6° LESSON 4: Addition and Subraction of Fractions

Lesson 4: Addition and Subtraction of Fractions

(Like and unlike fractions including mixed fractions)

Like and Unlike Fractions

• Like or similar fractions  are fractions with the same denominator. For example, $\frac{3}{7}$   and  $\frac{5}{7}$ are like fractions. 

• Unlike fractions are fractions with different denominators. For example,  $\frac{3}{5}$  and  $\frac{2}{3}$  are unlike fractions. 

How to Add or Subtract Like Fractions

• STEP 1: Simply add or subtract the numerators and copy the  same denominator

• STEP 2: Simplify your answer.

• Example 1:  $\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$  

• Example 2:   $\frac{4}{9}+\frac{5}{9}=\frac{9}{9}=1$   

More examples on addition of like fractions

• Example 3:  $\frac{1}{6}+\frac{2}{6}=\frac{3}{6}$  or  $\frac{1}{2}$  

• Example 4:  $\frac{8}{9}-\frac{2}{9}=\frac{6}{9}$  or  $\frac{2}{3}$  

• Example 5 :  $\frac{3}{4}+\frac{11}{4}-\frac{2}{4}$  or  $\frac{12}{4}$   $=3$  

Multiple Choice

Add: $\frac{3}{7}+\frac{4}{7}$  

•  $\frac{12}{7}$  

•  $1$  

•  $\frac{6}{7}$  

•  $\frac{9}{7}$  

Multiple Choice

Subtract: $\frac{12}{5}-\frac{2}{5}$  

•  $\frac{9}{5}$  

•  $\frac{7}{5}$  

•  $2$  

•  $\frac{3}{2}$  

Multiple Choice

Evaluate  $\frac{9}{10}\ +\frac{1}{10}-\frac{8}{10}$  

•  $\frac{2}{3}$  

•  $\frac{1}{5}$  

•  $\frac{1}{10}$  

•  $\frac{3}{4}$  

PROBLEM SET 1: Solve the following in your notebook. 

• 1.     $\frac{3}{4}-\frac{1}{4}$  

• 2.     $\frac{11}{7}+\frac{3}{7}$  

• 3.     $\frac{8}{15}-\frac{3}{15}$  

• 4.     $\frac{3}{5}+\frac{4}{5}-\frac{1}{5}$  

• 5.      $\frac{7}{8}-\frac{3}{8}$  

• 6.      $\frac{3}{11}+\frac{20}{11}$  

• 7.       $\frac{10}{7}-\frac{6}{7}$  

How to Add or Subtract Unlike Fractions

• STEP 1: Rewrite the two fractions as like fractions by finding the Least Common Multiple(LCM) of the two denominators.

• STEP 2: Perform the indicated operation.

• STEP 3: Simplify your answer when possible.

Example 1:   $\frac{2}{3}+\frac{1}{4}$  

• The denominators are  $3$   and  $4$  .  $LCM\left(3,4\right)=12$  

• Amplify  $\frac{2}{3}$  by   $4$  to get   $\frac{8}{12}$  . Why use  $4$  ?

• Amplify   $\frac{1}{4}$  by   $3$  to get   $\frac{3}{12}$ . Why  use  $3$ ?

• Rewrite $\frac{2}{3}+\frac{1}{4}=\frac{8}{12}+\frac{3}{12}\$  

• Solve and simplify: $\frac{8}{12}+\frac{3}{12}=\frac{8+3}{12}=\frac{11}{12}$  

A graphical illustration of    $\frac{2}{3}+\frac{1}{4}$  

Example 2:   $\frac{5}{8}-\frac{1}{6}$  

• The denominators are  $8$   and  $6$  .  $LCM\left(8,6\right)=24$  . Why?

• Amplify  $\frac{5}{8}$  by   $3$  to get   $\frac{15}{24}$ . Why use  $3$  ? 

• Amplify   $\frac{1}{6}$  by   $4$  to get   $\frac{4}{24}$ . Why  use   $4$  ? 

• Rewrite   $\frac{5}{8}-\frac{1}{6}=\frac{15}{24}-\frac{4}{24}$  

• Solve and simplify:   $\frac{15}{24}-\frac{4}{24}=\frac{15-4}{24}=\frac{11}{24}$  

Figure to Illustrate   $\frac{5}{8}-\frac{1}{6}$  

Example 3    $\frac{3}{8}+\frac{2}{5}$  

• The denominators are  $8$  and  $5$  . So  $LCM\left(8,5\right)=40$  . Why?

