How to Divide and Multiply by Negative Numbers

Step-by-Step Guide

1. 1

   Step 1: Divide a positive number by a negative number.

   To do this, divide the integers as usual, then place a negative sign in front of the quotient.
   
   A positive number divided by a negative number is always negative.
   
   This also is the rule when dividing a negative number by a positive number.For example:10÷5=2{\displaystyle 10\div 5=2}10÷−5=−2{\displaystyle 10\div
   -5=-2}−10÷5=−2{\displaystyle
   -10\div 5=-2}
2. 2

   Step 2: Divide a negative number by a negative number.

   To do this, divide the integers as usual, and ignore the negative signs.
   
   A negative divided by a negative always equals a positive.For example:10÷5=2{\displaystyle 10\div 5=2}−10÷−5=2{\displaystyle
   -10\div
   -5=2} , To do this, divide the numbers as usual, then add a negative sign to the quotient.
   
   A positive number divided by a negative number will always be negative, regardless of whether the number is a whole number or a fraction.
   
   The same is true when dividing a negative number by a positive number.
   
   Remember that dividing by a number is the same as multiplying by its reciprocal.For example:58÷−4{\displaystyle {\frac {5}{8}}\div
   -4}=58÷−41{\displaystyle ={\frac {5}{8}}\div {\frac {-4}{1}}}=58×−14{\displaystyle ={\frac {5}{8}}\times {\frac {-1}{4}}}=−532{\displaystyle ={\frac {-5}{32}}} , To do this, divide the numbers as usual, and ignore the negative signs.
   
   A negative number divided by a negative number will always be positive, regardless of whether the number is a whole number or a fraction.
   
   Remember that dividing is the same as multiplying by the reciprocal.
   
   For example:−58÷−4{\displaystyle {\frac {-5}{8}}\div
   -4}=−58÷−41{\displaystyle ={\frac {-5}{8}}\div {\frac {-4}{1}}}=−58×−14{\displaystyle ={\frac {-5}{8}}\times {\frac {-1}{4}}}=532{\displaystyle ={\frac {5}{32}}} , To do this, multiply the integers as usual, then add a negative sign to the product.
   
   A positive number multiplied by a negative number is always negative.For example:10×5=50{\displaystyle 10\times 5=50}−10×5=−50{\displaystyle
   -10\times 5=-50}10×−5=−50{\displaystyle 10\times
   -5=-50} , To do this, multiply the integers as usual, and ignore the negative signs.
   
   A negative number multiplied by a negative number is always positive.For example:10×5=50{\displaystyle 10\times 5=50}−10×−5=50{\displaystyle
   -10\times
   -5=50} , To do this, multiply the numbers as usual, then add a negative sign to the product.
   
   A positive number times a negative number will always be negative, regardless of whether the number is a whole number or a fraction.
   
   For example:58×−4{\displaystyle {\frac {5}{8}}\times
   -4}=58×−41{\displaystyle ={\frac {5}{8}}\times {\frac {-4}{1}}}=−208{\displaystyle ={\frac {-20}{8}}} , To do this, multiply the numbers as usual, and ignore the negative signs.
   
   A negative number times a negative number will always be positive, regardless of whether the number is a whole number or a fraction.
   
   For example:−58×−4{\displaystyle {\frac {-5}{8}}\times
   -4}=−58×−41{\displaystyle ={\frac {-5}{8}}\times {\frac {-4}{1}}}=208{\displaystyle ={\frac {20}{8}}} , 224÷−7{\displaystyle 224\div
   -7} Remember that a positive number divided by a negative number will equal a negative number.
   
   Since 224÷7=32{\displaystyle 224\div 7=32}, you know that 224÷−7=−32{\displaystyle 224\div
   -7=-32}. , A peregrine falcon can dive (lose height) at a rate of 320 km/hr.
   
