Operations with Fractions and Decimals

​Operations with Fractions, Decimals, and Percents

• ​Percents MUST be converted to fractions or decimals before performing any operations.

• ​Becareful with your decimal places when performing operations with decimals. ( It is best to use your calculator)

• ​When multiplying fractions (do not cross multiply), multiply numerators then multiply denominators and write your resulting fraction (sometimes stated as multiplying straight across). ALWAYS simplify.

​Operations with Percents

​Find 45% of 120.

• convert the % to a decimal

( move the decimal 2 places to the left and remove the % symbol)

• Of means multiply: multiply 0.45 by 120 to get 54

• 45% of 120 = 54

​24 is what percent of 168?

• Divide 24 by 168 (we divide to figure out what was multiplied) 24/168 = .15

• Move the decimal 2 places to the right and add the % symbol. 15%

• 24 is 15% of 168.

Multiple Choice

What is 25% of 80?

• 20

• 48

• 80

• 95

Multiple Choice

18 out of 23 is what percent ?

• 78.3%

• 91.3%

• 87.5%

• 29.5%

Multiple Choice

What percent is 34 of 46 ?

• 73.9%

• 59.8%

• 88.4%

• 33.3%

​Operations with Decimals

• Use your calculator for operations with decimals.

• Do not round too early in the problem. The calculator will carry all of the decimal places for you.

​How to round a decimal:

Multiple Choice

Which of the following numbers will NOT round to 26.36 when rounding to the nearest hundredth?

• 26.364

• 26.367

• 26.358

• 26.361

Multiple Choice

If 53.6 was rounded to the nearest tenths place, which of the following could have been the original number?

• 53.62

• 53.66

• 53.68

• 53.54

Multiple Choice

If 159.34 was rounded to the nearest hundredths place, which of the following could have been the original number?

• 159.337

• 159.345

• 159.333

• 159.331

​Operations with Fractions...

• When adding or subtracting fractions, You must have a common denominator.

• When multiplying fractions, multiply straight across

• When dividing fractions: Keep the first fraction. Change the operation to multiplication. Flip the second fraction and multiply.

• ALWAYS SIMPLIFY YOUR RESULTS!

Match

Match the following fraction to it's simplest form.

• 8/18

• 25/35

• 6/8

• 6/21

• 10/20

4/9

5/7

3/4

2/7

1/2

• 4/9

• 5/7

• 3/4

• 2/7

• 1/2

Adding fractions with a common denominator

• Add the numerators

• Keep the denominators the same

Multiple Choice

$$\frac{1}{6}+\frac{3}{6}=$$  

Do not simplify

• $$\frac{2}{6}$$  

• $$\frac{4}{6}$$  

• $$\frac{4}{12}$$  

Multiple Choice

Which of the following equations is true?

• $$\frac{4}{8}+\frac{2}{8}=\frac{6}{16}$$  

• $$\frac{5}{10}+\frac{2}{10}=\frac{7}{10}$$  

• $$\frac{2}{7}+\frac{2}{7}=\frac{5}{7}$$  

Multiple Choice

Is this a correct answer?

• Yes, the student correctly added.

• No, you cannot add unlike denominators

• No, 5 + 7 is not 12

• No, 2 + 3 is not 5

2 Ways to find a common denominator

• multiply the denominators together

• find the least common multiple

• sometimes the LCM is one of the denominators. check to see if one of the denominators will divide into the other. If it does, that is your least common multiple.

Multiple Select

Choose 2 possible common denominators for these fractions.

5/6 and 3/8.

• 24

• 18

• 48

• 36

• 56

Adding fractions with different denominators

• Multiply the denominators (to get a common denominator - QCD)

• Multiply the numerator of the first fraction by the opposite denominator

• Multiply the numerator of the second fraction by the opposite denominator

Multiple Choice

$$\frac{3}{4}+\frac{2}{5}=$$  

• $$\frac{6}{20}$$  

• $$\frac{6}{9}$$  

• $$\frac{19}{14}$$  

• $$\frac{23}{20}$$  

Multiple Choice

$$\frac{4}{5}+\frac{5}{6}=$$  

• $$\frac{9}{30}$$  

• $$\frac{25}{24}$$  

• $$\frac{49}{30}$$  

• $$\frac{9}{11}$$  

To Multiply Fractions - you do not need common denominators!!

• make sure you have two fractions

• if you have a whole number, make it a fraction by putting it over 1

• if you have a mixed number, convert it to an improper fraction

Multiple Choice

What is 1/6 x 2?

Do not simplify

• 2/6

• 8/12

• 12/6

Multiple Choice

What is 1/2 x 1/4?

• 1/6

• 1/8

• 2/8

• 2/6

​Dividing Fractions

Mr. Mefford

Match

Match the following fraction with the reciprocal

• 1/6

• 3/4

• 2/7

• 9/10

• 3/8

6

4/3

7/2

10/9

8/3

• 6

• 4/3

• 7/2

• 10/9

• 8/3

Multiple Choice

5/6 $$\div$$  3/4 =

Divide the fractions. Simplify the answer.

• 15/24

• 20/18

• 10/9

• 18/24

Multiple Choice

8/3 $$\div$$  5/4

Divide.

• 15/32

• 32/15

• 3/14

• 7/24