CBEST Test Prep
CBEST Math Test Tips - Page four.
Mental Math Tips
Let's do 5 1/4 + 6 3/7. Since we are adding, I can add the whole numbers, 5 + 6 = 11 and set them aside. I now want to work on 1/4 + 3/7. I know that these are both less than 1/2, so I will not get another whole number. My answer will be 11 and something. But I can also narrow it further. I know it will be larger than 11 1/4 or 11 3/7. I can now eliminate all answer choices 11 3/7 or less, and 12 or larger. Consider the following choices:
a. 11 1/4
b. 11
c. 12 3/4
d. 11 19/28
e. 11 6/11
The obvious choice is d. It is between 11 and 12, and it cannot have a denominator of 11. Why ? I will let you figure that out because it will be a good exercise in logic.
The same holds true for subtracting. Get closer and closer to the boundary as you need to.
Let's try 10 3/5 + 12 7/9.
You should logically conclude it is greater than 22. Also, 3/5 + 7/9
will be more than 1 but less than 2. Why ? because 3/5 and 7/9 are both
more than 1/2, so they will add to a number greater than 1. It won't we
2 or more however, because both fractions are less than 1. We now know
the answer is more than 13, but less than 14. I can eliminate all
answers
23 or below, or 24 or above. I now need to work on getting a closer
answer
by looking at what 3/5 + 7/9 is. 3/5 is equal to 2.5/5 + 0.5/5 and 7/9
is equal to 4.5/9 + 2.5/9. The two fractions that represent halves,
2.5/5
and 4.5/9 are no longer needed because I added them to make another
whole
number. I now have 0.5/5 and 2.5/9. I should logically conclude it will
be somewhere near 1/3. The quickest way to get a common denominator is
multiply them both. Here it is 5 x 9 or 45. The denominator in the
answer
will be 45 or a number that will divide into it evenly. We should check
the answer choices to see if we can eliminate all but one.
a. 23 27/45
b. 23 17/45
c. 23 10/14
d. 23 2/3
e. 24 7/45
The answer is logically concluded to be b. Answer a has too high of a fraction. 27/45 is more than 1/2 and we are looking for something around a third. Answer c does not have a good denominator. 45 can not be divided by anything to get 14. Answer d is again too high, as is 24.
Subtracting is similar.
Now lets work on fractions, decimals, and percents.
Know how they all relate to each other.
1/4 = .25 = 25%
2/4 = 1/2 = .50 (or .5) = 50%
3/4 = .75 = 75%
*Note: All fourths are equal to .25 or 25%. Relate this to quarters
of a dollar.
1/3 = .33 = 33%
2/3 = .66 = 66%
*Note: This is slightly rounded off, but will suffice for multiple
choice tests.
1/5 = .20 ( or .2. The extra zero is not needed.) = 20%
2/5 = .40 = 40%
3/5 = .60 = 60%
4/5 = .80 = 80%
* Note: All fifths are equal to .20 or 20%.
1/8 = .125 = 12.5%
2/8 = 1/4 = .25 = 25%
3/8 = .375 = 37.5%
4/8 = 2/4 = .50 = 50%
5/8 = .625 = 62.5%
6/8 = 3/4 = .75 = 75%
7/8 = .875 = 87.5%
*Note: All eighths are equal to .125 or 12.5%
1/9=.1111...
2/9= .2222...
3/9=.3333...
* Note: Every 9th is a repeating decimal of what is on top! Round off
accordingly.
* Every 9th is worth about .11 or 11%
1/10 = .10 = 10%
2/10 = 2/5 = .20 = 20%
3/10 = .30 = 30%
.....And so on. Each tenth is equal to .10 or 10%
Have good working knowledge of the above.
[ Continue to CBEST Test Mental Math Page Five... ]
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