Adding and Subtracting Rational Numbers on a Number Line

​Adding and Subtracting Rational Numbers

November 2022​

Standard

NC.7.NS.1 - Apply and extend previous understanding of addition and subtraction to add and subtract rational numbers using the properties of operations, and describing real world contexts using sums and differences

Learning Objectives

• SWBAT add and subtract positive and negative integers

• SWBAT add and subtract rational numbers

Fill in the Blank

18 - (-12)

Fill in the Blank

-22 + -11

Fill in the Blank

20 + (-9)

Fill in the Blank

-25 - 10

​Adding/Subtracting Fractions

• Make sure your denominators are the same (if they are not, you will have to change them)

• Add the numerators and keep the like denominators​

~Cross multiply your denominators by your numerators

~Multiply your denominators to get like denominators​

​Multiply Denominators and Numerators

~Find your least common multiple​

​~Make sure to multiply your numerator by the same number you multiply the denominator by

​Least Common Denominator

​Methods for getting like denominators

​Adding/Subtracting Decimals

• Align your decimals so that they are stacked on top of eachother

• You may add zeros to fill in any empty spaces

• Add or subtract like you normally would (make sure you borrow if you need to)​

​Remember your integer rules for adding and subtracting when you are working with rational fractions and decimals

Multiple Choice

solve 

• - 2/9

• - 5/9 

• 2/9

• no there

Multiple Choice

What are the rules for subtracting integers?

• Change to multiplication and use the opposite of the second number.

• Change subtraction sign to addition and use the opposite of the second number.

• Find the opposite of both numbers and then add. 

• Subtract like normal and keep the larger sign. 

Multiple Choice

- ⁷/₈ - ¹/₂

• - ¹¹/₇

• - ⁸/₁₁

• -1 ³/₈

• -1 ¹/₈

Multiple Choice

-5.7 + 0.9

• 2.1

• -4.8

• -8.3

• -10.7

Multiple Choice

4/9 + (-2/3) = 

• 1 1/9

• -1 1/9

• 2/9

• -2/9

Multiple Choice

Find  -6.23 - 7.5

• 13.73

• 1.3

• -1.2

• -13.73

Multiple Choice

-3/7 + 4/5

• 43/35

• -13/35

• -43/35

• 13/35

Multiple Choice

⁸/₁₅  +  (-⁶/₁₅)

• 14/15

• -2/15

• 2/15

• -14/15

Multiple Choice

2.75 - (-1.25)

• 4

• -4

• 1.5

• -1.5

Multiple Choice

Rewrite the problem as addition.

-5.66 - (-4.1)

• 5.66 + (-4.1)

• -5.66 + 4.1

• -5.66 + (-4.1)

• -5.66 - 4.1

Multiple Choice

$$-\frac{3}{10}-\left(-\frac{2}{5}\right)$$  

• $$-\frac{1}{10}$$  

• $$\frac{1}{10}$$  

• $$\frac{7}{10}$$  

• $$-\frac{7}{10}$$