Fracons, Decimals, Percent and Raos

Fracons, Decimals, Percent and Raos

Fractions / Rational Numbers mn, where m and n are integers and n ≠0 , is called a rational number

Reducing

To reduce a rational number to the lowest terms, divide the numerator and the denominator by the greatest common factor (GCF).
Example 1:
a) 1624=16÷ 824 ÷ 8=23
b) -9-36=936=9 ÷ 936 ÷ 9=14
c) 21-35=-2135=-21 ÷ 735 ÷ 7=-35
16: 1,2,4,8,16
24:1,2,3,4,6,8,12,24
GCF(16,24)=8

Converting to Decimal

To convert a rational number into a decimal, divide the numerator by
the denominator.
Example 2:
a) 1624=0.666667..=0.67
b) -9-36=0.25
c) 21-35=-0.6
Terminating Decimal: 0.25 is a terminating is decimal
Repeating Decimal: 2611=2.36363636… is repeating decimal.
It does not terminate.
Convert a decimal to fraction (terminating decimals)
1. Place the number in the decimal, written as a whole number, in the numerator of the fraction.
2. Count the number of decimal places and add that many zeros to the 1 in the denominator
3. Recue to lowest terms

Example 3:
a)-0.4=-410=-25
b)0.125=1251000=18
c)-0.08=-8100=-8 ÷ 4100 ÷ 4=-225

Percent

Percent means per hundred.

Convert percent to decimal

To convert a percent to a decimal, divide the percent by 100%
Or
Move the decimal place two places to the left.
Example 4:
a) 65%=65%100%=65100=0.65
OR
65%=65.0%=0.65
b)0.5%=0.005 OR0.5100=0.005

Convert percent to a fraction

1. Remove the percent sign and make a fraction with the percent as the numerator and 100 as the denominator
2. Simplify the fraction (reduce to lowest terms)
Example 5:
a) 65%=65100
b) 0.5%=0.5100

Ratio

A ratio is the comparison of quantities with the same units
Example 6: Write each ratio as a fraction, in lowest terms.
a) 1_4=14
b) 20_12=2012=53

Example 7: Write each ratio as a percent
a) 1_4=1/4
=0.25 ← multiply by 100% or move the decimal place two anits to the right
=0.25 ×100%
=25%
OR
14=1 ×254 ×25
=25100
=25%
OR
14=14×100%
=100%4
=25%
b)20:12=2012
=53
=1.666…
=166.7%