Explain , equivalent fractions, least common denominator

Equivalent fractions are those fractions that when simplified, are the same.  They reduce to the same fraction in their simplest form.

For example,  12/15 and 24 /30  are equivalent fractions.  They both reduce to 3/5 in their simplest form.

Least common denominator: it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.  

For example, if you have 3/5 + 1/4 and want to add them, you need to get a common denominator

3/5 = 6/10 = 9/15=12/20

1/4 =2/8=3/12 =4/16=5/20

We can use equivalent fractions to help us find the common denominator of 20

replace 3/5 with 12/20 and 1/4 with 5/20  

3/5 + 1/4 = 12/20 + 5/20 = 17/20

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.