Mr. B's Weebly - Grade 8 Mathematicsmrbockstael.weebly.com/.../2437974/b-1b-2_extra_practice.pdfTarget B-1) Extra Practice 2 Lesson 3.2: Using Models to Multiply Fractions 1. Use the

Target B-1 Extra Practice 1

1 . What multiplication statement do the manipulatives represent? Assume that a

hexagon such as this one represents one whole.

° > \ A ^ \ A

" 'ZSX zXZ\ zXZ\

2. What multiplication statement does each diagram represent?

a) | | | | | ~ | | | | | | ~ j | | | | ~

b) I I I I I I I I I [ I

O l I I I I I I I I I I I I I I I I I I I I I

Copyright © McGraw-Hill Ryerson, 2008

3 . Determine the product using the number lines. Write the multiplication statement, including the product, on the blank line.

a ) 4 x |

<—|—i—i—|—i—i—|—i—i—|—• 0 1 2 3

b) 3 x I <—I—i—i—i—|—i—i—i—|—i—i—i—|—•

0 1 2 3

4. Determine each product.

a ) 5 x | = b ) 3 x | = C ) 6 x A =

5. Determine each product.

a ) | of 24 = b ) | of 12 = c ) ?n of 30 = ' 4 3 10

6. There are 28 students in a class. Three-quarters of the class takes the bus to school. How many students take the bus to school? Show your work.

7. A team won | of the 40 games that they played. How many games did they

win?


Extra Practice Answers

1 . a ) 4 x i

b) 3 x I

C) 5 x i

2. a) 3 x 2 5

b) 2 x | 6

3. a) 4 , and an appropriately marked number line

9

b) 4 , and an appropriately marked number line

4 . a ) |

b ) f

C ) 18 = 9 ' 10 5

5. a ) 6

b) 8 c) 21

6. 21

7. 25



1 . Complete the diagrams to determine each quotient.

a) J * 2 =

b)

c)

d)

T 3 =

-r 3 =

2. Fill in the blanks.

a) I f * is divided into two equal parts, how large is each part?

1 + 2 =

b) I f \ is divided into two equal parts, how large is each part? 6

i -5-2 =

c ) I f | is divided into three equal parts, how large is each part?

d) If | is divided into three equal parts, how large is each part?

4 + 3 =


)

3 . One-fourth of a cake is left. Conrad, Angela, and Francine want to share this portion equally. How much of the cake will they each get?

a) Write a division statement to answer this question. Determine the quotient.

b) Write a sentence answer.

4. Five-sixths of the grade 8 students in a school are taking band. These band students are divided into four equal groups. What fraction of the grade 8 students is in each of these groups?

a) Write a division statement to answer this question. Determine the quotient. Explain your reasoning.

b) Write a sentence answer.


1 . a) i , and correctly marked fraction strip

c) | , and correctly marked fraction strip

d) j | or \ , and correctly marked fraction strip

2- a) i b) -L c) i d) i ' 6 '12 ' 9 ' 4

3. a) 1 -s- 3 = -1-' 4 12

b) They would each get of the cake.

' 6 24

b) of the grade 8 students would be in each of the groups.


Target B-1 Extra Practice 3 BLM 6-1

1 . Fill in the blanks with the correct answer.

a) When paper folding to show | x | , fold the paper into ,

then into .

b) When drawing diagrams to show | x | / draw line segments to show

, then .

c ) The product of two proper fractions is than either of the fractions.

d) When estimating the product of two proper fractions, first decide if each

fraction is closer to , , or .

e) To multiply fractions, multiply the by the

and the by the .

2 . Determine each product using the rectangles below.

b) | x | =


3 . For each question, estimate and then calculate the product. Show your work. Express the final answer in lowest terms.

Est imate the Product Calculate the Product

• ) § * i

b ) | x |

4 . In Mr. Saari's grade 8 class, | of the students play hockey. Of these o

students, | are on a " rep" team. What fraction of students in Mr. Saari's

class is on a n r e p " team? Show your work.