   Assuming it can sustain this rate indefinitely, how long would it take a peregrin to reach a height of
   -240 km? Remember that a negative number (-240km) divided by a negative number (-320km/hr) will equal a positive number (number of hours).
   
   Since 240÷320=.75{\displaystyle 240\div 320=.75}, you know that −240÷−320=.75{\displaystyle
   -240\div
   -320=.75}.
   
   So the falcon would take .75 hours, or about 45 minutes, to dive 240 km. , 710÷−6{\displaystyle {\frac {7}{10}}\div
   -6} Remember that a positive fraction divided by a negative number will equal a negative number.
   
   Since 710÷6=710×16=760{\displaystyle {\frac {7}{10}}\div 6={\frac {7}{10}}\times {\frac {1}{6}}={\frac {7}{60}}}, you know that 710÷−6=−760{\displaystyle {\frac {7}{10}}\div
   -6={\frac {-7}{60}}}. , −56÷−3{\displaystyle {\frac {-5}{6}}\div
   -3} Remember that a negative fraction divided by a negative number will equal a positive number.
   
   Since 56÷3=56×13=518{\displaystyle {\frac {5}{6}}\div 3={\frac {5}{6}}\times {\frac {1}{3}}={\frac {5}{18}}}, you know that −56÷−3=518{\displaystyle {\frac {-5}{6}}\div
   -3={\frac {5}{18}}}. , Jason spends 5 dollars on donuts every morning.
   
   How much money will he lose on donuts after 5 days? Remember that a positive number (5 days) multiplied by a negative number (-5 dollars) will equal a negative number (money lost).
   
   Since 5×5=25{\displaystyle 5\times 5=25}, you know that 5×−5=−25{\displaystyle 5\times
   -5=-25}.
   
   So Jason loses $25 after 5 days of buying donuts. , −12×−5{\displaystyle
   -12\times
   -5} Remember that a negative number times a negative number will always equal a positive number.
   
   Since 12×5=60{\displaystyle 12\times 5=60}, you know that −12×−5=60{\displaystyle
   -12\times
   -5=60}. , Rebecca has a whole pie in her refrigerator.
   
   Over the course of three days, her house guest sneaks into the kitchen and eats 16{\displaystyle {\frac {1}{6}}} of the pie.
   
   How much pie has Rebecca lost? Remember that a negative fraction (−16{\displaystyle {\frac {-1}{6}}} of a pie) times a positive number (3 days), will equal a negative number (amount of pie eaten).
   
   Since 16×3=36=12{\displaystyle {\frac {1}{6}}\times 3={\frac {3}{6}}={\frac {1}{2}}}, you know that −16×3=−12{\displaystyle {\frac {-1}{6}}\times 3={\frac {-1}{2}}}.
   
   So Rebecca has lost half of her pie. , −47×−7{\displaystyle {\frac {-4}{7}}\times
   -7} Remember that a negative fraction times a negative number will equal a positive number.
   
   Since 47×7=287=4{\displaystyle {\frac {4}{7}}\times 7={\frac {28}{7}}=4}, you know that −47×−7=4{\displaystyle {\frac {-4}{7}}\times
   -7=4}
3. 3

   Step 3: Divide a positive fraction by a negative number.

4. 4

   Step 4: Divide a negative fraction by a negative number.

5. 5

   Step 5: Multiply a positive number by a negative number.

6. 6

   Step 6: Multiply a negative number by a negative number.

7. 7

   Step 7: Multiply a positive fraction by a negative number.

8. 8

   Step 8: Multiply a negative fraction by a negative number.

9. 9

   Step 9: Try this problem.

10. 10

    Step 10: Try this problem.

11. 11

    Step 11: Try this problem.

12. 12

    Step 12: Try this problem.

13. 13

    Step 13: Try this problem.

14. 14

    Step 14: Try this problem.

15. 15

    Step 15: Try this problem.

16. 16

    Step 16: Try this problem.

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