Unit 1: FRACTIONS

Parts-and-Whole

For each of the following, be accurate by measuring with a ruler

If this rectangle is one whole, find one-fourth

If this rectangle is one whole, find two-thirds

If this rectangle is one whole, find five-thirds

If this rectangle is one whole, find three-eighths

If this rectangle is one whole, find three-halves

If this rectangle is one-third, what could the whole look like?

If this square is three-fourths, what could the whole look like?

What fraction of the big square does the small square represent? (In other words, how many times can the small square fit into the larger one?)

Whole

What fraction is the large rectangle if the smaller one is the whole?

Whole

If the rectangle for each below is one whole,

a) find one-sixth b) find two-fifths

c) find seven-thirds

If the following rectangle represents two-third, what could the whole look like?

If the following rectangle is one-sixths, what does the whole look like?

If the following rectangle is four-thirds, what does the whole look like?

If the following triangle represents one-half, what does the whole look like?

Compare the following fractions. Which fraction in each pair is GREATER?

Use size of the parts, closer to 0, 1/2, 1, and drawings or models.

DO NOT USE MULTIPLICATION OR COMMON DENOMINATORS

and

and

and

and

and

and

and

and

and

and

and

and

and

Improper and Mixed Numbers

Improper Fractions: , , , more than a whole (the numerator is larger than the denominator) can always be written as mixed number ( a whole number and a fraction)

Method Make wholes

What makes a whole with this fraction?

How many can be made out of ?

= 1 whole = 1 whole = 1 whole ( total so far) and is left.

So, = 3

Method Divide the numerator by the denominator

3

= 7 22 = 3

- 21 1

Note: A fraction line is a division line.

Remainder 1 becomes the numerator

The denominator does not change

Practice: Choose a method to write each improper fraction as a mixed number.

=

Making a mixed number from an improper fraction:

Method

3 The 3 means there are 3 wholes: , , then there’s =

Method

6 3 Denominator (bottom) x whole number + Numerator (top), over the same denominator 4

4 x 6 + 3 =

4

do not change the denominator

Practice: Choose a method to write each mixed number as an improper fraction.

3 7 4

1 2 6

Equivalent Fractions

Fractions that mean the same amount of the whole

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24

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12

REMEMBER: the wholes we are comparing are the same size

Practice

2 shaded out of 4 boxes is the same as 1 shaded out of 2 boxes if the wholes are the SAME SIZE

x 2

x 2

÷ 7 ÷ 7

Write two (2) equivalent fractions for the following situations.

Writing Equivalent Fractions

To write equivalent fractions, multiply or divide the numerator and denominator by the same factor:

Examples: = =

How to tell if fractions are equivalent:

Is the numerator and denominator multiplied or divided by the same factor?

Cross-multiply; if the products (answers) are the same, the fractions are equivalent.

Example: and

Practice: Which of the following situations show equivalent fractions? Show how you know (multiply or divide by the same factor, or cross multiply).

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/// ////// ///

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REMEMBER the “Golden Rule”: “What you do to the top, you do to the bottom”

8 x 6 = 48 these are EQUIVALENT fractions12 x 4 = 48

A. Stephanie ate of Kit Kat bar; Sam ate of his Kit Kat bar.

B. Kathy drove km, Ken walked km and Kim ran km.

C. of Tim’s money was loonies and of Jim’s were loonies.

D. Jack got on his test. Jake got .

E. There are boys in Ms. Mckinnon’s class. There are girls in Ms. Macleod`s class.

F. Scott shot baskets, Paul shot and Steve shot .

G. Sue ate of her pizza. Steve ate of his pizza.

H. Stan read pages of his book; Jan read pages and Frank read pages.

I. Ann made serves during the volleyball game; Nathalie made serves.

J. Dan ate pieces of skittles; Harry ate pieces.

K. Nancy read pages of her book and Beth read pages.

L. Roxanne drank ml of her juice. Rick drank ml.

Simplifying Fractions: writing equivalent fractions in lowest terms.

Example: can be simplified to by dividing both the denominator and numerator by the same factor, 2.

x 4

x 4

x 9

x 9

7 x

7 x

Practice: Express in the simplest form.

= = = = =

Adding and Subtracting Fractions

The denominators have to be the same before we add or subtract the numerators

We add or subtract the numerators only

DO NOT ADD OR SUBTRACT THE DENOMINATORS!

If the denominators are not the same, we must find a common denominator.

Rewrite the fractions with the common denominator.

Simplify if possible and rewrite as a mixed number if needed.

Example : + = = 1 Example : - = - = - = =

Example : + = + = + = = 1

Practice: Find the sum.

+ = + = + =

+ = + = + =

+ = + = + =

Practice: Find the difference.

- = - = - =

- = - = - =

- = - = - =

Practice: Add or subtract.

- = + = - =

+ = - = + =

x 3

x 3

4 x

4 x

3 4

+ + = + + =

- + = + - =

Adding Mixed Numbers

Method Add the whole numbers Add the fractions; DO NOT FORGET TO HAVE A COMMON DENOMINATOR Add the whole number to the fraction Simplify to the lowest terms if possible

Example: 4 + 2 = Step 4 + 2 = 6

Step + = + = + = = 1

Step 6 + 1 = 7

Method Write the mixed numbers improper fractions Add the fractions; DO NOT FORGET TO HAVE A COMMON DENOMINATOR Simplify if possible and rewrite as a mixed number if needed

Example: 4 + 2 = 3 x 4 + 1 + 4 x 2 + 3 = + = + = = 7

Practice: Choose a method to find the sum.