• Amplify  $\frac{3}{8}$  by  $5$  :   $\frac{15}{40}$  

• Amplify  $\frac{2}{5}$  by  $8$  :   $\frac{16}{40}$  

• Add:  $\frac{15+16}{40}\ =\frac{31}{40}\ \$  

Multiple Choice

 $\frac{2}{3}+\frac{1}{4}=?$  

•  $\frac{7}{12}$  

•  $\frac{11}{12}$  

•  $\frac{10}{11}$  

•  $\frac{1}{9}$  

Multiple Choice

 $\frac{5}{8}-\frac{3}{7}=?$  

•  $\frac{11}{56}$  

•  $2$  

•  $\frac{53}{87}$  

•  $\frac{11}{29}$  

Multiple Choice

 $\frac{7}{8}-\frac{5}{9}=?$  

•  $\frac{17}{72}$  

•  $\frac{1}{3}$  

•  $\frac{27}{50}$  

•  $\frac{23}{72}$  

Alternative: The Butterfly Method 

(By cross multiplication)

Use the Butterfly method:    $\frac{3}{5}+\frac{4}{7}$  

•   $\frac{3}{5}+\frac{4}{7}=\frac{3\cdot7+5\cdot4}{5\cdot7}=\frac{21+20}{35}$  

•  $=\frac{21+20}{35}\$  

•  $=\frac{41}{35}\ \ or\ 1\frac{6}{35}$  

Use the Butterfly method:    $\frac{3}{4}-\frac{5}{8}$  

•   $\frac{3}{4}-\frac{5}{8}=\frac{3\cdot8-4\cdot5}{4\cdot8}$  

•  $=\frac{24-20}{32}\$  

•  $=\frac{4}{32}\ \ or\ \ \frac{1}{8}$  

How to Add or Subtract Mixed Numbers?

• Convert the mixed numbers to improper fractions.

• Add or subtract the fractions. You might need to find the Least Common Multiple of denominators.

• Convert your answer back to a mixed number.

Illustrative Example 1:     $3\ \frac{2}{5}+4\ \frac{1}{5}$  

• Convert to improper fractions:  $3\ \frac{2}{5}+\ 4\ \frac{1}{5}\ =\ \frac{17}{5}+\ \frac{21}{5}$  

• Add the fractions:  $\frac{17}{5}+\frac{21}{5}=\frac{38}{5}$  

• Convert  back to mixed numbers:   $\frac{38}{5}=7\ \frac{3}{5}$  

Illustrative Example 2:     $3\ \frac{2}{3}+4\ \frac{1}{2}$  

• Convert to improper fractions:  $3\ \frac{2}{3}+\ 4\ \frac{1}{2}\ =\ \frac{11}{3}+\ \frac{9}{2}$  

• Add the fractions:  $\frac{11}{3}+\frac{9}{2}$ .  The   $LCM\left(3,2\right)=6$  .  We  amplify  $\frac{11}{3}$  by  $2$   and  also amplify   $\frac{9}{2}$  by   $3$  to get   $\frac{11}{3}+\frac{9}{2}=\frac{22}{6}+\frac{27}{6}=\frac{49}{6}$  

• Convert  back to mixed numbers:   $\frac{49}{6}=8\ \frac{1}{6}$ 

Illustrative Example 3:     $4\ \frac{2}{5}-\ \frac{7}{10}$  

• Convert to improper fractions:  $\ 4\ \frac{2}{5}-\frac{7}{10}\ =\frac{22}{5}-\ \frac{7}{10}\$  

• Subtract the fractions:  $\frac{22}{5}-\frac{7}{10}$ .  The   $LCM\left(5,10\right)=10$  .  We  only need to amplify  $\frac{22}{5}$  by  $2$  $\frac{22}{5}-\frac{7}{10}=\frac{44}{10}-\frac{7}{10}=\frac{37}{10}$  

• Convert  back to mixed numbers:   $\frac{37}{10}=3\ \frac{7}{10}$  

Example 4:     $3\ +\ 2\ \frac{2}{5}$  

• This problem can be added  directly without following the steps.

•  $3+\ 2\ \frac{2}{5}\ =\ 5\ \frac{2}{5}$  

• Let's model the problem in the next slide.

• The problem can be solved mentally. Just simply add the whole number parts and then just copy the fraction parts.

Example 4:  What about     $3\ -\ 2\ \frac{2}{5}$  ?

• This problem can't be added  directly without following the steps.

•  $3-\ 2\ \frac{2}{5}\ =\ 3-\ \frac{12}{5}$  

• Note that  $3-\frac{12}{5}=\frac{3}{1}-\frac{12}{5}$  

•  $\frac{3}{1}-\frac{12}{5}=\frac{15}{5}-\frac{12}{5}=\frac{3}{5}$  
  

• Let's model the problem in the next slide.

• The problem calls for subtraction. We take away  $2\ \frac{2}{5}$  from  $3$  . See figure.

• The answer is the unshaded part which is  $\frac{3}{5}$  

Multiple Choice

 $2\ \frac{3}{7}+1\ \frac{2}{7}\ =?$  

•  $2\ \frac{1}{7}$  

•  $3\ \frac{32}{77}$  

•  $3\ \frac{5}{7}$  

•  $4\ \frac{3}{7}$  

Multiple Choice

 $2\ \frac{2}{5}-\ 1\frac{2}{3}\ =?$  

•  $\frac{11}{15}$  

•  $\frac{13}{15}$  

•  $1\ \frac{1}{15}$  

•  $1\ \frac{3}{4}$  

Multiple Choice

 $3\ \frac{2}{3}-\ \frac{5}{8}\ =?$  

•  $\frac{11}{24}$  

•  $2\ \frac{1}{38}$  

•  $3\ \frac{1}{24}$  

•  $2\ \frac{23}{24}$  

End of Lesson 4

Please ask me if you have questions. If not, then proceed to Worksheet 4.