Multiplying & Dividing Fractions & Mixed #'s

Multiplying & Dividing Fractions & Mixed #'s

Multiplying Fractions

• You do not need common denominators

• Multiply the numerators straight across the top

• Multiply the denominators straight across the bottom

• Simplify your answer

Multiplying Fractions

• Multiply 1 times 1. Then multiply 2 times 3. 

• Your numerator would be 1 and your denominator would be 6.

•  $\frac{1}{2}$  x  $\frac{1}{3}$   =  $\frac{1}{6}$  

• Since you cannot simplify, your answer is  $\frac{1}{6}$  

Multiple Choice

Solve: 

 $\frac{3}{5}$  x  $\frac{1}{2}$  

•  $\frac{4}{7}$  

•  $\frac{3}{10}$  

•  $\frac{2}{3}$  

Multiple Choice

Solve:

 $\frac{2}{3}$  x  $\frac{1}{5}$  

•  $\frac{3}{8}$  

•  $\frac{2}{3}$  

•  $\frac{2}{15}$  

Simplifying

• You can simplify BEFORE you multiply or after

• If you simplify before, you will look at the numerator & denominator diagonal to each other

• 
  
   $\frac{2}{7}$   x  $\frac{3}{8}$  
  

• The 2 and the 8 can be simplified by 2 since 2 goes into both 2 and 8 equally. The numerator of 2 becomes a 1 and the denomiator of 8 becomes 4. 

• You can now multiply  $\frac{1}{7}$   x   $\frac{3}{4}$  =  $\frac{3}{28}$  

Multiple Choice

 $\frac{1}{3}$   x   $\frac{3}{7}$   

•  $\frac{3}{24}$  

•  $\frac{3}{10}$  

•  $\frac{2}{4}$  

•  $\frac{1}{7}$  

Multiple Choice

 $\frac{5}{6}$  x  $\frac{3}{5}$  

•  $\frac{8}{30}$  

•  $\frac{1}{2}$  

• 2

•  $\frac{8}{11}$  

Dividing Fractions

• Remember KEEP, CHANGE, FLIP (KCF)

• You will KEEP the first fraction, CHANGE your operation to multiplication, and FLIP the second fraction.

• Flipping a fraction means you are using its "reciprocal"

•  $\frac{3}{4}\ \div\frac{5}{6}$ using KCF becomes  $\frac{3}{4}$  x $\frac{6}{5}$  

• Cross simplify and multiply straight across the top and bottom

Multiple Choice

Solve:

 $\frac{1}{4}\ \div\ \frac{1}{3}$  

•  $\frac{3}{4}$  

•  $\frac{1}{12}$  

• 1

•  $\frac{2}{7}$  

Multiple Choice

Solve:

 $\frac{1}{6}\div3$  

•  $\frac{1}{12}$  

•  $\frac{1}{2}$  

•  $\frac{1}{18}$  

• 2

Multiple Choice

Solve:

 $\frac{1}{2}\ \div\ \frac{3}{4}$  

•  $\frac{3}{8}$  

•  $\frac{3}{2}$  

•  $\frac{2}{3}$  

• 2

Multiplying Mixed Numbers

• Change mixed numbers into improper fractions

• For Example:

   $2\ \frac{2}{3}$  would be  $\frac{8}{3}$  

• Once all mixed numebrs are improper fractions, cross reduce if possible

• Multiply straight across the top and bottom

• Simplify

Multiplying Mixed Numbers

•  $4\ \frac{2}{3}\$  x  $\frac{4}{5}$  

•  $\frac{14}{3}$   x  $\frac{4}{5}$  =  $\frac{14\ x\ 4}{3\ x\ 5}$  =  $\frac{56}{15}$  

•  $\frac{56}{15}\ =\ 3\ \frac{11}{15}$  

Multiple Choice

Solve: 

Write your answer as a mixed number

 $5\ \frac{4}{5}\$  x  $1\ \frac{1}{3}$  

•  $5\ \frac{4}{15}$  

•  $7\ \frac{11}{15}$  

•  $6\ \frac{5}{8}$  

Multiple Choice

Solve:

