Math Review for HESI A2 2015
Changing fraction to decimals can also be a method of comparing fractions by size. Which is larger 1/3 or 1/6
1/3 = 0.333 1/6 = 0.166
Change 2/5 to a decimal
2/5 = 2 divided by 5 5 goes into 2.0 o.4 times
Subtract 3 1/4 - 1 5/6
3 (1*3/4*3) - 1 (5*2/6*2) 3 3/12 1 10/12 = 1 12/12 = 12/12 + 3/12 = 15/12 = 2 15/12 2 15/12 - 1 10/12 = 1 5/12
Add 2 5/6 + 3 1/2
3 1/2 = 1*3/2*3 = 3 3/6 (add fractions and change to like fractions) 2 5/6 + 3 3/6 = 5 8/6 (add whole numbers) = 1 2/6 + 5 = 6 2/6 (change from improper fractions to whole/mixed number) = 6 1/3 (reduced)
Ratios are always expressed in lowest terms, the colon indicates division and therefore a ratio is a fraction
3:4 3 is the numerator and 4 is the denominator =3/4
Subtract 4/5 - 3/10
4/5 - 3/10 = 4*2/5*2 - 3/10 = 8/10 - 3/10 = 5/10 = 1/2
4/3 = 12/x
4x = 36 cross multiply (4x)/4 = 36/4 divide x = 36/4 x = 9 Check 4/3 = 12/9 4*9 = 12*3 36 = 36
Subtract the mixed numbers 5 - 2 3/8
5 = 4 8/8 (regroup 1 from the whole number) = 4 8/8 - 2 3/8 (subtract) = 2 5/8
Divide 6 by 2 2/5
6 = 6/1 2 2/5 = (2*5)/5 + 2/5 = 12/5 change to improper fraction (6/1) / (12/5) 6/1 * 5/12 (invert and multiply) = 5/2 = 2 1/2 (reduce)
Reduce 6/8
6/8 = 2*3*5/2*2*2 (list prime factors of both) = 3/2*2 = 3/4 (find common factors and cancel them out)
When changing percent to fractions, decimals and ratios, place the number over 100 and reduce to lowest terms. 8%
8/100 = 2/25 1/4% = 1/4 /100 = 1/4 * 1/100 = 1/400
To change to decimal, move the decimal point two places to the left (add zeros as needed) 25%
= 0.25
Solving for x in a ratio/proportion 12:9 = 8:x
= 12x = 72 move x to the left and isolate = (12x/12) = (72/12) multiply then divide x =6 Check 12:9 = 8:6 9*8 = 12*6 72 = 72
Dividing fractions, invert the fraction you are dividing by then multiply Divide 3/8 / 1/2
= 3/8 * 2/1 = 3/4 (use canceling to reduce)
When multiplying fractions you don't have to find a common denominator, just multiply across Multiply 2/3 * 3/8
= 6/24 = (6/6)/(24/6) reduce = 1/4
Change 1/4% to a decimal
=0.014
To change a ratio, change it to a fraction and reduce to lowest terms, then place numerator as the first term and denominator as second 10%
=10/100 = 1/10 = 1:10
Relating decimals and fractions Change 0.25 to a fraction in lowest terms
=25 move decimal 2 places =25/100 = (25/25)/(100/25) reduce =1/4
Changing % to fraction Change 75% to a fraction
=75/100 = (75/25)/(100/25) = 3/4
Change 75% to a decimal
=75/100 = 3/4 (divide numerator of fraction)
Mixed numbers Multiply 4 1/2 * 2 1/3
=9/2 * 7/3 change to improper fraction = 3/2 * 7/1 reduce by canceling = 21/2 simplify =10 1/2
Mixed Numbers "rules"
Add fractions first (change to like fractions) Add whole numbers If sum of fraction is an improper fraction change it to a whole or mixed number Add any whole numbers from fractions total to the whole number total Reduce to lowest terms
Add 5/8 + 7/8 =
Add numerators 5 + 7 = 12 = 12/8 Change to mixed # 12/8 = 1 4/8 (divide numerator by denominator = answer is a whole # and remainder b/c new numerator) Reduce 1 1/2 (divide the numerator and denominator by their greatest common factor)
Divide 5 1/3 by 4 1/2
Change to improper fraction and multiply whole number by the denominator then add the result to the numerator 5 1/3 = (5*3)/3 + 1/3 = 16/3 4 1/2 = (4*2)/2 + 1/2 = 9/2 =(16/3)/(9/2) = (16/3) * (2/9) = 37/27 = 1 5/27
Change a fraction to a decimal
Divide the numerator by the denominator and add zeros as needed. If numerator doesn't divide evenly into denominator carry division three places
Add 3/4 + 5/6 =
Find LCD: 3/4 = 3*3/4*3 = 9/12 5/6 = 5*2/6*2 = 10/12 9/12 + 10/12 = 1 7/12
Subtract 7/8 - 1/8
Subtract numerators then reduce 7 - 1/8 = 6/8 6/8 / 2/2 = 3/4
