Math Sat Prep

7/27/2019 Math Sat Prep

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MATH SAT PREP:SHORTCUTS AND

TRICKS TO SAVE TIMEWHILE TESTING!Bell-works


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Shortcut #1:

Divisibility by 3 If the sum of the number is

divisible by 3, then that number is

also divisible by 3.

(Note): The word divisible

indicates that no remainder exists

in the answer to a divisionproblem.


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Example 1:

Is 1,545 divisible by 3?

Step 1: Add the digits of the number

1,545.1+5+4+5=15

Step 2: If the sum of th digits of any numberis divisible by 3, then that number is divisibleby 3. The sum of the digits of 1,545 is 15 and15 is divisible by 3 (15/3=5)


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Example 2:

Is 5,602 divisible by 3?

Step 1: Add the digits of 5,602

5+6+0+2=13

Step 2: If the sum of the digits of a numberis not divisible by 3, then that number is notdivisible by 3. The sum of the digits of 5,602is 13 and 3 does not go into 13 evenlywithout a remainder. Therefore, 5,602 is

NOT divisible by 3.


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EXERCISES:Determine if the number is divisible by 3.

Do so without actually dividing thenumber.

1. ) 7,032

2.) 15,363 3.) 3,510

4.) 70,153

5.) 6,231 6.) 3,031


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Shortcut #2:

Divisibility of numbers with a

repeating digit

Two numbers with repeating digits are

divisible if both the following twoconditions exist:

1.) The repeating digit of the dividend is

divisible by the repeating digit of the divisor

and

2.) The number of digits of the dividend is

divisible by the number of digits.


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DEFINITIONS: Note: The divisor is the number that is

divided into the dividend in the example,

153, 15 is the dividend and 3 is thedivisor. The answer to a division

problem is the quotient.


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Example: 444,444,444 is divisible by

which number?

A.) 44 B.) 22 C.) 2,222 D.) 222 E.) 555

Step 1: Exclude 555 because the digit of 4 in444,444,444 is NOT divisibly by the digit of 5in 555.

Step 2: Choices a, b, c, and d all meet thefirst condition, so now test the secondcondition. The number 444,444,444 has 9digits, therefore, choose an answer whose

number of digits will divide into 9. Thechoices of 44 and 22 each have two digits. 9is NOT divisible by 2, so 44 and 22 are notcorrect. The choice 2,222 has 4 digits and 9is not divisible by 4, so 2,222 is NOT thecorrect answer.


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Step 3: The choice 222 has 3 digits. 9

is divisible by 3, therefore 444,444,444

is divisible by 222. Thus the answer ischoice d.


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EXERCISES:1.) 5,555 is divisible by which number?

a) 111 b) 555 c)22 d)55

2.) 333,333 is divisible by which number?

a) 1,111 b)111 c) 3,333 d) 33,333

3.) 888,888,888 is divisible by which number?

a) 333 b) 44 c) 888 d) 2,222

4.)444,444 is divisible by which number?

a) 2,222 b) 22,222 c) 22 d)333

5) 666,666,666 is divisible by which number?

a) 3,333 b)333 c)6,666 d) 555

6) 999,999 is divisible by which number?

a) 333 b) 9,999 c) 44 d) 3,333


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Shortcut #3:

Cross-Multiply toCompare Two Fractions

Note: When comparing fractions, it is often not

necessary and too time consuming to findcommon denominators.

Multiply the denominator of each fraction by the

numerator of the other fraction in an upwarddirection. The fraction with the greateranswer above itself is the greater fraction.


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Example: Which fraction

is greater? 5 or 4

8 9 Step 1: Multiply the denominator of one

fraction by the numerator of the other

fraction. This multiplication must beperformed in an upwards diagonaldirection. Place each answer above thenumerator that was multiplied.

45 32

5 4

8 9


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Step 2: The fraction with the greater

number above itself is the greater

fraction. 5/8 is greater than 4/9because 45 is greater than 32.


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Exercises:

Which fraction is greater?(Hint: Use cross-multiplication)

1.) 2 / 3 or 3 / 4 2.) 7 /10 or 5 / 9

3.) 4 / 7 or 3 / 5

4.) 3 / 7 or 4 / 9


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Shortcut # 4:If each numerator is 1 less than

its denominator, then the

fraction with the greatest

numerator is the greatest

fraction.


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Example: Which fraction

is greatest? 1 2 3 4 52 3 4 5 6

Step 1: Notice that each numerator is 1less than the denominator. If this

pattern exists, then the greatest fraction

is the one with the greatest numerator.

5/6 has the greatest numerator,

therefore it is the greatest fraction.


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Exercises:Which fraction is

greatest?1.) 1 3 4 7

2 4 5 8

2.) 3 5 10 12

4 6 11 13

3. ) 11 1 9 2

12 2 10 3


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