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

MATH SAT PREP: SHORTCUTS AND TRICKS TO SAVE TIME WHILE TESTING!. Bell-works. Shortcut #1: Divisibility by 3. If the sum of the number is divisible by 3, then that number is also divisible by 3.

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

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  1. MATH SAT PREP:SHORTCUTS AND TRICKS TO SAVE TIME WHILE TESTING! Bell-works

  2. 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.

  3. 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 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 (15/3=5)

  4. 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 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.

  5. 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

  6. Shortcut #2:Divisibility 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. Shortcut #3:Cross-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.

  12. 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

  13. 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.

  14. 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

  15. Shortcut # 4:If each numerator is 1 less than its denominator, then the fraction with the greatest numerator is the greatest fraction.

  16. 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.

  17. 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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