PACKET - EQUIVALENT & COMPARE FRACTIONS

Fractions:

EQUIVALENT fractionS

&

COMPARE fractions

unit 6

(Section 2)

math packet

Use a Fraction Model Compare With Like Denominators

Compare With Like Numerators

Use a Number Line to Compare to a Benchmark Like A

Find Common Denominators

Represent Equivalent Fraction using Fraction Bars, Area Models, Multiplication & Division, and Number Lines

UNDERSTANDING EQUIVALENT FRACTIONS

VIDEO INTRODUCTION: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-visualizing-equiv-frac/v/equivalent-amount-of-pizza

LESSON OBJECTIVES:

• Use models to identify equivalent fractions.

• Use a number line to identify equivalent fractions.

Look at the Fraction strips.

The fractions

A

,

G

, and

e

have different numerators and denominators. But

A

is equal to

G

.

A

_,

G

_{, and}

e

_{are called equivalent fractions.}

What are equivalent fractions?

One whole

1 out of 2 equal parts =

A

2 out of 4 equal parts =

G

4 out of 8 equal parts =

e

guided learning

▶_{Find the equivalent fractions.}

▶_{Find the missing numerators and denominators.}

1 3 3 6

▶_{Use the fraction bars to name equivalent fractions.}

▶_{Explain WHY these fractions are equivalent.}

___________________________________________________________________ ___________________________________________________________________

One whole

C

_{of the bar is shaded.}

C

₌

C

₌ (1)

(2)

create equivalent fractions

VIDEO INTRODUCTIONS:

• https://learnzillion.com/lessons/1732-identify-equivalent-fractions-using-a-number-line • https://learnzillion.com/lessons/617-recognize-equivalent-fractions-using-number-lines

Look at the number lines.

The number lines show

A =

G =

e

.

☞

EQUIVALENT FRACTIONS

☜

have the same location on a number line!

Use a number line to find equivalent fractions.

Letter A on number line 1 represents

C

.

Letter A on number line 2 represents

P

.

guided learning

▶_{Fill in the missing fractions on the number lines. Use the number lines to find the equivalent}

fractions.

C = = D = =

▶_{Name the fractions marked on each number line.}

(1) (2)

let’s practice

▶_{Find equivalent fractions of}

K

_.

▶_{Create two (2) same-sized rectangular models to show two fractions equivalent to}

O

_.

▶_{Use the number lines to find equivalent fractions of}

J

_.

J = = M = =

(1)

_K

of the bar is shaded.

K

₌

K

₌

(2)

more equivalent fractions

▶_{Use multiplication and division to find equivalent fractions.}

You can multiply both the numerator and the denominator by the same number to find an equivalent fraction.

You can divide both the numerator and the denominator by the same number to find an equivalent fraction - but the trick is to find a number that both the numerator and denominator

guided learning

▶_{Use models and multiplication to find equivalent fractions.}

U = = U = =

▶_{Use models and division to find equivalent fractions.}

Q

= =

(1) (2)

(3)

let’s practice

▶_{Use the multiplication method to find an equivalent fraction. Then, use the number lines to}

show how the two fractions are equivalent.

Fractions are equivalent only if they have the same location on a number line.

(1) (2)

let’s practice

▶_{Use the division method to find an equivalent fraction. Then, use the number lines to show}

how the two fractions are equivalent.

Fractions are equivalent only if they have the same location on a number line.

(1) (2)

problem solve

▶

_Solve.

Ella had a candy bar and she wanted to share it with her friends, Bryan and Josh. So,

Ella gave Bryan

C

of the bar and she gave Josh

m

of the bar.

Part 1:

Did Ella give Bryan and Josh equal amounts of the candy bar? Explain your

answer in words, with a number line, or any other strategy you learned to find

equivalent fractions.

compare FRACTIONS using models

VIDEO INTRODUCTION: https://www.youtube.com/watch?v=nH7s9SIjwus https://www.youtube.com/watch?v=CrD95h3FeL4

LESSON OBJECTIVES:

• Show fractions as points or distances on a number line. • Compare and order fractions.

• Compare and order fractions using benchmark fractions.

You can compare two or more fractions by shading equal-sized models. Look at the two models below. There is less shaded area in the model of

A

than in the model of

D

.

