Welcome to IRSC’s LIVE Virtual Lesson

on:

Adding and Subtracting Mixed Numbers (With and Without

Common Denominators)

Instructor: Lara DiMartino

How to participate in this session:

Raising your hand

What you will learn today:

1. How to change a mixed number to an improper fraction.

2. How to change an improper fraction to a mixed number.

3. How to add mixed numbers to whole numbers, mixed numbers, and proper fractions.

4. How to subtract mixed numbers from whole numbers, mixed numbers, and proper fractions.

Let’s compare terms…

• Proper fraction: ¾– The top is smaller than the bottom.

• Mixed Number: 2 ¼– There is a whole number with a proper

fraction.• Improper Fraction: 12/7–The top is larger than the bottom.

• Whole Number: 3–Multiples of 1. Ex: 1,2,3,4, 5 and so on.

Converting a Mixed Number to an Improper Fraction

3 1/4

1. Multiply the denominator by the whole number. 3 x 4= 12

2. Add this product to the numerator. This is our new numerator.

12 + 1= 133. Put the new numerator over the original

denominator. 13/4

Converting an Improper Fraction to an Mixed Number

12/91. Divide the denominator into the numerator. 12 ÷ 9 = 1 with a remainder of 3.2. The quotient 1 becomes the whole number.3. The remainder becomes the new

numerator. 1 3/?4. Keep the original denominator. 1 3/9

* Reduce when necessary! 1 1/3

Adding Mixed Numbers with Common Denominators

1. Add the numerators.

2. Keep the common denominator.

3. Add the whole numbers.

* Reduce when necessary!

Adding Mixed Numbers with Unlike Denominators

1. First, convert the mixed numbers to improper fractions.

2. Then find a common denominator.3. Rewrite the improper fraction using the new common

denominator.4. Add the numerators of the two new fractions. 5. Place that sum over the common denominator.6. Convert this improper fraction answer to a mixed

number. * Reduce when necessary!

Subtracting Mixed Numbers with Common Denominators

1. Subtract the numerators.

2. Keep the common denominator.

3. Subtract the whole numbers.

* Reduce when necessary!

Subtracting Mixed Numbers with Unlike Denominators

1. First, convert the mixed numbers to improper fractions.

2. Then find a common denominator.3. Rewrite the improper fraction using the new

common denominator.4. Subtract the numerators of the two new fractions. 5. Place that difference over the common denominator.6. Convert this improper fraction answer to a mixed

number. * Reduce when necessary!

Borrowing

1. Find a common denominator, if there isn’t one already.2. Rewrite the fraction using the new common

denominator.3. Borrow 1 from the whole number.4. Add the borrowed 1, in fraction form, to the fraction.5. Subtract the numerators of the two new fractions. 6. Place that difference over the common denominator.7. Subtract the whole numbers.

* Reduce when necessary!

Review!! Finding a Common Denominator

Example: 3/4 + 1/8 =

1. First, list the multiples of each denominator. 4: { 4, 8, 12, 16…}

8: { 8, 16, 24…}2. Then look for the least common multiple that

appears in each list. (This number (8) has to be evenly divisible by both original denominators (4 and 8).

Our new common denominator is : 8!!!!

Review 2: Finding a common denominator.

3/7 + 2/5

7: { 7, 14, 21, 28, 35…} 5: { 5, 10, 15, 20, 25, 30, 35…}

*Find the least common multiple. Both original denominators (7 and 5) must be able to

divide evenly into the new common denominator. 35 is our new common denominator!!!

Review!! Calculating the new numerator(s).

Example: 3/4 /8 8/4 = 2 THEN 2 X 3 = 6 6/8 + 1/8 /8 (Keep the same) + 1/8

1. Divide the original denominator (4) into the new one (8).

2. Take that quotient (2) and multiply it by the old numerator (3) . That product (6) is the new numerator.

Review 2: Calculating the new numerators.

4/7 ? /35 35/7= 5 then 5 X 4 = 20/35 -2/5 ? /35 35/5= 7 then 7 X 2 = - 14/35

Any Questions?

Type your questions in the chat window please for whiteboard

practice.

Print your participant window.

• Why? To email to your instructor as proof of attendance. To get 1 hour of credit towards your 10 hours this week.

• How? Place your cursor and left click your mouse on the participant window. On your keyboard, hold down the SHIFT and PRINT SCREEN keys. Then open a Word document and paste (Ctrl + V). Last, attach your word document to an email and send it to your instructor.

Final Comments

• This session has been recorded for you to play back and view at any time.

• If you have any questions regarding this topic at a later time, don’t hesitate to contact your instructor.

• Don’t forget to use the Smarthinking tutor feature within your class site. A tutor is available to you 24 hours a day.

Thank you for coming!

I hope you will take advantage of our future LIVE virtual lessons and will attend some of those sessions as well.

Have a great day!