Subtracting to Solve Word Problems

Subtraction…….Order matters!!!!!!!! We are not able to rearrange the values to solve!

1245−312=¿7

12−29=¿

2136−836

=¿1336 - 3 = - 3

9310

Proper fractions may be written horizontally or vertically. We will use thevertical form to work with mixed numbers.

Three and one-fourth feet are cut off of aboard that is twelve and one-third feet long.

How long is the remaining part of the board?

Order matters!!!! Think about what the problem is saying as you begin to solve!

12-3

= 12= - 3

9

We are writing mixed number subtraction problems vertically for a reason!Practice this process correctly!

I bought of a gallon. How muchpaint do I have left?

2-

2-

2

M years younger than my dog.How old is my cat?

5- 2=

5-2

3 years old

Borrowing in Subtraction

• As you know, order matters in subtraction. Sometimes we have to borrow from the “first” whole number in order to subtract the fraction in the problem.

In our first examples, we will write a whole number as a mixed number.

Process Example

Jerri has read 14 books. Her brother has read4 ¾ books. How many more books has Jerri read?

14- 4 =

We will have to borrow “one” from our 14 so we can subtract the fraction. We willwrite this one that we borrow in fourths……we have to have a common denominator!

13- 4 =

9more books

If 3 ½ ounces of cough syrup is used from an 8 ounce bottle, howmuch cough syrup is left?

8 - 3 =

7 - 3 =

4ounces

A coach filled up a cooler with water until it weighed 8 pounds. After the game,the cooler weighed 3 pounds. How much lighter was the cooler after the game?

8- 3 =

7 - 3

4 pounds

What have we accomplished?

• In the first part of this lesson we have subtracted fractions from other fractions.

• We have also regrouped with whole numbers so we could subtract other fractions and mixed numbers.

Review and Extend

Yesterday we subtracted mixed numbers and regrouped with whole numbers.

Today we will extend this idea and regroup with mixed numbers. These problems have THREE sections:Problem Rewritten Problem (LCD) Regrouped Problem

Regrouping in Subtraction

• The next two examples will have mixed numbers that will be regrouped during the borrowing process.

• This involves several steps. We will discuss these steps, and you will also see a great shortcut for the new fraction in the problem!

• Be patient.

Process Example

Cora has 4 cups of flour. A recipe she is making requires 2 cups of flour. How much will she have left over?

4=- 2 =

4- 2

1cups

First we need a common denominator!!!

4=- 2 =

Now we can see that we have to borrow!

3 + =

4 + what we had

3

2

Let’s go back to the step where we regroup.

2

We borrow from the 4, leaving a whole number of 3.

3

(our 1) +

4 3

2+44

A full garbage truck weighed 6 ½ tons. After dumping the garbage, the truckweighed 4 tons. How much garbage was dumped?

6 =- 4 =

6 =- 4 = 4

5

Borrow from the 6

Borrow from the 6

The one we borrowed

The one we borrowed

1 tons

The combined length of two pieces of wood is 3 feet. If the longer pieceof wood is 2 ¾ feet, how long is the shorter piece?

3 =- 2 =

3 =- 2 =

- 2

2

of a foot

Group PracticeJesse bought 8/9 of a pound of chocolates and ate 1/3 of a pound. How much was left?

=

=

Shawn bought 5 yards of canvass. He used3 yards. How much was left?

5 =- 3 =

5 - 3

2

My dog lost 3 pounds. He had weighed 19 pounds. How much doeshe weigh now?

19- 3

Callie ran 8 miles on Sunday. Joel ran 7 miles.How much farther did Callie run?

8 =- 7 =

8 - 7 = 7

= 7

15

Please add this problem to your notes.

What did we accomplish?

• We solved three types of subtraction word problems.

• We practiced borrowing from a whole number as well as regrouping within a mixed number to successfully solve the problems!