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?

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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?