Addition of Rational Numbers

​Fractions

&

Decimals

What you have already learned

about + & - numbers

works with

fractions & decimals

too!

- 2 + 1 = 1

*Negatives can be written in front because the entire fraction is on the left of zero

Multiple Choice

What is the first step in solving this problem? 
⅘ + ½ =

• Add the top parts of the fraction

• Rewrite the fractions in the simplest form. 

• Find a common denominator. 

• Make each fraction into an improper faction. 

Multiple Choice

What is the least common denominator for 1/3 and 3/4?

• 6

• 4

• 3

• 12

Match

Match the following with their equivalent common denominators.

• $$\frac{1}{2\ }+\frac{2}{5}$$

• $$\frac{2}{3}+\ \frac{5}{6}$$

• $$\frac{1}{3}+\frac{4}{5}$$

• $$\frac{7}{8}+\ \frac{1}{2}$$

• $$\frac{5}{9}+\frac{5}{6}$$

• $$\frac{5}{10}+\frac{4}{10}$$

• $$\frac{4}{6}+\frac{5}{6}$$

• $$\frac{5}{15}+\ \frac{12}{15}$$

• $$\frac{7}{8}+\frac{4}{8}$$

• $$\frac{10}{18}+\frac{15}{18}$$

​​Common denominators are still needed when fractions contain negatives

• Rewrite using the least common denominator

• Add the numerators

• Keep the common denominator

-16 + 5 =

6

Type answer on the next slide

Dropdown

$$-\frac{16}{6}+\frac{5}{6}=$$ ​ ​ ​

Select answer

then reduced in simplest form = ​ ​​

Select answer

Multiple Choice

Add

$$-\frac{7}{8}+\frac{1}{4}=$$  

• $$-\frac{5}{8}$$  

• $$\frac{5}{8}$$  

• $$-\frac{6}{4}$$  

• $$\frac{6}{4}$$  

Multiple Choice

$$2+\left(-\frac{7}{2}\right)$$  

HINT: How many halves are in 2 whole pizzas = ?

rewrite the 2 wholes as ?/halves

Now you have common denominators!

• $$1\ \frac{1}{2}$$  

• $$2\ \frac{1}{2}$$  

• $$-1\ \frac{1}{2}$$  

• $$-2\ \frac{1}{2}$$  

Multiple Choice

Following the integer rules, would you add or subtract the fractions?

HINT: Mean Girls

• add, the answer would be positive

• add, the answer would be negative

• subtract, the answer will be positive

• subtract the answer will be negative

​Decimals follow to the same negative patterns too!

​Type answer on the

next slide

Dropdown

2.7 + ( -3.4 ) = ​ ​

Select answer

Multiple Choice

Add

$$−12.5+15.3$$  

• -27.8

• 27.8

• -2.8

• 2.8

Multiple Choice

Add

$$−8.15+(−4.3)$$  

• -2.1

• 2.1

• -12.45

• 12.45

Fill in the Blank

Add:

$$\ \ -6.8\ +\ \left(-1.9\right)\ =\$$  

​Adding Rational Numbers

​Rewrite the fraction as a decimal.

​Same signs. Add.

​Check the signs of the original numbers.

Dropdown

All fractions are ​

Select answer

Match

Match the following

• $$\frac{1}{2}$$

• $$\frac{1}{3}$$

• $$\frac{2}{3}$$

• $$\frac{1}{4}$$

• $$\frac{3}{4}$$

0.5 or 50%

0.333333.... or 33.33..%

0.6666666... or 66.66...%

0.25 or 25%

0.75 or 75%

• 0.5 or 50%

• 0.333333.... or 33.33..%

• 0.6666666... or 66.66...%

• 0.25 or 25%

• 0.75 or 75%

Match

Match the following

• $$\frac{1}{5}$$

• $$\frac{3}{5}$$

• $$\frac{2}{5}$$

• $$\frac{4}{5}$$

• $$\frac{1}{8}$$

0.2 or 20%

0.6 or 60%

0.4 or 40%

0.8 or 80%

0.125 or 12.5%

• 0.2 or 20%

• 0.6 or 60%

• 0.4 or 40%

• 0.8 or 80%

• 0.125 or 12.5%

Match

Match the following

• $$\frac{3}{8}$$

• $$\frac{5}{8}$$

• $$\frac{7}{8}$$

• $$\frac{1}{10}$$

• $$\frac{3}{10}$$

0.375 or 37.5%

0.625 or 62.5%

0.875 or 87.5%

0.1 or 10%

0.3 or 30%

• 0.375 or 37.5%

• 0.625 or 62.5%

• 0.875 or 87.5%

• 0.1 or 10%

• 0.3 or 30%

Multiple Choice

Change 5/6 to a decimal.

• .8333...

• .56

• .65

• 1.2

Fill in the Blank

$$Convert\ this\ fraction\ to\ a\ decimal:\ \ \ \frac{3}{7}\$$  

* Round to the HUNDREDTHS place

Multiple Select

$$5.5\ +\ 3\ \frac{1}{4}=$$  

CHOOSE 2 ANSWERS

• 8.75

• $$8\ \frac{3}{4}$$  

• 8.6

• $$8\ \frac{3}{5}$$  

• None of these

Multiple Select

$$-2\ \frac{3}{4}\ +\ \left(-0.5\right)$$  

CHOOSE 2 ANSWERS

• $$3\ \frac{1}{2}$$  

• $$-3\ \frac{1}{4}$$  

• 3.5

• -3.25

Multiple Choice

Find the sum: $$(-5.2)+1\frac{51}{100}$$  

• $$-3.69$$  

• $$-3.71$$  

• $$6.71$$  

• $$-4.31$$  

Multiple Choice

Find the sum: $$1\frac{1}{8}+\left(-3.5\right)$$  

• $$-2\frac{3}{8}$$  

• $$-4\frac{5}{8}$$  

• $$2\frac{3}{8}$$  

• $$-\frac{1}{8}$$  

Poll

How confident do you feel about adding rational numbers?

• I am a ROCKSTAR

• I am pretty good

• I am okay

• Help me. Please