PACKET - Mixed Numbers & Decompose Fractions




Core Standards: 4.NF.3 - 4.OA.3 - 4.NBT.4 - 4.OA.5 1

MATH supplemental

activity guide

Mixed Numbers

Improper Fractions

Decompose Fractions

Identify & Represent Mixed Numbers Identify & Represent Improper Fractions

Locate Mixed Numbers and Improper Fractions on a Number Line Add & Subtract Fractions with Like Denominators

Add & Subtract Mixed Numbers Problem Solve

Name __________________________________

Test Date __________________________

practice & review:

Multi-digit Addition & Subtraction

adding proper FRACTIONS

If the following rectangle is divided into eight equal parts, how many shaded parts are there?

There are 3 light shades and 2 dark shades, for a total of 5 shaded parts. Mathematically, this can be represented as:

Notice how easy it is to add up fractions the like or common denominators. All you have to do is add the numerator values. The denominators did not change because

the total number of parts did not change!

▶_{Add the following fractions. You may use the fraction blocks if needed.}

MODEL ADDING FRACTIONS:

Create Models to Represent Adding Fractions

now you try!

▶Create a model to represent the following fraction addition problems.

PRACTICE

▶Write a fraction equation & create a model to represent that equation.

1. Write an equation to show

f

as a sum of two or more fractions. Draw a model that represents the equation.

Equation:

d + b + b = f

Model:

2. Write an equation to show

R

as a sum of two or more fractions. Draw a model that represents the equation.

Equation: Model:

3. Write an equation to show

W

as a sum of two or more fractions. Draw a model that represents the equation.

Equation: Model:

4. Write an equation to show

n

as a sum of two or more fractions. Draw a model that represents the equation.

Equation: Model:

PROBLEM SOLVE

1. A pizza was cut into 8 equal slices. Andrew and Robert will share

f

of the pizza.

Use fractions to write two (2) different ways that Andrew and Robert could share the pizza between them. They do not get the same amount.

A. Andrew _________________ Robert _________________

B. Andrew _________________ Robert _________________

2. There is a group of 6 slices of pie. Kayla and Olivia share

R

of the slices of pie.

Use fractions to write two (2) different ways that Kayla and Olivia could share the slices of pie. They do not get the same amount.

A. Kayla _________________ Olivia _________________

B. Kayla _________________ Olivia _________________

SUBTRACT PROPER FRACTIONS

▶You already learned how to add fractions with like denominators. Now, try

mixed numbers:

What Do They Look Like?

INTRODUCE THE TOPIC: https://www.youtube.com/watch?v=f3VCJsdSRaQ

A mixed number has a whole part and a fraction part.

☞

What does a mixed number look like?

☜

▶How many slices is each circle broken into? ___________________

▶What does that number represent? ___________________

▶How many whole circles are there? ___________________

▶What does this number represent? ___________________

▶How many slices are shaded in the third circle? ___________________

▶What does this number represent? ___________________

▶Can you name the mixed number this model represents? _________________

Core Standards: 4.NF.3 - 4.OA.3 - 4.NBT.4 - 4.OA.5 9

identify mixed numbers

modeling mixed numbers

▶Shade the portions of each model to represent the given mixed number.

tasty treats

▶Name the mixed number that each model represents.

REAL-WORLD EXAMPLE

Julia made two peanut butter and jelly sandwiches. She cut the sandwiches into 4 pieces each. After eating some, she had 5 pieces left. What fraction of the sandwiches

does Julia have left?

Each sandwich has 4 equal pieces. There are 5 pieces left. Count the wholes and the parts.

So, 1

F

of the sandwiches are left.

PRACTICE

problem-solving practice

Draw models to represent the following word problems.

You may use fraction tiles to solve the following problems.

1. Bailey ate 2

L

cups of popcorn during the movie. Jason ate 2

R

cups of popcorn during the movie. Who ate more popcorn? Show your work and explain.