3 + 1 = 4 + 6 =

x 6

x 6

x 5

x 5

3 4

2 + 2 = 1 + 2 + 3 =

Subtracting Mixed Numbers

Method Borrowing Subtract the fractions first; DO NOT FORGET TO HAVE A COMMON DENOMINATOR If the subtraction cannot be performed, borrow 1 from the first whole number Make a whole in fractional form using the common denominator Subtract the whole numbers Subtract the fractions; simplify if possible Add the whole number(s) and the fraction

Example: 7 - 2 = Step 7 - 2 = 7 - 2

Step 6 + - 2 = 6 - 2 =

Step 6 – 2 = 4

Step - = = 4

Method Write the mixed numbers as improper fractions Subtract the fractions; DO NOT FORGET TO HAVE A COMMON DENOMINATOR Simplify if possible and rewrite as a mixed number if needed

Example: 4 - 2 = 3 x 4 + 1 - 4 x 2 + 3 = - = - = = 1

Cannot take 25 from 24

6 is the same as 7 wholes

Practice: Choose a method and find the difference.

3 - 1 = 6 - 4 =

2 - 2 = 8 - 2 =

Solve the following problems.

Beth ate of cheese pizza and Scott ate of the same pizza. How much

pizza was eaten? How much was left?

Harvey gas tank showed full at the beginning of the week. On Friday, the

gas gauge read full. How much gas did he use in a week?

Anne worked 2 hours on Monday, 3 hours on Wednesday and 4 on

Friday. How many hours did she work in total?

The Nadeau family drove from Ottawa to Cambridge to see relatives. They

drove for 3 hours, stopped for hour for lunch and continued to Cambridge

for another 2 hours.

a) How long were they driving?

b) How long did the total trip take?

Anne bought 7 meters of rope for a school project. She used 5 of it. How

much rope was not used?

Beth planted 2 rows of beans, 3 rows of peppers and 4 rows carrots.

a) How many rows of vegetables did she plant?

b) How much more carrots than peppers did she plant?

STOP and Review…

Fill in the blank

613

___________is on top and it tells us _________________________________________________________

________________is on bottom and it tells us _________________________________________________

Fill in the blanks

# parts Fraction Word2 Half

Quarters

Place the following fractions on the number line below: 2 , , , 1

0 1 2

Place the following fractions in the proper column in the table below.

3 3

Proper fractions Improper Fractions Mixed Number

Write a single fraction for 3 . How do you know you are right?

Rewrite as a mixed number or as an improper fraction as necessary.

9 6

3 4 3

Which is greater? Briefly explain why.

4 or 35 4

11 or 1010 11

7 or 38 8

22 or 450 8

2 or 23 5

13 or 725 16

Place in order from least to greatest.

5, 6, 7¸ 3, 11 8 11 8 2 22

Multiplying Fractions (Do not need common denominators)

Multiply the numerators together (the two top numbers) Multiply the denominators together (the two bottom numbers) Simplify if possible and rewrite as a mixed number if needed

Example: x = =

Whole number multiplied by a fraction

The whole number can be written as a fraction with a denominator of 1 Follow the multiplication rule

Example: 9 x = x = = 6

‘of’ means multiply

Mixed Number multiplied by a Mixed Number

Write the mixed numbers as improper fractions Follow the multiplication rule Simplify if possible and rewrite as a mixed number if needed

Example: 2 x 1 = x = = 3 = 3

Practice: Find the product.

x = 11 x =

x =

of 8 = x = of =

x = of = x =

Practice: Solve.

x x = 2 x 1 =

of 2 = 3 x 4 =

1 x 1 = 5 of 4 =

During the summer Scott work 4 hours for 8 weeks. How many hours did he

work in total?

What is of 60?

Harvey takes 1 weeks to paint a house. How many weeks will it take to paint

15 houses on the block?

How many minutes are there in 5 hours?

Dividing Fractions (Do not need common denominators)

Keep the first fraction the same Change the division to multiplication Write the reciprocal of the second fraction (switch the numerator and the denominator of

around) Follow the multiplication rule (multiply the numerators together and the denominators

together) Simplify if possible and rewrite as a mixed number if needed

Mixed Numbers: write the mixed numbers as improper fractions, then follow the above steps

Example: = x = = 1 = 1

Example: 2 2 = = x = = 1

Practice: Find the quotient.

= =

= 3 =

6 = 2 =

3 1 = 4 3 =

Practice: Solve.

2 = 4 4 =

1 4 2 =

Sally is getting ready to cut a 20 meter ribbon into smaller pieces of meters

each. How many meter pieces of ribbon will she have?

Do the exponent first

Do the division next

Scott and Vitto are have of a pizza to share. How much will each boy get?

How many boards 1 meters long can be cut from a board that is 11 meters long?

You are going to a birthday party and bring 10 litres of ice-cream. You

estimate that each guest will eat 1 cup (there are 4 cups in one litre).

How many guests can be served ice-cream?

1 ÷ 1 ÷ 3 =

Order of Operations with Fractions using BEDMAS

B = bracketsE = exponentsD = divisionM = multiplicationA = additionS = subtraction

2

Example: ÷ 2 + -

÷ 2 + x -

A S

D M

E

B

Whatever comes first from left to right

Whatever comes first from left to right

START

Get a common denominator forthe addition

Get a common denominator forthe subtraction

÷ 2 + - x =

+ - + =

- = - = =

Practice: Solve following the order of operations

- + = + x =

2

x + = ÷ + x =

+ x + 1 =

Simplified answer: dividing the numerator and denominator by the factor 2

÷ + ÷ 1 =

5 - 3 + 3 =

÷ x 1 - =

Extra Practice

A. + G. -

B. + H. +

C. - I. + -

D. - J. -

E. + K. +

F. + L. -

M. During four days the Gatineau River went up of a metre, down of a metre, down of a metre and finally up of a metre. What was the net change? Don’t forget to state up (+) or down (-) in your answer.