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fractions!

FRACTIONSFRACTIONS

Basic Fractions

Comparing Fractions

Adding Fractions

SubtractingFractions

Fraction Fun!

What are fractions?

What are fractions?What are fractions?What are fractions?What are fractions?

• Fractions are for counting PART of something • Fractions are for counting PART of something • The denominator tells us how many pieces something is cut into.

• The numerator tells how many fractional pieces there are

Basic FractionsBasic Fractions

A fraction is part of an entire object.A fraction is part of an entire object.

1/4 is pink

1/2 is pink

3/4 is pink

4/4 or one whole

is pink

Comparing FractionsComparing Fractions

If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction.

For example: 5/8 is larger than 3/8

all of the pieces are the same and five pieces are more than three pieces.

If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction.

For example: 5/8 is larger than 3/8

all of the pieces are the same and five pieces are more than three pieces.

Comparing, cont.

Comparing Fractions, cont.Comparing Fractions, cont.

If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction.

For example:

5/8 is larger than 5/16

Each fraction says there are five pieces. If an object is divided into 8 pieces, each piece will be larger

than if the object were split into 16 pieces. Therefore five larger pieces are more than five

smaller pieces.

If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction.

For example:

5/8 is larger than 5/16

Each fraction says there are five pieces. If an object is divided into 8 pieces, each piece will be larger

than if the object were split into 16 pieces. Therefore five larger pieces are more than five

smaller pieces.

Adding FractionsAdding Fractions

Adding fractions with COMMON denominators is simple.

Just add the numerators together, and place the resulting answer in the top of a fraction and use the existing denominator for the bottom

number. Then reduce the fraction, if possibleFor example:

3/8 + 2/8 = 5/8

Adding fractions with COMMON denominators is simple.

Just add the numerators together, and place the resulting answer in the top of a fraction and use the existing denominator for the bottom

number. Then reduce the fraction, if possibleFor example:

3/8 + 2/8 = 5/8

Adding, cont.

Adding FractionsAdding Fractions

You can only add together fractions that have the same denominator, so you must first change one or

both of the fractions so that you end up with two fractions having a common denominator.

The easiest way to do this, is to simply select the opposite fraction's denominator to use as a top and

bottom multiplier.

Please look at the example on the next page…

You can only add together fractions that have the same denominator, so you must first change one or

both of the fractions so that you end up with two fractions having a common denominator.

The easiest way to do this, is to simply select the opposite fraction's denominator to use as a top and

bottom multiplier.

Please look at the example on the next page…

Adding, cont.

Adding FractionsAdding FractionsExample: You have the fractions 2/3 and 1/4

Select the denominator of the second fraction (4) and multiply the top and bottom of the first fraction (2/3) by that number:

4/4 x 2/3 = 8/12

Select the denominator of the first fraction (3) and multiply the top and bottom of the second fraction (1/4) by that number:

3/3 x 1/4 = 3/12

These two fractions (8/12 and 3/12) have common denominators - the number 12 on the bottom of the fraction.

Add these two new fractions together:

8/12 + 3/12 = 11/12

Example: You have the fractions 2/3 and 1/4

Select the denominator of the second fraction (4) and multiply the top and bottom of the first fraction (2/3) by that number:

4/4 x 2/3 = 8/12

Select the denominator of the first fraction (3) and multiply the top and bottom of the second fraction (1/4) by that number:

3/3 x 1/4 = 3/12

These two fractions (8/12 and 3/12) have common denominators - the number 12 on the bottom of the fraction.

Add these two new fractions together:

8/12 + 3/12 = 11/12

Subtracting FractionsSubtracting Fractions

To subtract two fractions with the same denominator, subtract the numerators and place that difference over the common

denominator.Look at a pizza cut into 8 pieces. Each piece is 1/8 of the pizza. Here we have 7 pieces or 7/8 of

the pizza.

Now take away 3/8 or 3 pieces.

We’re left with 4 pieces!