1. a) halves, thirds, or thirds, halves b) quarters, thirds, or thirds, quarters c) less

d) 0, \ , 1 e) numerator, numerator, denominator, denominator

2. a) | , and a correctly marked rectangle

b) ^ , and a correctly marked rectangle

3. a) i x 1 = i ; i ' 2 2' 2

b) I x 1 = I ; A ' 2 2' 15

c ' 2 x 2 ~ 4 ' 32

4. | of Mr. Saari's is on a "rep" team.



1 . The diagram below models 2 | x 3 ? . Use the diagram to complete the

questions.

a) Fill in the blanks to find the partial areas. Label the area of each of the regions in the diagram as you calculate it below.

Partial Areas:

2 x 3 = 6 2 3 1

x ^ =

X =• =

+ b) Add the areas: 6 + + + _ c ) Estimate the product: x =

d) Write the mixed numbers as improper fractions and multiply:

2l = 3 ? = ' J 3

Express the answer in lowest terms.

2. Show the improper fractions as mixed numbers. Write the fraction in lowest terms. The first line is partially completed.

. 1 5 _ 4 , 4 , 4 , ' 4 4 4 4

b)

c )

d)

9 =

2 26 =

12 20 =

6


3. Complete the table.

Multiplication i j l p f Mixed ; i : ^Numbers \ •

Multiplrcation /; 'q£Ift|feoper

Friictfdhs

Product Expressed

a s Improper Fract ion;

Product Expressed as Mixed Number

Example 1§ x 2 J 5 x 9

3 X 4 45 12

3 ^ = 3 3

a) x 4 b) 2§ x 1§

c ) 1 ? X 1 ?

d) * i x 2 4 6 2

4. Jasmine worked 3~ h a day for five days. How many hours did Jasmine work

altogether? Show your work.



1 . a) 2 x ?_ = 4 . 3 x 1 = 3 ; 2 x l = 2 ' 3 3 ' 2 2' 3 2 6

b) 6 + l | + l | + §

= 8 + 6 + 6 + 6

c) Estimates may vary. Example: 3 x 4 = 12

rl\ 5 . 11 . 5_ 11 _ 55 _ q 1 2 ' 3 ' 2 x 3 ~ 6 ~ y 6

2. a) 2 = 3-3-

§ - \ 2 , 2 , 2 , 2 , ! _ 4 i D ^ 2 + 2 + 2 + 2 + 2 ~ ^ 2

C ) l 2 + 12 + 1 2 = 2 l 2 = 2 6 _j» 6 , 6 . 6 . 2 -> 2 -j 1 d ) 6 + 6 + 6 + 6 = 3 6 = 3 3

3. a) | x 4 ; M ; 5 |

u i l ¥ 3 . 2 1 . 3 _ . l ° ^ 3 2 ' 6 ' - : > 6 ~ J 2

r l 7 7 . 4 9 . ? J L w 4 5 ' 20 ' z 20

- j \ UL v- 5 . 55 . A _7_ 6 2 ' 12 ' ^ 1 2

4. 164-h 4


Target B-1 Extra Practice 5 WESSMSSMM

1 . Fill in the blanks. Then, write the division statement, including the quotient, that matches the diagram.

Example

—I I — i 1 1 —

in I I I 1 , 1 I I I

I I I I I I

How many ^ s in 1? 1 - r ^ = 4

in i

i

i

i

a) How many in ?

1 1 I 1 1 1 | 1 r

I in I I 1 1

I I I I I I I I I I I I I L

b) How many in ?

2. Divide using a common denominator. Show your work.

a > 3 . 1 _ h , 5 . 2 _ a > 4 T 8 " b ) 6 T 3 "

C ) 2 | ^ | = d ) 3 ^ 1 !

