Relate Fractions, Decimals, and Percents

Lesson 6: Fraction, Decimals and Percentages

A percent is a fraction whose denominator is  $100$  .

•  $50\%\ =\ \frac{50}{100}\ \ or\ \ \frac{1}{2}$ 

•  $25\%\ =\ \frac{25}{100\ }\ \ or\ \ \frac{1}{4}$  

•  $20\%\ =\frac{20}{100}\ \ or\ \ \frac{1}{5}$  

•  $28\%\ =\ \frac{28}{100}\ or\ \ \frac{7}{25}$  . Why? 

•  $68\%\ =\ \frac{68}{100}\ or\ \ \frac{17}{25}$  . Why?

Percent Grid

• The grid has a total of  $100$  small squares.

• There are  $43$   shaded small squares on the grid. This represents  $43\%$  

Percent Grid

• What percent is shown in the figure?

• Answer:  $77\%$  

Percent Grid

• What percent is shown in the figure?

• Answer:   $84\%$  

Percent Grid

• What percent is shown in the figure?

• Answer:  $47\%$  

SOME TRICKS

• When the number of squares is not equal to 100, amplify the fraction corresponding to the shaded part so that the denominator becomes  $100.$  

• An example:   $\frac{19}{20}\ =\frac{19\cdot5}{20\cdot5}\ =\frac{95}{100}=95\%$  

The case of having only 50 squares

• What percent is shaded?

• Answer:   $\frac{15\ \cdot2}{50\ \cdot2}=\frac{30}{100}\ =\ 30\%$  

The case of having only 50 squares.

• What percent is shaded?

•  $\frac{10\cdot2}{50\cdot2}=\frac{20}{100}\ =\ 20\%$  

The case of having only 25 squares.

• What percent is shaded?

•  $\frac{5\cdot4}{25\cdot4}=\frac{20}{100}\ =\ 20\%$  

The case of having only 20 squares.

• What percent is shaded?

•  $\frac{5\cdot5}{20\cdot5}=\frac{25}{100}\ =\ 25\%$  

The case of having only 10 squares.

• What percent is shaded?

•  $\frac{5\cdot10}{10\cdot10}=\frac{50}{100}\ =\ 50\%$  

The case of having only 5 squares.

• What percent is shaded?

•  $\frac{3\cdot20}{5\cdot20}=\frac{60}{100}=\ 60\%$  

A glass holds 20 ml of juice . If there are  8 ml of juice remaining then what percent is this?

• Answer:   $40\%$  .  How?

What percent of the class are boys? girls?

• Boys = $40\%$  

• Girls =  $60\%$  

• What percent of the figure is shaded?

Fill in the Blanks

What percent is shaded in the figure?

Fill in the Blanks

What percent is shaded in the figure?

Fill in the Blanks

What percent is shaded in the figure?

Fill in the Blanks

What percent is shaded in the figure?

Fill in the Blanks

What percent is shaded in the figure?

Relationship between Fraction, Decimal and Percent

• A fraction can be written as a decimal and as a percent.

•  $35\%\ =\frac{35}{100}\ \left(or\ \frac{7}{20}\right)\ =\ 0,35$  

Relationship between Fraction, Decimal and Percent

•  $28\%\ =\frac{28}{100}\ \left(or\ \frac{7}{20}\right)\ =\ 0,28$  

•  $90\%\ =\frac{90}{100}\left(or\ \ \frac{9}{10}\right)\ =0,9$  

• What fraction is shaded?

• What percent of the whole figure is shaded?

Multiple Choice

$$75\%$$  = ?

• $$\frac{75}{100}\$$  

• $$\frac{7}{100}$$  

• $$\frac{5}{100}$$  

Multiple Choice

$$97\%$$  = ?

• $$\frac{9}{100}\$$  

• $$\frac{16}{100}$$  

• $$\frac{97}{100}$$  

Multiple Choice

What does this statement mean?  "  $$80\%$$  of the whole Antofagasta already got the Covid-19 vacccine"

• $$8$$ people already got the vaccine

• $$80$$   people already got the vaccine

• $$80\ \ out\ of\ 100$$  people already got the vaccine
  

Multiple Choice

Write   $$86\%$$  as a decimal.

• $$86$$  
  

  
  

• $$0,86$$   

• $$8,6$$  
  

Multiple Choice

Write   $$56\%$$  as a fraction in simplest form. 

• $$\frac{11}{25}$$  
  

  
  

• $$\frac{14}{25}$$   

• $$\frac{17}{25}$$  
  

Multiple Choice

Write  $$\frac{7}{25}$$  as a decimal.

• $$0,28$$  
  

  
  

• $$0,14$$   

• $$0,7$$  
  

Multiple Choice

Write  $$\frac{7}{25}$$  as a percent.

• $$28\%$$  
  

  
  

• $$14\%$$   

• $$7\%$$  
  

RULE OF THREE

• When the denominator cannot be amplified to  $100$  by multiplying a certain number,  then an alternative method is the RULE OF THREE.

• The RULE OF THREE is explained in the next slide. 

What percent is shaded?

• The fraction shaded is  $\frac{5}{8}$ . What percent does this represent?  It is   $62,5\%$  . How?

What percent is shaded?

• The fraction shaded is  $\frac{5}{6}$ . What percent does this represent?  It is   $83,3\%$  . How?