We just subtracted the numerators!Subtracting,

cont.

Subtracting FractionsSubtracting Fractions

To Subtract Fractions with different denominators:

• Find the Lowest Common Denominator (LCD) of thefractions

• Rename the fractions to have the LCD• Subtract the numerators of the fractions• The difference will be the numerator and the LCD will be

the denominator of the answer.• Simplify the Fraction

Click here to learn more about the LCD

LCDLCD

To find the least common denominator, list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. Example: Suppose we wanted to add 1/5 + 1/6. We would find the least common denominator as follows...

•First list the multiples of each denominator. Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,... Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...

•Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.

•Therefore, the least common denominator of 1/5 and 1/6 is 30.

To find the least common denominator, list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. Example: Suppose we wanted to add 1/5 + 1/6. We would find the least common denominator as follows...

•First list the multiples of each denominator. Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,... Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...

•Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.

•Therefore, the least common denominator of 1/5 and 1/6 is 30.

LCD, cont.

LCDLCD

For more LCD help click here!

Fraction Fun!Fraction Fun!

If you eat 1/4 of this pizza how much will

be left?

If you eat 2 pieces of this pizza and your friend eats 1 how many 10ths did you

eat altogether?

Answer

Fraction Fun!Fraction Fun!

All the children are going to share the pizza. We will cut enough pieces so each child can have

one, and the pieces should all be the same

size.

If 7 children shared the pizza equally, what

fraction of the pizza did each child get?

Answer

Fraction Fun!Fraction Fun!

Answers

1. What fraction of the circle is shaded green?

2. What fraction of the circle is shaded red?

3. What fraction would you write

for the color RED?

4. What fraction would you write

for the color green?

3/4 left 3/10 eaten

More Fun!

Back to

Question

1/71/7

More Fun!

Back to

Question

Back to

Question

1. 4/6 or 2/3

2. 2/3

3. 3/8

4. 1/8

Concept MapConcept Map

2005 Connecticut Mathematics 2005 Connecticut Mathematics Curriculum FrameworkCurriculum Framework

2005 Connecticut Mathematics 2005 Connecticut Mathematics Curriculum FrameworkCurriculum Framework

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

How are quantitative relationships represented by numbers?

Numerical and Proportional Reasoning – Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

How are quantitative relationships represented by numbers?

Standards 2.1 and 2.2

2.1 Students should understand that a variety of numerical representations can

be used to describe quantitative relationships.a. Represent numbers in expanded and regrouped forms in the base ten

place value system.b. Recognize that a fraction with the same numerator and denominator

represents the whole object or an entire set.c. Use fractions to measure and to represent points on a ruler or number

line.

2.2 Students should use numbers and their properties to compute flexibly and

fluently, and to reasonably estimate measures and quantitiesa. Use strategies that involve place value patterns and algebraic properties

to estimate, add and subtract.b. Approximate solutions to problems involving computation through the

use of efficient methods. c. Solve multiplication and division problems using rectangular arrays,

number patterns, skip counting and repeated addends.d. Compare fractions, identify equivalent fractions, add and subtract

fractions with like and unlike denominators using models and pictures.

2.1 Students should understand that a variety of numerical representations can

be used to describe quantitative relationships.a. Represent numbers in expanded and regrouped forms in the base ten

place value system.b. Recognize that a fraction with the same numerator and denominator

represents the whole object or an entire set.c. Use fractions to measure and to represent points on a ruler or number

line.

2.2 Students should use numbers and their properties to compute flexibly and

fluently, and to reasonably estimate measures and quantitiesa. Use strategies that involve place value patterns and algebraic properties

to estimate, add and subtract.b. Approximate solutions to problems involving computation through the

use of efficient methods. c. Solve multiplication and division problems using rectangular arrays,

number patterns, skip counting and repeated addends.d. Compare fractions, identify equivalent fractions, add and subtract

fractions with like and unlike denominators using models and pictures.

Grade 3Grade 3