3. Write the reciprocal.

a) | b ) | e ) 2 § d ) 4 §

4. Divide using multiplication. Show your work.

• > § + § = b ) 2 ^ l | = .

c > I - I = d ) 8 + l | =


5. For each question below, do the following:

• Write the division statement that matches the problem,

• Estimate the answer, showing your work.

• Divide, and then write the sentence answer.

a) How many | cup portions are in 11 cups of sugar?

Division-Statement Est imate Calculation

b) Sabrina has 3 ^ L of ice cream to share equally among herself and her

nine friends at her birthday party. How much ice cream will each get? _ • —— — • ;- - ;•• Division Sta tement Est imate Calculation


i . a ) i ; l i ; l |

b) 3 ; 2 3 ; 2 3

2. a) 6 b) 1

T = 3

* % = 3

c ) 3 i d) 3 ^ ' 12

3. a) 3 b) | or i i c) | d) -5-' 22

4. a) -9- b) 1 ± 1 10 ' 2

c ) 5 i d ) 4 |

5. a) 1 | -f- | ; 2 -r 1 = 2 . There are two portions,

b) 3 f -r 10; 3 -r- 10 = ^ . Each will get \ .


Target b-1 ) Extra Practice 1

Lesson 3.1: Using Models to Multiply Fractions and Whole Numbers

1. Write each repeated addition as a multiplication statement in two ways.

} 5 5 5 5 5 7 7 7 7

h\ — + — + — + — ' 8 8 8 8 \ 1 + 1 + 1+1+ 1+1+1+1

C ) 9 9 9 9 9 9 9 9

2. Multiply. Draw a picture to show each answer.

, ) 7 x 1 b ) ~ x4 c ) 8x1 d ) i « 6

3. Ella baby-sits for - h before school each morning.

a) How many hours does she baby-sit in a 5-day work week?

b) How many hours does she baby-sit in 4 weeks?

4. Multiply. Draw a picture to show each answer. Explain any patterns you see.

a) 6x1 b ) 9 x A c ) 6 x A d) 9x1 f 4 12 ' 12 ' 2

5. Ian's monthly allowance is $21. In January he starts saving for a 2

birthday gift in June. Each month he saves - of his allowance.

The gift he wants to buy costs $110. Will Ian have enough money? Explain.

Extra Practice 1 Answers 1. a ) | x 5 or 5 x | b) | x 4 or 4 x |

c) | x 8 or 8 x |

c ) f =10 d ) f = |

3. a) j h = 3 | h b) f h= 15 h

9 1 4. All the answers are j = 4^ as a mixed number.

The fractions in parts a and c are equivalent. In parts b and c, the whole number and numerator are interchanged. The fractions in parts b and d are equivalent. The pictures show that all the questions have the same product.

5. In the six months from January to June, Ian will save | of $21 = $14.

$14x6 = $84 Ian needs $110-$84 = $26

Target B-1 ) Extra Practice 2

Lesson 3.2: Using Models to Multiply Fractions

1. Use the rectangle to find each product.

a ) - x - b ) - * - c ) - x I 1 3 5 ' 3 4 ' 7 2

2. Draw a rectangle on grid paper to find each product.

a) 4 x I b ) | x 1 7 8 3 7 4 5

5 1 ^ 3 w 4 x

5 9

3 - 2 ^ 1 x ± 9 10

e) x 0

2 1 , . 4 2 g) - x - ) - x _

3. One-third of the students in Mrs. Hayko's class walk to school. Of the students who do not walk, four-fifths take the bus. a ) Use counters to illustrate the product. b) What fraction of the students in Mrs. Hayko's class take the bus to school? c ) How many students might there be in her class?

