÷

3÷

A fraction in simplestform is also known as a reducedfraction or a fraction expressed in lowestterms.

Answers should always be given in lowestterms.



Objective:

• Icanaddandsubtractfractionswiththesamedenominators..

Practice

Solve. Express your answers in lowest terms..

a. + =1 13 3

b. + =1 57 7

c. + =2 49 9

d. 5 3

10 10+ =

e. 1 36 6+ = f. 11 5

20 20+ = g. 3 2

8 8+ = h. 10 8

12 12− =

i. 17 821 21

− = j. 13 315 15

− = k. 9 510 10

− = l. 7 29 9− =

Subtracting fractions with the same denominator.

Keep the denominator the same; subtract the numerators.

Example: 7 312 12

−

7 3 47 3 4 Therefore, 12 12 12

− −

Adding fractions with the same denominator

Keep the denominator the same; add the numerators.

Example: 1 24 4

1 2 31 2 3 Therefore, 4 4 4



Objective:

• Icanaddandsubtractfractionswiththedifferentdenominators..

Practice

Solve. Express your answers in lowest terms..

a. 2 13 7+ = b.

1 36 4+ =

c. 1 42 9+ = d.

6 310 8

+ =

e. 5 5

20 8+ = f.

3 221 3

+ =

g. 10 112 4

− = h. 17 521 7

− =

i. 9 3

10 20− = j.

7 19 3− =

2 8 10 40

7 35 8 40

Example 1: You need a common denominator. 8 and 10 are both factors of 40.

Change:

Change: Subtract:

7 28 10−

35 8 2740 40 40

−

1 3 4 12

Example 2: Common denominator: 12

Change:

Add: OrCommon denominator: 4

Change:

Add:

1 34 12

3 3 6 112 12 12 2

1 1 2 14 4 4 2

3 1 12 4



Objective:

• Icanmodeltheadditionandsubtractionoffractions.

Grid Model

Note: Use the columns and rows of a grid to represent different denominators.

Example 1: 1 13 4+ =

Example 2: 3 15 3− =

Practice

Draw the grid that represents best the solution. For this activity you do not need to simplify the fraction.

a. + =1 13 3

b. + =1 57 7

c. + =2 49 9

Total squares = 12Number of shaded squares = 7

Answer = 7

12

Total squares = 14Number of shaded squares left = 4

Answer = 4

15

1 of 3 rows = 14

colour in 4 squares 1 of 4 columns = 13

colour in 3 squares

3 of 5 rows = 35

colour in 9 squares1 of 3 columns = 1

3erase 5 squares



d. 1 24 3+ = e. 1 3

5 4+ = f. 1 3

3 10+ =

g. 3 14 3− = h. 4 2

5 3− = i. 6 2

7 6− =

j. 8 49 6− = k. 7 1

8 2− = l. 2 1

3 4− =



Summary and Practice:

• Usingwhatyoulearnedanswerthefollowingquestions.

1. On the chart below, summarize the steps needed to add or subtract fractions with the same denominator and fractions with different denominators.

Same Denominators Different Denominators

Steps to add fractions

Steps to subtract fractions

2. Express the fractions in lowest terms.

a. 618

b. 954

c. 1648

d. 1421

3. Using the grid below, write an addition equation represented by the grid.



4. Model using a grid.

a. 3 16 3+ b. 9 3

10 4−

5. 13

of entries in a pet show are cats. 12

of the entries are dogs.

What fraction of the animals is not a cat or a dog?

6. George spent 28

of his spare time playing video games, 26

practising basketball, 14

practising guitar, and the remainder watching TV. What fraction represents the time he spent watching TV?

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w1 - lesson 3: fractions and mixed numbers 7 - week 1...3. 4 6, 6 9, and 8 12 are all equivalent...

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