Download Properties of Multiplication and Division

Properties of Multiplication and Division
1. Use properties of operations to find the quotient.
A. -1.9
B. -5.4
C. 5.4
D. 1.9
2. Indicate which property is illustrated in Step 3.
Step 1
=
Step 2
=
Step 3
=
A. inverse property of addition
B. inverse property of multiplication
C. associative property of addition
D. associative property of multiplication
3. Use properties of operations to find the quotient.
A. 0.16
B. 6.25
C. -18.56
D. 40.96
4. Use properties of rational numbers to multiply the following.
83 × (-24.51)
A. -2,034.33
B. 58.49
C. -1,949.67
D. -1,992.51
5. Use properties of rational numbers to multiply the following.
-7 × 688.76
A. -4,833.32
B. -4,821.32
C. -4,816
D. -4,815.24
6. Solve the following.
2,484 ÷ -400 =
A. -5.79
B. 5.79
C. 6.21
D. -6.21
7. Which of the following is true about the quotient below?
A. The quotient is equal to 0.
B. The quotient is undefined because the numerator is negative.
C. The quotient is undefined because the denominator is zero.
D. The quotient is equal to -5.
8. A ferry carries passengers a distance of
miles across a river. The ferry made 30 trips
across the river in one day. Which of the following is true?
A. The ferry traveled
B. The ferry traveled
C. The ferry traveled
total miles in one day.
total miles in one day.
total miles in one day.
D. The ferry traveled
total miles in one day.
9. Which expression represents another method of computing the product given below?
A. (-1)(-1.45 - 76)
B. (-1)(-1.45 + 76)
C. (-1)(-1.45 × 76)
D. (-1)((1 × 76) + (0.45 × 76))
10. Use properties of rational numbers to multiply the following.
A.
B.
C.
D.
11. Tonya has a small picture with a length of
inches. She wants to enlarge the picture by a
factor of 7 and frame it. Which of the following is true?
A. The enlarged picture has a length of
inches.
B. The enlarged picture has a length of
inches.
C. The enlarged picture has a length of
inches.
D. The enlarged picture has a length of
inches.
12. Which expression represents another method of computing the product given below?
A.
B.
C.
D.
13. Use properties of operations to find the quotient.
A.
B.
C.
D.
14. Solve the following.
-20 ÷ 50 =
A. 0.16
B. 0.4
C. -0.16
D. -0.4
15. A diver descended at a constant rate of 16.71 feet every 3 minutes. Which of the following is
true?
A.
B.
C.
D.
After one minute, the diver was at -8.355 feet.
After one minute, the diver was at -5.57 feet.
After one minute, the diver was at 5.57 feet.
After one minute, the diver was at 8.355 feet.
16. A ceiling fan can rotate 150.5 times per minute. The fan rotated a total of 2,426.06 times.
Which of the following is true?
A. The fan rotated for 17.12 minutes.
B. The fan rotated for 18.12 minutes.
C. The fan rotated for 15.12 minutes.
D. The fan rotated for 16.12 minutes.
17. Which of the following is equivalent to
?
A.
B.
C.
D.
18. Which expression represents another method of computing the product given below?
A.
B.
C.
D.
19. Use properties of operations to find the quotient.
A.
B.
C.
D.
20. Solve the following.
A.
B.
C.
D.
Answers
1. A
2. B
3. B
4. A
5. -6. B
7. D
8. -9. C
10. C
11. D
12. D
13. B
14. C
15. -16. B
17. D
18. B
19. D
20. C
21. B
22. B
23. -24. A
25. --
Explanations
1. To divide -11.4 by 6, first divide the decimals ignoring the negative sign.
01.9
6 11.4
06
054
054
000
1. The decimal point in your answer will line up with the decimal point of
the dividend. Fill in zeros as needed.
