| Percent - a special type of portion | Percent Models | Ratios | | Relationships:decimal fractions, usual fractions, percent and ratio | rates | fast quiz |

Percent - a special type of fraction

0.25, 1/4, 25%

These expression tell us what portion of the square is coloured orange.

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The indigenous percent come indigenous the expression "per cent" and also literally means "a part of one hundred". A percent is a part, or fraction, the end of 100. For example:

100% | =100/100 | =1 | = 1.0 (decimal) | |

50% | = 50/100 | = 5/10 | = 1/2 | = 0.5 = 0.50 (decimal) |

25% | = 25/100 | = 5/20 | = 1/4 | = 0.25 (decimal) |

40% | = 40/100 | = 4/10 | = 2/5 | = 0.4 (decimal) |

5% | = 5/100 | = 1/20 | = 0.05 (decimal) | |

0.5% | = 5/1000 | = 1/200 | = 0.005 (decimal) |

We have the right to see that to create a percent together a fraction we express the percent together a portion with a denominator of 100. We might then be able to simplify the portion further.

For example, 75% = 75/100 = 3/4

To refer a fraction as a percent us must very first convert the portion into hundredths (in simple cases we have the right to do this through using tantamount fractions) and then replace "/100" by the percent "%" sign.

For example, 4/5 = 80/100 = 80%

We have the right to see that we express a percent as a decimal by separating by 100.

For example,

25% = 25/100 = 0.25 (twenty-five hundredths) |

47.3 % = 47.3/100 = 0.473 (forty seven hundredths and 3 thousandths) |

200% = 200/100 = 2 |

To express a decimal as a percent us multiply the decimal number by 100.

For example,

0.108 = 0.108 x 100 = 10.8% |

0.75 = .75 x 100 = 75% |

1.2 = 1.2 x 100 = 120% |

**Some percents expressed as fractions and also decimals**

| = 0.125 (decimal) | |

= 0.236 (decimal) | ||

= 0.333 (decimal, rounded to 3 decimal places) | ||

= 0.5 = 0.50 (decimal) | ||

= 0.667 (decimal, rounded come 3 decimal places) | ||

= 1.1 (decimal) | ||

= 1.5 (decimal) | ||

=2.0 (decimal) |

Example 1: 30 the end of 50 to apologize in a box are too bruised come sell. What percent the apples can not be sold?

Working Out | Thinking |

30 the end of 50 apples room bruised. To stand for 30/50 as a percent we need to discover out how numerous apples out of 100 room bruised. By identical fractions we know that 30 the end of 50 equates to 60 the end of 100, for this reason 60% the the apples are bruised. us could additionally say that, 3/5 the the apples are bruised 0.6 the the apples space bruised. |

Example 2: Ryan spent 25 minute in the bank, 11 minutes of i m sorry was spent waiting in a queue. What percent of time did he invest waiting in the queue?

Working Out | Thinking |

Ryan spent 11 minutes the end of 25 minutes waiting in a queue. To revolve this right into a percent we room asking, 11 out of 25 minutes equals how many minutes out of 100 minutes? We can see that 11 mins the end of 25 mins amounts to 44 mins the end of 100 mins by equivalent fractions (because we know 25 x 4 = 100) . We can say the Ryan spent 44%, 0.44 or 11/25 of his time in the financial institution waiting in a queue. |

Example 3: What percent is 7 cm of 20 cm?

Working Out | Thinking |

To find out what percent 7 the end of 20 is, we should ask: 7 out of 20 is how countless out of 100? 5 groups of 20 make 100, for this reason 7 out of 20 is 35 out of 100 (5 x 7 the end of 5 x 20). Therefore 7/20 amounts to 35%, or 0.35 if we stand for it as a decimal. |

Percent models

**Dual-scale number heat model**

We deserve to use the dual-scale number line, likewise called the proportional number line, to illustrate example 1 indigenous above.

Recall instance 1: 30 out of 50 to apologize in a box room too bruised to sell. What percent the apples cannot be sold? | |

Thinking | |

The left side of the number line listed below has a percent scale. The appropriate side the the number line has a number scale. We have the right to label each scale using the information we are offered in the problem. | We understand that there space 50 apples in total, ie. 50 apples equals 100% the the apples. We recognize that 30 out of the 50 apples space bruised and also we require to uncover what percent this is. In more complex problems this dual-scale number line is a great way that organising the information we are given and also to job-related out what details we should find. Once we have represented the trouble in this means we have the right to write a ratio equation straight from the number line. 30/50 = ?/100 By identical fractions we know that 30/50 = 60/100. (Or we could have just noticed that it is a "multiply by 2" relationship, therefore 30 x 2 = 60) Therefore 60% that apples room too bruised to sell. |

The dual-scale number line design is discussed further in the other pages of the Percent, Ratio and also Rates topic.

**Elastic tape measure model**

The ice cream measure version is a great linear model of percent. Teachers can quickly make this models utilizing a ruler, such as a 1 metre ruler, and elastic. The elastic demands to be marked with a percent scale. It can then be stretched to the wanted length.

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For example, what is 60% that 50?

To discover the answer us line increase the zeros that the ruler and the elastic. Us then stretch the elastic so the 100% present up through the whole amount, which in this situation is 50. We then look because that 60% ~ above the elastic and also read the equivalent amount ~ above the ruler. We deserve to see listed below that 60% that 50 is 30.

The intentionally is no to usage this design accurately. That is a great way of mirroring that percent always involves a proportional to compare of something to 100.

1 metre ruler Elastic |

By manipulating the tape measure, this model deserve to be offered for the 3 varieties of percent problems, debated in Percent Examples. Examples of which are,

What is 20% of 50?** What percent is 10 the 50? 30% of what number is 15?**

(Note: for a lesson, a teacher will require elastics tape procedures of miscellaneous lengths, because the elastic can only be extended - it cannot be shrunk).