4. Which of the following statements are equivalent? Draw area models to explain your answers.

a ) | o f | b ) 2 o f f

0 f o f f d) | o f |

e ) | o f f 0 f o f f

Extra Practice 2 Answers

30 15

c) For example, 15 or 30 students

2 5 4. a and c both equal — ; b and d both equal -

e and f both equal

a)

27

10

b> l o f l 2 9 X T

w . ! l i x i :

c) "TJ

d ) 14 2 . 3 — of — 2 9 r

1 f 3 i i i 2 o f 9 i r r r

0

5 , 3 5 ° f 2


Lesson 3.3: Multiplying Fractions

Multiply. Estimate to check.

a) | x - b) - A x 4 c) 4 x } 3 9 ' 4 5 7 2 1 4

d) 7 3

5 X _

3

e) — x 1 f) - x 1 g) - x ' 8 3 ' 5 2 B J 7

1 3

h) 10 3

x I 8

Daphne replaced light bulbs in her mother s store.

She had | of a box of light bulbs. She used | of the bulbs.

a ) What fraction of the box of light bulbs was left?

b) How many light bulbs might be in a full box? Explain.

3. Estimate each product. ^ 7 v 7 15 1 \ 32

a) b) 7^X3 c) y x

5 3

4. The product of two fractions is f. One fraction is f.

What is the other fraction?

5. Multiply. Simplify before multiplying if possible. \ 7 18 u\ 9 ^ $

a > 9 X 2 1 b > 10 X 18 C> 15 X

20 28

x!5 X 21

Multiply. Simplify before multiplying if possible. \ 7 18 u\ 9 ^ $

a > 9 X 2 1 b > 10 X 18 C> 15 X

20 28 d) 7

20 x!5 X 21


e)2

2. a) of the box of light bulbs was left.

1 1 b) A dozen, or any multiple of 12, because •- and - have a common denominator of 12.

7 1 7 1 3. a) — is 3 — and - is around 1, the product should be about 3 - .

2 2 8 2 b) — is close to 1, 1 * - = 1 ; the product should be about - .

12 3 3 F 3 32 5

c) — is close to 6 and - is between 1 and 2, closer to 2, so the product should be about 12. 3

5. a) 2 3 ' 21


Lesson 3.4: Multiplying Mixed Numbers

1. Write the mixed number and improper fraction represented by each picture.

c )

2. Use estimation. Which suggested estimate is closer to the given product? a ) 3§ x i | 3 or 8 b ) 2§ * 4^ 8 or 15 c) 2^ * j§ 3 or 6

3. Multiply. Estimate to check.

a ) 2 | x i i b ) 4 | x ?,1 C ) 5^ *2- d) | x 3 ^ ' 5 2 ' 8 3 ' 6 4 7 8 5

Amber made 5 - pitchers of iced tea for her friends.

They drank | of the iced tea.

How many pitchers of iced tea did they drink?

5. Carlos has 1 ~ cups of flour.

He uses - of the flour to make pizzas for the school fundraiser.

How much flour does Carlos use?


* x 1 5 . . 3 19 x „ 7 27 1. a) 2 - o r - b) 4 - or — c) 2 — or

2. a) 8 b) 8

10 10

c)3

3. a) 3 10

b) 1 7 - -' 12

C) 14 — ' 24

d) 2

4. 3 ^

5. 1-8


Lesson 3.5: Dividing Whole Numbers and Fractions

l . Use a number line to find each quotient.

a) i) 4 - I 3

ii) 4 - -' 3

<—r -» 1 -t < + -— - i ^ < i +•— *

0 1 2 3 4 • 4

b)i) | ^ 2 ii) 1+4 ' 5

0 —i •

1

2. Find each quotient. Use fraction circles to illustrate the answers.

a) 2 + - b) 3 + -' 3 J 4

c) 4 - -' 3

d) 5 - -7 5

3. Use a number line to find each quotient.

a) - - 3 b) - - 3 ' 4 f 5

c) - H-4 ' 8

d) - -5-4 ' 3

4. 2 Samuel uses - of a roll of ribbon to tie one balloon for the school dance. 3

He has 12 rolls of ribbon. How many balloons can he tie?

5. 3 A student knows that - x 4 is the same as 4 x

3

4 4 ' 3

The student assumes that 4 - is the same as 4

1+4. 4

Is the student correct? Use number lines to prove or disprove this assumption.