2. Divide 11 by 6 to get 1 plus a remainder. Place 6 below 11.
3. Subtract 6 from 11 to get 5. Bring the 4 down from 11.4.
4. Divide 54 by 6 to get 9. Place 54 below 54.
5. Subtract 54 from 54 to get 0.
Since -11.4 is negative and 6 is positive, the quotient will be negative.
Therefore, -11.4 ÷ 6 = -1.9.
2. The property illustrated in Step 3 is the inverse property of multiplication.
The inverse property of multiplication states that any non-zero number multiplied by its
reciprocal results in a product of one.
3. To divide -16 by -2.56, first divide the decimals ignoring the negative signs.
For the divisor 2.56, move the decimal 2 places to the right to get rid of the decimal point. Do the
same for the dividend.
 2.56 becomes 256
 16 becomes 1600
Now do the division as you normally would.
0006.25
256
1600.00
1536
00640
00512
001280
001280
000000
1. The decimal point in your answer will line up with the decimal point of
the dividend. Fill in zeros as needed.
2. Divide 1600 by 256 to get 6 plus a remainder. Place 1536 below 1600.
3. Subtract 1536 from 1600 to get 64. Bring the 0 down from 1600.00.
4. Divide 640 by 256 to get 2 plus a remainder. Place 512 below 640.
5. Subtract 512 from 640 to get 128. Bring the 0 down from 1600.00.
6. Divide 1280 by 256 to get 5. Place 1280 below 1280.
7. Subtract 1280 from 1280 to get 0.
Since -16 is negative and -2.56 is negative, the quotient will be positive.
Therefore, -16 ÷ (-2.56) = 6.25.
4. Write -24.51 as -24 + (-0.51). Then, use the distributive property and simplify.
83 × (-24.51) = 83 × (-24 + (-0.51))
= (83 × (-24)) + (83 × (-0.51))
= -1,992 + (-42.33)
= -2,034.33
5. --
6. Write 688.76 as 688 + 0.76. Then, use the distributive property and simplify.
-7 × 688.76 =
=
=
=
-7 × (688 + 0.76)
(-7 × 688) + (-7 × 0.76)
-4,816 + (-5.32)
-4,821.32
7. A positive divided by a negative is equal to a negative.
2,484 ÷ -400 = -(2,484 ÷ 400)
= -(6.21)
= -6.21
8. -9. By definition, the quotient of any number and zero is undefined.
Therefore, the quotient,
, is undefined because the denominator is zero.
10. To find the total distance traveled by the ferry in one day, multiply the distance across the
river by the number of trips.
So, the ferry traveled
total miles in one day.
11. In the given expression, the term -1.45 can be written as follows.
Apply the distributive property.
So, another method of computing the given product is given by the following expression.
12. Write 253 as 200 + 50 + 3. Then, use the distributive property and simplify.
13. To find the length of the new picture, multiply the length of the original by the scale factor 7.
Therefore, the enlarged picture has a length of
14. In the given expression, the term
inches.
can be written as follows.
Apply the distributive property.
So, another method of computing the given product is given by the following expression.
15. -16. To divide a mixed number by a mixed number, first convert both mixed numbers to improper
fractions, and then multiply by the reciprocal of the second fraction.
17. A negative divided by a positive is equal to a negative.
-20 ÷ 50 = -(20 ÷ 50)
= -(0.4)
= -0.4
18. Divide the distance traveled, -16.71 feet, by 3 minutes. The distance traveled is negative
because the diver is descending.
Therefore, after one minute, the diver was at -5.57 feet.
19. Divide the number of rotations by the rotations per minute.
Therefore, the fan rotated for 16.12 minutes.
20. If p and q are integers, and q is not zero, then the following is true.
Therefore, of the choices given,
21. In the given expression, the term
is equivalent to
.
can be written as follows.
Apply the distributive property.
So, another method of computing the given product is given by the following expression.
22. To divide a decimal by a fraction, first convert the decimal to a fraction, and then multiply by
the reciprocal of the second fraction.
23. -24. A negative divided by a negative is equal to a positive.
25. --