2. Sarah needs 1

A

cups of flour for pancakes and 1

H

cups of bananas for banana

bread. Does Sarah need more flour or more bananas? Show your work and explain.

LOCATE MIXED NUMBERS ON A NUMBER LINE

INTRODUCE THE TOPIC: https://www.youtube.com/watch?v=4pmaZEE-FgA

Based on the data on the number line below, can you place a dot on the location that represents 3

A

?

If you placed the dot exactly between the 3 and 4, you are correct.

In the mixed number 3

A

, the location must come after the whole number 3, but before the whole number 4.

3. 4.

I

I

I

I

I

I

I

I

I

I

I

1. 2.

practice & problem solving

▶Name the mixed numbers represented on the number lines below.

IMPROPER fractions -

What Makes a Fraction Improper?

Look at the model below. Each circle is broken into 3 equal parts, or thirds. Written as a mixed number, the shaded portion of the model represents 1

D.

Since each circle is broken into 3 equal parts, the denominator is 3. There are a total of 5 shaded thirds, so 1

D

can also be written as .

Improper fractions

Here is another way to think about improper fractions and their relationship to mixed numbers.

How many halves are there in 2

A

?

There are 5 halves in 2

A

- So, 5 halves =

Core Standards: 4.NF.3 - 4.OA.3 - 4.NBT.4 - 4.OA.5 19

How many fourths are there in 1

H

? _______

________ fourths = ________

How many thirds are there in 1

C

? _______

________ thirds = ________

How many fifths are there in 1

L

? _______

naming improper fractions

DECOMPOSE FRACTIONS

▶Fractions can be decomposed, or broken down, into smaller components.

To decompose a fraction means to find the two, or more, fractions that when added together give you the value of the fraction you started with. You can decompose fractions in many ways, as

long as your representation is a balanced equation.

d + b + b = f

or

f = d + b + b

practice decomposing fractions

▶Decompose the following fractions into the sum of the fractions.

1.

n =

2.

d =

3.

R =

4.

x =

5.

R =

6.

D =

7.

F =

decomposing MIXED NUMBERS

Mixed numbers can be decomposed, or broken down, into smaller components.

Often times, there is more than one way to decompose a mixed number sum.

1

+

1

+ b =

2

b

or

i + i + b =

2

b

PRACTICE Decomposing MIXED NUMBERS

Decompose the following mixed numbers into the sum of the mixed numbers. 1.

5

D =

renaming improper fractions as mixed numbers

You can easily DECOMPOSE an improper fraction to change it into a mixed number.

GUIDED PRACTICE

-

Name each improper fraction as a mixed number

Core Standards: 4.NF.3 - 4.OA.3 - 4.NBT.4 - 4.OA.5 23

1.

4. 3.

2.

Write as a mixed number.

▶_{First, determine how many fifths}

represent the whole.

▶_{Then, determine how many fifths}

are left.

▶_{When finished, add the whole to the}

remaining fifths.

▶_{So, = 1}

M

9 5 9 5 9 5

N

M

1

M

+ 3

2 5 4

7

PRACTICE

SPIRAL REVIEW

▶Estimate the product. _{(Remember to round the 3-digit number first!)}

▶Column addition.

▶Subtract across zeros.

Core Standards: 4.NF.3 - 4.OA.3 - 4.NBT.4 - 4.OA.5 25

4 0 0

− 3 7 9

6 0 0

− 2 1 6

7 0 0

PROBLEM solve challenge

Marta picked

e

cup of blueberries. Her sister picked

d

cup of blueberries. They used

g

cup of all the blueberries they picked to make muffins.

What was the amount, in cups, left of the blueberries they picked?

Show your work.

Taxi cab “A” and taxi cab “B” left the cab station at the same time and headed in the same direction. After five minutes, cab “A” was 5

e

miles from the station and cab “B” was 2

c

miles from the station. How much farther from the station was cab “A”

than cab “B”?