1. a) i) 12 ii) 6 b) i) -7 7 5

ii) i 5

2. a) 6 b)4 c ) 6 d) 25

3. a) - b) -5 32 7 6

4. 18 balloons

5. No, 4 -s- 1 = 4

1 3 5 - and -

3 4 ^ 4 = 1

16

3 3 4 4

3 3 4 4

3 1 4 4

< f' N i 4 f V n f x f /"\ 4 f - V - 1

0 1 2 3 4

3 3 3_ 3 16 16 16 16

< t - V H h V n i - V - i f-^j f i t \ • 0 1 2 3 1

4 4 4


Lesson 3.6: Dividing Fractions

1. Write the reciprocal of each fraction,

a) | b ) | c) — ' 11

d) 17

12

2. Use a copy of each number line to illustrate each quotient,

a) 1 2 , , y o r> I — i * » 1 1 >——i 1 1 —

b) 11 - I 10 " 5

c) 2*1 ' 9 3

d) ' 12 4

3. Use multiplication to find each quotient.

a ) I + I ' 5 3

b) 3 . 2 c)

10 7

4. Use common denominators to find each quotient. \ 5 . l

a ) — - -' 12 4

b) 5 10 c) 3 2

d)

5. Write three division questions that have - as their quotient.


L a) ^ b) I C) -1 8 ' 9

2. a) 2 5 s

b)6

. 1 1 1 1 1 1 5 5 5 5 5 5

12 10

I i . i x I i 0 1

3. a) 4 b) I? c) 11 5 ) 16 j 25

4. a) 1? b) 3 ± c) l i

3 _ 9 3 3 . 1 1 22


Lesson 3.7: Dividing Mixed Numbers

1. Write each mixed number as an improper fraction.

a) 2 - b ) \ - c ) 3 -f 7 ' 6 7 8

d) >y 3 5

2. Use common denominators to find each quotient.

a) i f b ) 2f -M^ c) 4 § - M ^ d) J 2 8

3. Use multiplication to find each quotient.

a) 35-I20 b ) 6^2^ c) 5 ^ 2 ^ d)

4. Divide. Estimate to check.

a) 2 - - 1- b ) 3-̂ - 2 - c) 1- - 2 -' 3 4 ' 5 4 ' 8 5

d) 3 2

5. Which statement has the greatest value? How do you know?

a) 2 - - - b) 2- + - c ) 2 - x 1 ' 4 3 7 4 3 } 4 3

d) 2 - - - e) 2 - -i- - f) 2 - + -7 4 3 4 1 7 4 4


1. a) 1 6

7 ' 5

2. a) 12 b ) 2 J | d) e |

3. a) 3— ' 23

7 52 . 25 d) *°

' 43

4.a) 2 -' 15

b) 1 9-7 55 112 3

5 2 | - r i = g i ; dividing a number by - will give a greater answer than adding to the number, multiplying the

1 1 3 number by - , subtracting - from the number, or dividing the number by 3; adding - to the number will give a

3 3 4 lesser answer than dividing by - .


Lesson 3.8: Solving Problems with Fractions

Solve the following problems. Estimate to check the reasonableness of your solutions.

1. During a one-hour phone-in talk show, 8 callers made calls that took 3| min each.

a) How many minutes were used by the 8 callers?

b) What fraction of the hour was used by these callers?

c) How many minutes were left for other callers?

d) What traction of the hour was left in the talk show for other callers?

2. Ms. Lecky ordered pizza for a party. l | of the vegetarian pizza and 2 j of the ham and pineapple pizza were not eaten. How much pizza was left?

3. A dressmaker needs 3| m of fabric to sew one dress.

How many dresses can the dressmaker make with 28 m of fabric?

3 2

4. A dock is 7̂ m high. The portion of the dock above water one day was measured at 2̂ m high.

How much of the dock structure was above water that day?

