Today we will solve simple problems involving the subtraction of fractions and mixed numbers

Today we will solve simple Today we will solve simple problems involving the problems involving the

subtraction of fractions and subtraction of fractions and mixed numbers.mixed numbers.

Solve=work outSolve=work out

Simple=easySimple=easy

In 3In 3rdrd and 4 and 4thth grade, you grade, you learned how to subtract learned how to subtract fractions like:fractions like:

2/3 -1/3= 1/32/3 -1/3= 1/3

5 5 2 2

6 6 6 6 =-

36

Parts of a FractionParts of a Fraction

3

4

= the number of parts

= the total number of parts that equal a whole

Parts of a FractionParts of a Fraction

3

4

= numerator

= denominator

Which number is circled?Which number is circled?

3

4 = denominator

Which number is circled?Which number is circled?

3

4

= numerator

¾ looks like¾ looks like

1/43

4 1/4

1/4

¾ looks like¾ looks like

1/43

4 1/4

1/4

¾ looks like¾ looks like

3

4

1/4

1/4

1/4

Mixed NumberMixed Number

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

= 1 34

What is the mixed What is the mixed number?number?

= 3 34

What is the mixed What is the mixed number?number?

= 4 34

What is the mixed What is the mixed number?number?

= 5 12

Common MultipleCommon Multiple

A number that is a A number that is a multiple of two or more multiple of two or more numbers.numbers.

Some multiples of 4 & 6

12, 24, 36

Least Common MultipleLeast Common Multiple

The smallest common The smallest common multiple of a set of two or multiple of a set of two or more numbers.more numbers.

6 = 6, 12, 18, 24, 30, 36

8 = 8, 16, 24, 32, 40, 48

Subtracting Like Subtracting Like DenominatorsDenominators

1/444

1/4

1/414

34

1/4

- =

Only subtract the numerators

Subtract these Subtract these fractionsfractions

1/5

1/51/5

1/5

45

15

- =35

Subtract these Subtract these fractionsfractions

1/4

1/4

1/434

14

- =24

It’s important to know how It’s important to know how to add fractions because…to add fractions because…

It will be on the CST’s!

How else will you know how to share your pizza with your techer?

Why else is it important?

Shortcut for Finding the Least Shortcut for Finding the Least Common Denominator or Least Common Denominator or Least

Common MultipleCommon Multiple

1319-

Check to see if the smaller denominator divides evenly into the larger denominator.If it does, use the larger denominator for your LCD or LCM.

3 will divide evenly into 9, so 9 is your LCD or LCM.

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Find the multiples of Find the multiples of each denominator.each denominator.

1= 5, 10, 15, 20, 25, 30

1= 10, 20, 30, 40, 50-

5

10

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Compare the lists of multiples. Compare the lists of multiples. Circle the common multiples Circle the common multiples between the two lists.between the two lists.

15 = 5, 10, 15, 20, 25, 301

10 = 10, 20, 30, 40, 50-

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Use the lowest common Use the lowest common multiple as the denominator.multiple as the denominator.

15 = 5, 10, 15 ,20 ,25 ,301

10 = 10, 20, 30, 40, 50-

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

This number is also called the This number is also called the least common denominator.least common denominator.

15 = 5, 10, 15 ,20 ,25 ,301

10 = 10, 20, 30, 40, 50-

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Rewrite the fractions using Rewrite the fractions using the least common denominator the least common denominator or least common multiple.or least common multiple.

151

10 -

10

10

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Find the equivalent fractions Find the equivalent fractions for 1/5 & 1/10 with 10 as the for 1/5 & 1/10 with 10 as the denominator.denominator.

151

10 -

10

10

You know that 1/10 is equal to 1/10 so

Put a 1 over theBottom 10.

1

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Find the equivalent fractions Find the equivalent fractions for 1/5 & 1/10 with 10 as the for 1/5 & 1/10 with 10 as the denominator.denominator.

151

10 -

10

10

To find the topnumber, ask yourselfwhat do you multiply

the 5 by to get 10.1

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Find the equivalent fractions Find the equivalent fractions for 1/5 & 1/10 with 10 as the for 1/5 & 1/10 with 10 as the denominator.denominator.

151

10 -

10

10

That’s right 2. Sinceyou are looking for

the equivalent fractionyou know the top

number must also bemultiplied by 2.

1x 2 =x 2 =

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Find the equivalent fractions Find the equivalent fractions for 1/5 & 1/10 with 10 as the for 1/5 & 1/10 with 10 as the denominator.denominator.

151

10 -

10

10

To find the top numberjust multiply 2 x 1 toget your equivalent

fraction.1x 2 =x 2 = 2

To Subtract Fractions With To Subtract Fractions With Unlike DenominatorsUnlike Denominators

Now just add the Now just add the numerators.numerators.1

51

10 -

10

10

Remember whensubtracting

fractions you never subtract the

denominators.

1x 2 =x 2 = 2

101

Subtract these FractionsSubtract these Fractions

1218-

Use the shortcut to find the

Least CommonDenominator

(LCD).

8

8

Subtract these FractionsSubtract these Fractions

1218-

Now find theequivalent

fractions for1/2 & 1/8.

8

8x 1 =

x 4 =

Ask what do you multiply 2 by to get 8and what do you multiply 8 by to get 8.

Subtract these FractionsSubtract these Fractions

1218-

Since you arewriting equivalent

fractions, nowmultiply the topnumbers by the

same number you did in the bottom.

8

8x 1 =

x 4 =x 1 =

x 4 =

Subtract these FractionsSubtract these Fractions

1218-

Now multiplyacross.

8

8x 1 =

x 4 =x 1 =

x 4 =

1

4

Subtract these FractionsSubtract these Fractions

1218-

Subtractyour new

numerators.

8

8x 1 =

x 4 =x 1 =

x 4 =

1

4

38

Subtract these FractionsSubtract these Fractions

2513-

Find the common

Multiples for5 and 3. WriteThis numberAs your newdenominator.

15

15

Subtract these FractionsSubtract these Fractions

2513-

Ask yourselfwhat you

multiply thebottom number

by to get 15.

15

15x 5 =

x 3 =

Subtract these FractionsSubtract these Fractions

2513-

Multiply thetop numberby the samenumber you

did in thebottom.

15

15x 5 =

x 3 =x 5 =

x 3 =

Subtract these FractionsSubtract these Fractions

2513-

Multiplyacross.

15

15x 5 =

x 3 =x 5 =

x 3 =

5

6

Subtract these FractionsSubtract these Fractions

2513-

Now subtractyour new

numerators.15

15x 5 =

x 3 =x 5 =

x 3 =

5

6

115

Subtract these FractionsSubtract these Fractions

5618-

24

24x 3 =

x 4 =x 3 =

x 4 =

3

20

1724

Subtract these FractionsSubtract these Fractions

2319-

9

9x 1 =

x 3 =x 1 =

x 3 =

1

6

59

Subtract these FractionsSubtract these Fractions

4523-

15

15x 5 =

x 3 =x 5 =

x 3 =

10

12

215

What did you learn?What did you learn?

•Solve=to work it out•Subtracting fractions with the same denominator I just subtract the numerator and the denominator stays the same.•What happens when I want to subtract fractions with different denominators?