Answer:
When you multiply a number by 10, 100, 1,000 and so forth, do you move the decimal point to the left or to the right as many places as there are zeroes in the multiplier? To the right
When you’re multiplying, does the order of the factors matter? No, for example a*b = b*a
Does the law of grouping apply to multiplication? Yes, for example (a*b)*c = a*(b*c)
Multiply by moving the decimal point.
a. 24.6 × 100 = 2460
b. 37 × 1,000 = 37000
c. 0.367 × 10,000 = 3670
d. 0.005 × 100,000 = 500
Use a shortcut method of your choice to complete the multiplication problems.
a. 973 × 80 = 973 × 8 x 10 = 7784 x 10 = 77840
b. 56 × 2,000 = 56 x 2 x 1000 = 112 x 1000 = 112000
c. 5.7 × 300 = 5.7 x 100 x 3 = 570 x 3 = 1710
d. 0.46 × 50 = 0.46 x 10 x 5 = 4.6 x 5 = 23.0
Use rounding to determine if the following answers are reasonable. Round each of the factors to the nearest ten, then multiply.
a. 587 × 92 = 590 x 90 = 590 x 9 x 10 = 5310 x 10 = 53100. Then, 54,004 is reasonable
b. 117 × 19 = 120 x 20 = 2400, then, 222.3 is not reasonable
Do the law of order and the law of grouping apply to division? No, a÷b is not the same as b÷a and (a÷b)÷c ≠ a÷(b÷c)
A catering service is running a special on a shrimp appetizer—one dozen appetizers for $33.95. So far, they’ve sold 4 dozen to Customer A, 6 dozen to Customer B, and 8 dozen to Customer C. How much should they collect altogether for the three sales? $33.95*(4 + 6 + 8) = $611.1
How much change would you receive from a $20.00 bill if you purchased 15 items that cost $1.23 each? 20 - 15*1.23 = $1.55
The owner of an appliance store bought 15 washers at $279 each and 18 dryers at $229 each. How much did the dealer spend in all? 15*279 + 18*229 = $8307
Divide. Give special attention to the order of division.
a. 72 ÷ 9 ÷ 2 = 8 ÷ 2 = 4
b. (18 ÷ 6) ÷ 3 = 3 ÷ 3 = 1
c. 45 ÷ 5 ÷ 3 = 9 ÷ 3 = 3
d. 144 ÷ (12 ÷ 2) 144 ÷ 6 = 24
Divide. Use one of the shortcut methods you learned.
a. 5,600 ÷ 20 = 280
b. 475 ÷ 25 = 19
c. 650 ÷ 50 = 13
d. 7,280 ÷ 80 = 91
You need 12 gallons of paint to paint the exterior of your house. At one store the paint sells for $19.95 a gallon. At a second store the same brand of paint sells for $37.98 for two gallons. Which store is less expensive? $37.98 for two gallons is the same as $37.98 ÷ 2 = $18.99 per gallon, then. the second store is less expensive. How much would you save by purchasing your paint at the less expensive store? 12*19.95 - 12*18.99 = $11.52
Your current salary is $30,900 per year. You’ve just accepted a new position at a company that’s to pay you $32,500 per year. How much more will you get per month at the new job? (Round your answer to the nearest dollar) 30,900 ÷ 12 = $2575 per month; 32,500 ÷ 12 = $2708 per month; 2708 - 2575 = $133 more per month
There are 144 square inches in a square foot. How many square feet are there in 2,592 square inches? 2592÷144 = 18 square feet
Jennifer borrowed $3,584 from her parents to use as a down payment on a piece of land she purchased. If she pays them $256 each month, how long will it take Jennifer to pay back the loan? 3,584 ÷ 256 = 14 months
Multiply. Then, check your work by switching factors.
a. 693 × 83 = 57519 = 83 x 693
b. 910 × 45 = 40950 = 45 x 910
c. 38 × 84 = 3192 = 84 x 38
d. 409 × 89 = 36401 = 89 x 409
The bedroom in your new home is 12 feet by 18 feet. The carpeting you’ve chosen costs $9 per square foot. How much will it cost to carpet your bedroom? 12 x 18 ÷ 9 = $24
Divide. Check your result by multiplying.
a. 8,918 ÷ 26 = 343 -> 26 x 343 = 8918
b. 630 ÷ 35 = 18 -> 35 x 18 = 630
c. 483 ÷ 23 = 21 = 23 x 21 = 483
d. 629 ÷ 17 = 37 -> 17 x 37 = 629
Use rounding to determine whether the following answers are reasonable.
a. 96 ÷ 48 = 100 ÷ 50 = 20 -> reasonable
b. 713 ÷ 99 = 713 ÷ 100 = 7.13, then, 72 is not reasonable