Write your answer as a mixed number

 $3\ \frac{3}{4}$  x  $2\ \frac{2}{5}$  

•  $6\ \frac{6}{20}$  

• 3

• 9

•  $5\ \frac{5}{9}$  

Diving Mixed Numbers

• Change the mixed numbers into improper fractions

• 
  

   $2\ \frac{3}{7}$  would be  $\frac{17}{7}$  

• Keep the first fraction, Change the sign to multiplication, Flip the second fraction

• Cross reduce if possible 

• Multiply straight across the top and bottom

Dividing Mixed Numbers

•  $4\ \frac{2}{3}\ \div\ \frac{4}{5}$  

• Change the mixed number to improper then Keep, Change, Flip:

•  $\frac{14}{3}$  x  $\frac{5}{4}$  =  $\frac{70}{12}$  =  $5\ \frac{10}{12}$  =  $5\ \frac{5}{6}$  

Multiple Choice

Solve:
Write your answer as a mixed number

 $1\ \frac{6}{7}\div1\ \frac{1}{7}$  

•  $1\ \frac{6}{1}$  

•  $1\ \frac{5}{8}$  

• 1

•  $1\ \frac{6}{49}$  

Multiple Choice

Solve:
Write your answer as a mixed number:

 $1\ \frac{5}{9}\div\frac{7}{8}$  

•  $\frac{7}{8}$  

•  $\frac{1}{2}$  

•  $1\ \frac{7}{9}$  

Multiple Choice

 $\frac{1}{9}$  x  $\frac{1}{4}$  

•  $\frac{1}{36}$  

•  $\frac{1}{5}$  

•  $\frac{1}{13}$  

Multiple Choice

 $\frac{1}{8}$  x  $\frac{1}{8}$  

• 1

•  $\frac{1}{2}$  

•  $\frac{1}{64}$  

•  $\frac{1}{16}$  

Multiple Choice

 $\frac{1}{2}$  x $\frac{3}{8}$  

•  $\frac{3}{16}$  

•  $\frac{4}{10}$  

•  $\frac{3}{4}$  

• 2

Multiple Choice

 $-\frac{1}{4}$  x  $-\frac{1}{2}$  

•  $-\frac{1}{8}$  

•  $\frac{1}{6}$  

•  $\frac{1}{8}$  

•  $-\frac{1}{6}$  

Multiple Choice

 $-\frac{3}{10}\div\frac{1}{6}$  

• -1  $\frac{4}{5}$  

•  $-\frac{3}{10}$  

•  $\frac{1}{5}$  

•  $1\ \frac{3}{7}$  

Multiple Choice

 $\frac{1}{4}$  x  $-\frac{4}{5}$  

•  $-\frac{1}{5}$  

•  $-\frac{5}{9}$  

•  $\frac{1}{5}$  

•  $\frac{5}{9}$  

Multiple Choice

 $\frac{1}{6}\div-\frac{1}{3}$  

•  $\frac{1}{2}$  

•  $\frac{1}{18}$  

•  $-\frac{1}{18}$  

•  $-\frac{1}{2}$  

Multiple Choice

 $3\ \frac{1}{5}\div1\ \frac{1}{3}$  

•  $3\ \frac{1}{5}$  

•  $2\ \frac{2}{5}$  

• 
  3

•  $2\ \frac{1}{2}$  

Multiple Choice

 $3\ \frac{1}{3}\div2\ \frac{6}{7}$  

•  $5\ \frac{6}{7}$  

•  $1\ \frac{1}{7}$  

•  $1\ \frac{1}{6}$  

• No Solution

Multiple Choice

 $3\ \frac{3}{5}$  x  $5\ \frac{1}{5}$  

•  $15\ \frac{3}{25}$  

•  $8\ \frac{4}{5}$  

•  $18\ \frac{18}{25}$  

•  $\frac{1}{2}$  

Multiple Choice

 $4\ \frac{2}{5}$  x $\frac{1}{3}$  

•  $1\ \frac{7}{15}$  

•  $4\ \frac{2}{15}$  

•  $4\ \frac{1}{2}$  

•  $5\ \frac{2}{3}$  

Poll

Take-Aways from today: How do you feel about Multiplying & Dividing Fractions and Mixed Numbers?

• Terrible, Awful! Fractions are so confusing!

• I feel pretty good, just need some more practice

• I've got this! You could give me a quiz and I'd make a 100!