Therefore,

A

is less than

D

.

This can be written as

A

<

D.

VOCABULARY • like fractions • unlike fractions • benchmark fraction

Compare Using Fraction Models

☞

REMEMBER

☜

practice

▶

_{Shade a fractional part of each drawing. Write the fractions in the comparison to make it true.}

(1)

(2)

(3)

compare FRACTIONS using number lines

VIDEO INTRODUCTION:

• https://learnzillion.com/lessons/103-compare-fractions-using-a-number-line

• https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-fractions-topic/cc-3rd-equivalent-fractions-number-line/v/comparing-fractions-visually-and-on-number-line

The number lines show

A

,

F

, and

H

.

From the number lines,

H

is greater than

A

.

F

_{is less than}

A

_.

In this example, the two fractions

F

and

D

are being compared. 1. Look at the

A

mark on the number line.

2. Label

F

and

D

on the number line.

3. Since the fraction

D

is located AFTER the

A

mark on the number line, it it greater than the fraction

F

.

practice

▶

_{Locate the pair of fractions on the number lines. Then compare using <, >, or =.}

(1)

(2)

(3)

more practice

▶

_{Use the fraction number lines on the right}

to compare the following fractions. Remember to look at the location of the fractions compared to

A

.

▶

_{Compare using >, <, or =.}

Mrs. Browning asked her class to help with safety patrol.

e

of the class went with her to help younger students onto the buses. Mr. Tobias took

A

of the class to help students at the crosswalk.

Compare the fractions of the class that went with each teacher using < , > , or =.

(1) (2) (3)

(4) (5) (6)

VIDEO INTRODUCTION:

• https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/fractions-with-like-denominators-numerators • https://learnzillion.com/resources/48625/

guided learning

▶

_Complete.

Danny and Keith buy an equal-sized pizza each. Danny eats

K

of his pizza, and Keith eats

M

of his. Who eats less?

Rachel bakes two equal-sized chicken pies. She cuts each pie into 6 equal parts.

Clara eats

Q

of a pie, and Priscilla eats

P

of the other pie.

Who eats more?

Priscilla gives her remaining pie to Tim. What fraction of the pie does Tim eat?

(1)

K

_{is less than}

M

_.

eats less.

(2)

(a)

is greater than

eats more.

(b)

Tim eats of the pie.

Order the fractions from greatest to least.

In order from greatest to least, they are: , ,

guided learning

▶

_{Order the fractions from least to greatest.}

▶

_{In order from least to greatest they are:}

Use models to order fractions with like denominators.

is the greatest.

compare fractions with like numerators

VIDEO INTRODUCTION:

• https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/fractions-with-like-denominators-numerators • https://learnzillion.com/lessons/1739-compare-fractions-with-the-same-numerator-by-reasoning-about-their-size

Which is greater,

L

or

Q

?

L

is greater than

Q

.

The greater fraction is the one with the smaller denominator! Compare fractions with like numerators.

guided learning

▶

_Complete.

Which is less,

d

or

L

? Which is greater,

C

or

U

?

is less than is greater than

Which is less,

t

or

V

? Which is greater,

L

or

g

?

is less than is greater than

▶

_{EXPLAIN: Why do the parts of a whole get bigger when the denominator gets smaller?}

___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________

(1) (2)

compare unlike fractions by finding equivalent fractions

VIDEO INTRODUCTION: https://www.youtube.com/watch?v=e6JbEBbTx40

What would you do to compare the following fractions?

f H

Now, you have unlike denominators. So, you can find equivalent fractions until you have like

denominators. Let’s see how.

Look at the denominators. Since 4 is a factor of 8, find an equivalent fraction for H where

the denominator is 8. You can multiply the numerator and the denominator of a fraction by any nonzero whole number, as long as you multiply both by the same whole number! For example, you can multiply the numerator and the denominator by 2, allowing you to find an equivalent fraction for H.

Now that you know

g

is the same as H, you can see that g is greater than

f

.

Therefore,

▶_{Prove it with fraction models:}

practice

▶

_{Compare fractions by naming equivalent fractions.}

R C t J

d H S D

⃝

⃝

⃝

⃝

(1) (2)

guided learning

▶

_{Find an equivalent fractions. Then compare.}

Which is greater,

A

or

v

?

