6th Grade Math Textbook, Fundamentals

Think

1 is close to the estimate of 1.

The answer is reasonable.

1

8

 &KDSWHU

5-7

Add and Subtract Mixed Numbers

Objective To add and subtract positive and negative mixed numbers

A company had a profit of $4 million in its first year. The

company had a loss of $3 million in its second year. How

much did the company gain or lose in all in its first 2 years?

To find the total profit or loss, add 4 ( (^3) ).
First estimate the sum by rounding to the nearest integer.
4  4  3 3 4 (3)  1

To add mixed numbers, rename each with a common denominator if necessary.

• Find the LCD of the fraction parts. Multiples of 4: 4, 8, 12...
  Multiples of 8: 8, 16, 24...
  The LCD of and is 8.


• Rename the fraction part of 4 using the LCD.  , so 4  4


• Add the mix numbers.
  First add the fraction parts.
  Then add the integer parts.
  Use the same rules as for adding integers.


• Express the sum in simplest form.


• Check by comparing the answer to your estimate.

So the company gained $1 million.

To write a sum in simplest form, sometimes you

need to rename the sum when the fraction part

is greater than or equal to 1.

Simplify the sum:  5 ( (^3) ) 8

• Divide the fraction part by the GCF.


• Then rename the fraction part as a
  mixed number by dividing the numerator
  by the denominator. Write the quotient as
  the integer part and the remainder over
  the divisor as the fraction part.


• Add the renamed fraction part to the
  original integer part, and write the sum.

So  8 in simplest form is 9.

To subtract a fraction from an integer or a mixed number,

rename the integer or mixed number and subtract.

1

8

1

4

1

2

18

12

18

12

11

12

7

12

1

8

2

8

1

4

2

8

1 • 2

4 • 2

1

4

1

8

1

4

1

8

1

4

1

8

1

4

4

( (^318) )
1
4 4
( (^3) )
118 simplest form
1
8
2
8
 8  8  8 Divide by 6, the GCF of
18 and 12.
3
2
18  6
12  6
18
12
 2
1
3
 1

R
 3
2
 23  (^112)
 8 ( (^121) ) 921 Add the integer and the
renamed fraction part.