Extra Practice 8 Answers 1. a ) 26 min b) — c) 34

' ' 30

2 . 2 ^ 24

3. 8 with — left over 27

4. SL 20


1 . List the following in the order of operations for fractions,

addition/subtraction (left to right), brackets, multiplication/division (left to right) - - - - * - •• • - *- • - 1 ' - - - - --" -' - •-- -'• •• • n i '-r-ii nm .mi- - ir. r t nr- -1, - to J . l ' r i >-.-..... -n„ - r - ti • • ... ..-.l-i .^ir"r,,- ) Y r - y ,

First

Second

Third

2 . Decide where each of the following statements is true or false. Circle the word True or False. I f the statement is false, rewrite the answer to make it true.

a) T r u e / F a l s e 5 - 3 x | = 1

b) T r u e / F a l s e 2 | - 2 x | = | |

c) T r u e / F a l s e 125 x | - 5 \ = 10

3 . Calculate. Show your work.

• » ( § - § H

b) ^ x ^ - U -3 4 9 9 3

c ) 2 § - l § + ( 4 § + ! )


4. For each question below, do the following:

• Write the expression that matches the problem.

• Calculate. Show your work.

• Include a sentence answer.

a) Super Mart had a sale. The first $200 Sara's father spent was discounted

by , and the amount he spent over $200 was discounted by | . Sara's

father bought $275 worth of groceries. What was the total discount?

b) In Mr. Jones's grade 8 class 20 students, or | of the class, bought class

photos. In Ms. Floyd's grade 8 class 18 students, or | of the class, bought

class photos. How many students were there in total in Mr. Jones's and Ms. Floyd's classes?


1. brackets, multiplication/division, addition/subtraction

2. a) F; 5 - 3 x i = 3 |

b) F; 2 g — 2 x ^ = 1 g c) T

3. a ) ^ b ) i c)2±± 1 48 2 30

4. a) 200 x JL + (275 - 200) x I ; 35. The total discount was $35.

b) 20 -r | + 18 -r | ; 55. There were 55 students in total.



Lesson 3.9: Order of Operations with Fractions

1. Evaluate.

») f - H H ) •»> f - f * H o (f-f)*(H)

2. What do you notice about the expressions and answers in question 1 ? Explain.

3. Emma thinks the answer to l | 1 x | is the same as the answer to l | + (| x |).

Is Emma correct? Explain your thinking.

4. Evaluate. Show all steps.

5. Add brackets to the expression -j^ + | - ^ ; | - | x | , to find as many different expressions

and solutions, as you can.

2 . + I - i __ I x I i_ + I ^ I _ i x i J L + I ^ I I x I 10 5 2 3 4 10 5 * 2 3 4 10 5 ' 2 ~ 3 4

J_ + i , _ I _ I x I i_ + l ^ I _ I x I i - 4 . 1 ^ 1 i v I 10 5 " 2 3 4 10 5 " 2 3 4 10 5 " 2 ~ 3 4

Extra Practice 9 Answers 1. a) 12

30 11 45

2. All the answers are different. Each question has the same numbers in the same order with the same operations. The only difference is the placement of brackets, thus the operations are completed in a different order resulting in different answers.

1 1 2 1 1 2

3. Emma is incorrect: 1̂ j X 3 = 4 and 1̂ + (4 X 3) = 9, in the first expression division occurs before multiplication, 2

the division results in 6 and r of 4 is 6. In the second case, the multiplication is done first because of the brackets

4. a)7? b ) -7 15 \R

c ) 3f

5. Possible solutions:

10 5 ' 2 3 4 60 i_ + i^i__l x 1 = 37

11 120

Documents

Mr. B's Weebly - Grade 8 Mathematicsmrbockstael.weebly.com/.../2437974/b-1b-2_extra_practice.pdfTarget B-1) Extra Practice 2 Lesson 3.2: Using Models to Multiply Fractions 1. Use the