You can use division to rewrite unlike fractions as like fractions.

Which is less,

N

or

G

?

Which is greater,

S

or

C

? (5)

is greater than

is greater than

Compare fractions with unlike denominators.

F

is less than

G.

_So,

N

_{is less than}

G

_.

guided learning

▶

_Compare.

Which is less,

D

or

p

? Which is greater,

S

or

H

?

▶

_{Use the number lines to compare fractions with the benchmark}

A

_.

Circle the fraction that is greater.

S

or

d

?

(1) (2)

D

x3

x3

Which is greater,

K

or

f

?

Write two fractions that are less than

H

.

_and

Write two fractions that are greater than

A

.

and (4)

(5)

From the number line,

S

is the greatest and

L

is the least.

In order from least to greatest, they are:

Compare and order unlike fractions.

guided learning

▶

_{Order the fractions from least to greatest.}

h F A h Y A

(1) _{, ,} (2) _{, ,}

let’s practice

▶

_{Draw fraction bars to show the following fractions on number lines.}

X

A

▶

_Compare.

Which is greater,

d

or

A

? Which is less,

A

or

y

?

▶

_{Compare. Choose > or <.}

Which is greater,

A

or

f

?

▶

_{Complete the sentences.}

More than

A

of the pattern is colored . (1)

(2)

(3) (4)

(5)

▶

_{Compare. Circle the correct answer.}

Which is less,

u

or

L

? Which is greater,

C

or

K

?

▶

_{Order the fractions from least to greatest.}

P

S A H

R

C

▶

_{Order the fractions from}

_greatest

_to

_least

_.

O m

R

, ,

, ,

, ,

, , , ,

, ,

(8) (9)

(10)

(12)

fraction of a set

▶_{Lesson Objectives:}

• Use a bar model to represent a fraction of a set. • Find a fractional part of a number.

• Multiply a fraction and a whole number.

Use a model to show a fraction of a set.

▶

_{Find the fraction of the set.}

Find

K

of 15.

5 units 1 unit 2 units

So,

K

of 15 is

Find

D

of 6.

3 units 1 unit 2 units

So,

D

of 6 is (1)

▶

_{Follow the steps to find the fractional part of each number.}

D

of 12 =

H

of 20 =

D

of 12 =

H

of 20 =

M

of 25 =

Y

of 28 =

M

of 25 =

Y

of 28 =

Here is another way to find a fractional part of a number.

multiply a fraction and a whole number

VIDEO INTRODUCTION: https://learnzillion.com/lesson_plans/7425-multiply-a-fraction-by-a-whole-number-using-visual-models-and-repeated-addition

When multiplying fractions by a whole number, first show the problem as an expression. Then model the expression by drawing a picture.

guided learning

Find 6 x

H

.

6 x =

=

▶_{Name a multiplication equation the models represent.}

________ x ________ = ________

________ x ________ = ________

Erica practiced her basketball free throws 4 days a week. She practiced

F

of an hour each

day. How many hours did Erica practice free throws.

There will be 6 people at Ellie’s party. She wants to bake enough pie so that each person can eat

J

of a pie. What is the number of pies Ellie should bake?

unit review

▶_{Name the equivalent fractions for the pie models in each problem.}

▶

_{Shade the pie models to represent equivalent fractions.}

▶

_{Use the number lines below to create a set of equivalent fractions. Do your best to}

accurately locate the fraction pairs.

(1) (2) (3)

(5) (4)

▶

_{Complete the multiplication process of naming equivalent fractions.}

▶

_{Complete the division process of naming equivalent fractions.}

▶

_{Use any strategy to compare the set of fraction pairs. Use >, <, or =.}

(7) (8)

(9) (10)

(11) (12) (13)

▶

_{Which fraction is equivalent to}

⅔

_?

▶

_{What fraction of the items in the box are scissors?}

▶

_{What fraction of the figure below is shaded?}

▶

_{Use the number lines provided to name equivalent fractions.}

(17)

=

(18)

(19)

▶

_{Represent the fractions of a set.}

(21)

(24) (23)