среда, 1 июня 2016 г.

Test 2. Multiplying natural numbers

Before proceeding to the solution of examples and problems be sure to read the theoretical part of the lesson 

Multiplying natural numbers

 1. 28 books. 88 pages in each book. How many pages in all books?

 а148040;      
 b)  147040;      
 c147060;      
 d147140.

 2. A video game company can fit 535 boxes of games into a truck. If the company has 47 full trucks, how many games does it have in total?

 а)  25145;      
 b26145;      
 c25245;      
 d25155.

 3. Each day, 1,035 new apps are uploaded to a web server. After 28 days, how many apps would have been uploaded?

 а28780;      
 b26980;      
 c28970;      
 d)  28980.

 4. The zookeeper gave 2 bags of peanuts to an elephant. There were 12 peanuts in each bag. How many peanuts did the zookeeper give to the elephant?

 а14;      b6;      
 c)  24;      d26.

 5. Ariel earns money by mowing lawns in his neighborhood. If he can mow 3 lawns in an hour, how many lawns can he mow working 30 hours a week?

 а60;      b)  90;      
 c33;      d99.

 6. Winona is tracking the amount of water that the people of her town use during the summer months. She calculates that 47,005 gallons of water are used every day. If Winona tracks the water usage for 112 days, how much water will be used during that time?

 а5264650;      
 b5264565;      
 c)  5264555;      
 d)  5264560.

 7. Basil launched his website this year. During the first three months of operation, his site recorded 835,884 hits. If he maintains that same monthly average, how many hits should he expect by the end of the fifteenth month?

 а)  4179420;       
 b12538460;
 c12538260;      
 d4179620.

 8. Maria did 25 sets of 15 jumping jack, 18 sets of 20 sit-ups, 21 sets of 12 push-ups, and 16 sets of 10 pull-ups. How many times did Maria do each exercise?

 а330 jumping jacks,  480 sit-ups,
      192 push-ups,  220 pull-ups;
 b)  375 jumping jacks,  360 sit-ups,
      252 push-ups,  160 pull-ups;
 c480 jumping jacks,  340 sit-ups,
      180 push-ups,  190 pull-ups;
 d225 jumping jacks,  520 sit-ups,
      312 push-ups,  200 pull-ups.

 9. Al did 22 sets of 15 jumping jack, 24 sets of 20 sit-ups, 16 sets of 12 push-ups, and 22 sets of 10 pull-ups. How many times did Maria do each exercise?

 а480 jumping jacks,  340 sit-ups,
      180 push-ups,  190 pull-ups;
 b375 jumping jacks,  360 sit-ups,
      252 push-ups,  160 pull-ups;
 c225 jumping jacks,  520 sit-ups,
      312 push-ups,  200 pull-ups;
 d)  330 jumping jacks,  480 sit-ups,
      192 push-ups,  220 pull-ups;

10. Hannah did 32 sets of 15 jumping jack, 17 sets of 20 sit-ups, 15 sets of 12 push-ups, and 19 sets of 10 pull-ups. How many times did Maria do each exercise?

 а225 jumping jacks,  520 sit-ups,
      312 push-ups,  200 pull-ups;
 b375 jumping jacks,  360 sit-ups,
      252 push-ups,  160 pull-ups;
 c)  480 jumping jacks,  340 sit-ups,
      180 push-ups,  190 pull-ups;
 d330 jumping jacks,  480 sit-ups,
      192 push-ups,  220 pull-ups.

11. Jorge did 15 sets of 15 jumping jack, 26 sets of 20 sit-ups, 26 sets of 12 push-ups, and 20 sets of 10 pull-ups. How many times did Maria do each exercise?

 а480 jumping jacks,  340 sit-ups,
      180 push-ups,  190 pull-ups;
 b)  225 jumping jacks,  520 sit-ups,
      312 push-ups,  200 pull-ups;
 c330 jumping jacks,  480 sit-ups,
      192 push-ups,  220 pull-ups;
 d375 jumping jacks,  360 sit-ups,
       252 push-ups,  160 pull-ups.

12. A video game company can fit 535 boxes of games into a truck. If the company has 47 full trucks, how many games does it have total?

 а)  25145;      b25150;      
 c24145;      d25245.

Test 1. Multiplying natural numbers

Before proceeding to the solution of examples and problems be sure to read the theoretical part of the lesson 

Multiplying natural numbers

 1. Solve:
 а782;      b796;     
 c)  792;      d802.

 2. Solve:
 а)  649;      b659;     
 c640;      d637.

 3. Solve:
 а2822;      b2834;     
 c2802;      d)  2812.

 4. Solve:
 а1927;      b)  1917;     
 c1911;      d1907.

 5. Calculate:

48 × 19.

 а902;      b914;     
 c922;      d)  912.

 6. Calculate:

15 × 55.

 а815;      b)  825;     
 c820;      d821.

 7. Calculate:

66 × 39.

 а2584;      b2572;     
 c)  2574;      d2554.

 8. Calculate:

44 × 83.

 а)  3652;      b3632;     
 c3656;      d3654.

 9. Calculate:

6 + (6 – 2) × 6.

 а28;      b32;     
 c24;      d)  30.

10. Write an expression for the calculation adds 5 and 6 and then multiply by 3.

 а(5 + 3)6;     
 b)  (5 + 6)3;     
 c(3 + 6)5;     
 d(5 – 6)3.

11. Write an expression for the calculation adds 3 and 8 and then multiply by 9.

 а(3 – 8)9;     
 b(3 + 9)8;     
 c)  (3 + 8)9;     
 d(9 + 8)3.

12. Write an expression for the calculation adds 34 and 6 and then multiply by 3.

 а(34 + 3)6;     
 b(34 6)3;     
 c(3 + 6)34;     
 d)  (34 + 6)3.

Lesson 5. Multiplying whole numbers

MULTIPLICATION Is multiplying whole numbers more difficult than adding or subtracting them?
Not really, if you remember to line up the numbers by place value. Then multiply the numbers by place value. Then multiply the entire top number by the ones place of the bottom number, and then by the tens place, and then by the hundreds place, and so on for larger numbers. Think of it as doing a few simple problems, one after the other. After you’ve finished multiplying, add the lines to find the product. The product is the answer to the entire multiplication problem.
The multiplication of two numbers  a  and  b  is denoted by
ab = c,
where  c  is the result of the multiplication of the numbers  a  and  b. Both numbers, a  and  b, are called factors (or multipliers), and  c  is the product of  a  and  b.

Remember…                          

Always multiply the entire top number by one bottom digit at a time. Use a different line for the product of each bottom digit.

There are certain rules or properties of math that are always true.
The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.
a × b = b × a

EXAMPLE:

5 × 2 = 10
2 × 5 = 10

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

(a × b) × c  = a × (b  × c)
(2 × 4) × 5 = 2 × (4 × 5)
8 × 5 = 2 × 20
40 = 40

The Identity Property of Multiplication states that the product of a factor and 1 is that factor.

4 × 1 = 4

The Properties of Zero state that the product of a factor and 0 is 0.

5 × 0 = 0

The Distributive Property combines the operations of addition and multiplication.

a × (b + c)  = (a × b) + (a × c)
3 × (2 + 5) = (3 × 2) + (3 × 5)
3 × 7 = 6 + 15
21 + 21

The Distributive Property states:

a × (b + c)  = (a × b) + (a × c)

This can help solve complex multiplication problems:
The same property also means that:

a × (b c)  = (a × b) – (a × c)

This can help solve complex multiplication problems:
Tasks to the lesson 5
Other lessons: