Monday, Nov. 18, 2013

Warm-up (independent, level 0 noise):Please complete this in your journal below the CQ

Add or Subtract the following Fractions:

1. +2. -3. 1 -

Challenge Question: How does knowing part-to-whole relationships help you add and subtract fractions?

Directions: Please come in and get your journal. On your next blank page, write today’s date on the top line. Title this page ~ Adding and Subtracting Fractions.Below the date, write the Challenge Question.

75

71

54

32

31

51

Definition:A fraction is an ordered pair of whole numbers, the 1st one is usually written on top of the other, such as ½ or ¾ .

The denominator tells us how many congruent pieces the whole is divided into, thus this number cannot be 0.

The numerator tells us how many such pieces are being considered.

numerator

denominatorba

We need a common denominator to add

these fractions.

7, 14, 21, 28, 35…

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

We need a common denominator to add

these fractions.

7, 14, 21, 28, 35…

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

The first number IN COMMONthat appears on both lists

becomes the common denominator

x 7

x 7

X 5

x 5 15

7

15 + 7 = 2222

We need a common denominator to add

these fractions.

7, 14, 21, 28, 35, 42, 49, 56, 63

8, 16, 24, 32, 40, 48, 56, 64, 72

x 7

x 7

x 8

x 8 32

2132 + 21 = 53

53

Try These

A B

C D

Try These

A

B

C

D

1727

1920

109

1312

Subtracting Fractions

Subtraction

• Subtracting fractions begins exactly the same way as adding fractions.

• The first thing you have to do is figure out if you CAN subtract them as they are.

• If not, you will need to convert a denominator so you can.

Let’s do one together• 1 ½ - ¼• You can see that one of them needs to be

converted so you can subtract them.• What will the common denominator be?• ANSWER: 4

Step #1 Step #2

• Identify the common denominator.• 1 ½ - ¼ • ANSWER: 4

• Since ¼ already has a denominator of 4 you don’t need to change it.

• But ½ needs to be converted to 4’ths.

Step #2 (continued)

• How do you convert ½ into 4ths?• (what number) x 2 = 4?• ANSWER: 2• Now, multiply both the numerator (top

number) and the denominator (bottom number) by 2.

• 1 x 2 = 2 2 x 2 = 4

Step #3• So now ½ has been converted to 2/4.• Now we have: 1 2/4 – ¼• Go ahead and subtract ONLY the numerators.

What did you get?• ANSWER: 1 ¼

BORROWING!!!• Generally, borrowing is the most difficult thing

to do in subtracting fractions.• There are 4 simple steps to follow and it works

for ANY fraction in ANY problem.• Don’t worry, it’s easy once you learn the steps.

Here is the problem• Let’s say that you got a problem like this:

• 3 ¼ - 15/16• First step: They can’t be subtracted as they

are.• Second step: What is the common

denominator? ANSWER: 16• Third step: Convert a fraction.

Let’s go through it• With a common denominator of 4 we need to

figure out: (what number) x 4=16?• ANSWER: 4

• SO: 4 x 1 = 4 4 x 4 = 16

Oops! What’s this?• The problem now reads like this:

3 4/16 – 15/16

• Normally you would now subtract. The problem is that 4 – 15 would be a negative number. We can’t have that!

• THUS, BORROWING IS NEEDED!

Borrowing• In this problem:

3 4/16 – 15/16• Borrowing is having to increase the value or

amount of 4/16 so that it’s bigger than 15/16.• In other words, we need to make 4/16 bigger

so that we CAN subtract.

Here’s how to do it• 3 4/16 needs to be changed somehow.• We’re going to take 1 whole number from the 3 and

add it to 4/16.• Would you agree that:

2 + 1 4/16 = 3 4/16?

• NOW COMES THE TRICKY PART.

The tricky part• 2 + 1 4/16 needs to

be changed a bit before we can subtract from it.

• Lets take 1 4/16 and “fix” it.

• Because 16 is the common denominator we need to write 1 in 16ths.

• We can write 1 as:2/2 = 13/3 = 14/4 = 1

• And so forth up to:16\16 = 1

SO NOW:16 + 4 = 2016 16 16

Try These

A B

C

Try These

A

C

B14

512

781