MATH SAT PREP: SHORTCUTS AND TRICKS TO SAVE TIME WHILE TESTING!

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MATH SAT PREPSHORTCUTS AND TRICKS TO SAVE TIME
WHILE 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 division
  problem.

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Example 1 Is 1,545 divisible by 3?

• Step 1 Add the digits of the number 1,545.
• 154515
• Step 2 If the sum of th digits of any number is
  divisible by 3, then that number is divisible by
  3. The sum of the digits of 1,545 is 15 and 15
  is divisible by 3 (15/35)

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Example 2Is 5,602 divisible by 3?

• Step 1 Add the digits of 5,602
• 560213
• Step 2 If the sum of the digits of a number is
  not divisible by 3, then that number is not
  divisible by 3. The sum of the digits of 5,602
  is 13 and 3 does not go into 13 evenly without 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 the number.

• 1. ) 7,032
• 2.) 15,363
• 3.) 3,510
• 4.) 70,153
• 5.) 6,231
• 6.) 3,031

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Shortcut 2Divisibility of numbers with a
repeating digit

• Two numbers with repeating digits are divisible
  if both the following two conditions 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, 15?3, 15 is the
  dividend and 3 is the divisor. 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 in
  444,444,444 is NOT divisibly by the digit of 5 in
  555.
• Step 2 Choices a, b, c, and d all meet the first
  condition, so now test the second condition. The
  number 444,444,444 has 9 digits, therefore,
  choose an answer whose number of digits will
  divide into 9. The choices of 44 and 22 each
  have two digits. 9 is NOT divisible by 2, so 44
  and 22 are not correct. The choice 2,222 has 4
  digits and 9 is not divisible by 4, so 2,222 is
  NOT the correct 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 is choice d.

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EXERCISES

• 1.) 5,555 is divisible by which number?
• 111 b) 555 c)22 d)55
• 2.) 333,333 is divisible by which number?
• 1,111 b)111 c) 3,333 d) 33,333
• 3.) 888,888,888 is divisible by which number?
• 333 b) 44 c) 888 d) 2,222
• 4.)444,444 is divisible by which number?
• 2,222 b) 22,222 c) 22 d)333
• 5) 666,666,666 is divisible by which number?
• 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 3Cross-Multiply to Compare Two
Fractions

• Note When comparing fractions, it is often not
  necessary and too time consuming to find common
  denominators.
• Multiply the denominator of each fraction by the
  numerator of the other fraction in an upward
  direction. The fraction with the greater answer
  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 be performed in an upwards
  diagonal direction. Place each answer above the
  numerator 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 4/9 because 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 4If 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 5 2 3 4 5 6

• Step 1 Notice that each numerator is 1 less
  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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