Math- Fractions Part II

This page contains practice problems, a review of problem solving and links to math sites around the World Wide Web. There are many links to help with homework questions as well as many games to practice math in a fun way.

The eighth chapter of the fifth grade math book focuses on multiplication and division of decimals. The standards for chapter 8 are:

Chapter 8

Number Sense: Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.

Number Sense: Understand the concept of multiplication and division of fractions.

Number Sense: Complete and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Algebra and Functions: Use a letter to represent an unknown number; evaluate simple algebraic expressions in one variable by substitution.

Mathematical reasoning: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

Mathematical reasoning: Apply strategies and results from simpler problems to more complex problems.

Mathematical reasoning: Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

This chapter connects with previous and future learning in this way:

Looking Back	Right Now   Fraction Concepts	Looking Ahead
In chapter 7, students learned how to find the greatest common factor (GCF) and the least common multiple (LCM), how to write fractions in simplest form, and how to compare and order fractions and mixed numbers.	In this chapter, students will learn how to add, subtract, multiply and divide fractions and mixed numbers.	In chapter 12, students will learn how to change fractions to decimals and percents and how to write a ratio as a fraction in simplest form.

The chapter has three sections of problem solving where the students are introduced to new strategies or are asked to apply previously learned concepts in new problems. The strategies for the fourth chapter are:

Too Much or Too Little Information pages 314-315

Solve a Simpler Problem pages 328-329

Finding Fraction Patterns pages 338-339

The Five Steps to Successful Problem Solving are:

Understand

What is the problem about?
What facts do I have?
What must I find?
Try to restate the problem in your own words.

Plan a Solution

Make a plan as to how you will solve the problem.
Think of the different strategies that you know and understand.
Ask: "How can I solve this problem?"

Solve the Problem

Decide the best way to actually solve the problem.
Choose the method of computation: pencil/paper, mental
math, calculator or manipulatives

 

Look Back

Check to see that the answer makes sense.
Think of a way to check the answer and then do so.
Ask yourself: "Does my solution make sense and does it answer the question that I have been asked to find?"

 

 

Practice~

Write + or - to make each statement true.

7/8 4/8 = 3/8

16/24 10/24 = 1/4

9/164/16 = 5/16

6/74/7 = 2/7

4/91/9 = 5/9

8/124/12 = 1/3

5/81/8 = 3/4

13/16 5/16 = 1/2

2/31/3 = 1

For each set of fractions, identify the pair which satisfies the given conditions.
3/4, 3/8, 1/2, 2/3, 4/16	The sum is 3/4
1/2, 2/5, 4/8, 1/10, 3/10	The sum is 1/2
7/8, 1/2, 3/8, 3/4, 1/16	The sum is 7/8
1/7, 9/14, 3/7, 1/2, 2/7	The sum is 1 1/7
1/5, 3/10, 4/15, 3/5, 4/5	The sum is 13/15

Dan played his guitar for 1/3 of an hour in the morning and 1/2 hour in the afternoon. Altogether, what part of an hour did he play the guitar?

Fran went outside for an hour. She walked for 2/6 hour, ran for 2/8 hour, and sat for the rest of the hour. What part of the hour did she sit?

Find the sum

2 1/2 + 1 5/8 + 3 3/4 = n

4 1/2 + 2 3/5 + 1 1/10 = r

3 2/3 + 1 1/2 + 4 3/4 = s

5 1/3 + 3 5/8 + 1 17/24 = z

2 7/10 + 4 3/4 + 3 2/5 = p

Solve each of the following and then put the differences in order from least to greatest.

3 1/ 3 - 1 2/3 = q

4 1/5 - 2 2/5 = x

9 1/4 - 7 3/4 = p

7 5/9 - 5 7/9 = b

8 1/8 - 6 7/8 = a

You are working in a department store and it is your job to wrap gifts. You must complete the following chart to give to your boss at the end of your shift to show how much ribbon you used in wrapping the gifts.

Color	Started with	Yards used	Yards left
RED	16 1/2	3 3/4
WHITE	20 3/4		10 1/3
BLUE		5 7/12	9 2/3
YELLOW	22 1/3	13 7/12

Write True or False for each of the following statements.
* MEANS TO MULTIPLY

3/4 * 5/12 = 5/16

7/8 * 4/5 = 11/40

5/6 * 4/7 = 10/21

1/3 * 2/3 = 2/6

3/5 * 1/3 = 1/5

2/3 * 3/8 = 6/11

3/4 * 3/9 = 1/4

5/8 * 2/5 = 7/13

All members of the drama club voted for their favorite actor. Half voted for Pam, 1/4 voted for Paco, 1/8 voted for Pete, 1/16 voted for Paula, and the rest voted for Pat. If 2 members voted for Pat, how many students belong to the drama club?

Use one or more of the following fractions to make the statements which follow true. The fractions may be used more than once.

1/8

1/5

1/4

1/3

1/2

7/12

3/8

5/6

3/5

3/4

2/3

is estimated to be 1/2

< 1/2

+ = 1

+ 1/3 < 1/2

3/4 + > 1/2

1/2 - < 1/3

+ > 1

- < 1

X 8 > 4

X is estimated to be 1/2

Express each composite number as a product of primes:

Composite Number	Product of Primes
14	2 X 7
18	2 X 3 X 3
21
27
30
32
36
45
48

Match each fraction in column A with its simplest form in column B

Column A	Column B
14/28	2/3
12/18	1/2
14/20	3/8
12/32	4/5
16/40	7/10
21/24	1/3
12/36	3/4
15/20	7/8

Find the least common multiple of each set of 3 numbers:

The numbers:	The Least Common Multiple
4, 6, 8
6, 9, 12
3, 5, 10
2, 8, 12
4, 10, 12

Draw the model which would help solve this problem:

Alex, Beth, and Sarah buy a pizza and cut it into 8 equal pieces. Alex eats 1/4 of the pizza, Beth eats 3/8 of the pizza and Sarah eats the rest.
What part of the pizza did Sarah eat?

Time to be Challenged-Can you beat the challenge, or will it beat you?

Ben's band includes a piano, a drum, a guitar, and a saxophone. Ben does not use his mouth to play his instrument. Keith and Brenda's instruments have strings. Ben, Mattie, and Brenda can carry their instruments. Who plays each instrument?	Maria's field hockey uniform shows a 2-digit number. The number is prime. If the digits are reversed, the number is still prime. The ones digit is 4 less than the tens digit. What number in on Maria's uniform?
Mr. Green, Mr. Black and Mr. Brown wear green, black and brown winter coats. "It's funny," says Mr. Green, "that none of our coats matches our names." "Big deal," says the man in the black coat. Who is wearing which coat?	How many minutes are represented by each fraction of an hour? You can find answers by shading a clockface. 3/4 of an hour 2/3 of an hour 1/12 of an hour 1/5 of an hour 5/6 of an hour

At the Valley View Picnic, 3/4 of the guests entered the boat race and 1/2 of the guests entered the sack race. There were 24 people at the picnic. How many people entered both races?	The numerator of a fraction is three less than the denominator. If the fraction is flipped, it is four times as great as the original fraction. What is the original fraction?
Three friends ate all but 1/4 of a jumbo pizza. Ned ate half as much as Scott. Alan ate one more slice than Ned. How many slices were in the pizza? How many slices did each friend eat?	Lynn had $12 and spent 3/4 of her money. Joe had $10 and spent 3/5 of his money. Who has more money left? How much more?

Fraction Math Links

AAAMath.com Sites

Take a Fraction Quiz	Play Soccer Shootout
Cross-Canceling Explained	Why invert and multiply?
Multiplying Practice with Reducing	Multiplying Fractions from Thinkquest
Help Builder Ted order his numbers Not really a fraction link, but good number sense!	Dividing Fractions from Thinkquest

to the fraction sites we've seen before~

Tutorials and Explanations~

Visual Fractions

Fraction Basics Explained

Equivalent Fractions

Greatest Common Factor

Least Common Multiple

Finding Least Common Multiples

Finding the Least Common Denominator

Comparing Fractions

Learn About Fractions with Pizza!

Comparing and Reducing Fractions

Improper and Mixed Fractions

Thinkquest Math Tutor

Index of Fraction Rules-tons of rules!

Fraction Help from the Math League

Dr. Math answers fraction questions

to more fraction practice

Equivalent fractions

Greatest Common Factors

Least Common Multiples

Simplifying Fractions

Converting fractions to mixed numbers

Converting mixed numbers to fractions

Comparing fractions with the same denominators

Comparing fractions with different denominators

Comparing fractions with different numerators and denominators

to fraction games and practice

Fractions and Patterns

GCF Basketball Game

Play Fraction Frenzy

Matching Fractions Game

Fraction Concentration Game

Equivalent Fraction Flash Cards

Fresh Baked Fractions Game

to the decimal, fraction, and percentage sites!

Decimals, Percentage, and Fractions

The Meaning of Percent

The Relationship between Percents and Decimals

The Relationship between Decimals and Percents

Percentages, Decimals and Fractions-Nice Summary Chart

Writing Fractions as Percents

Practice How Quick You Are

Time to Exercise the Brain~

Escape from Knab	Climb Math Mountain	Puzzler Archive	Cyberchase
Puzzler	The Train Race	Online Mankala	Play Bathroom Tiles
Who Wants to Win $1,000,000.00?	Grade Five Problems	Family Math Challenges	Online Math Games
What's the Best Way to get Paid?	Mystery Math	Coin Flipping	Math Hunt

to all the math sites that we love!

Great Help for Most for Place Value	Need help? Ask Dr. Math
Practice rounding with online flashcards	Math Dictionary for Kids
Online Flashcards-all operations	Tons of chances for practice-worksheets
Totally Tessellated	A+ Math Games
Runaway Math Practice	Late Delivery-Great Algebra Practice
Mystery Math-How do they do that?	Order of Operations
Puzzler	Math Baseball
Multiplication tips by kids	Exponent Basketball
The Fruit Game	Math Playground