Name ~~___________~__~____~..____ Reteaching

6-1 Using Mental Math to Multiply 2-Digit Numbers

You can multiply with mental math by using basic facts and patterns.

Example A: 5 x 5 = 25

5 >< 50 = 250

The product contains the number of zeros in each factor.

Example B: 5 x 6 = 30

5 x 60 = 300

50 x 60 = 3,000

50 x 600 30,000

When the product of a basic fact includes a zero, such as 5 x 6 30, that zero is not part of the pattern.

Multiply. Use mental math.

1. 20 x 20 =: 2. 50 x 1°= 3. 40 x 40 =

4. 30 >< 80 = 5. 60 x 600 6. 50 x 900 =

7. 70 x 300 = 8. 70 x 600 = 9. 40 x 500 =

----,~.--~--

10. Number Sense Tell what numbers go in the blanks.

To find 90 x 300, multiply ___ and ____ .

Then write ___ zeros at the end.

75

Name _______________________~ ________________________ ~~ l p~:t~ce J Using Mental Math to Multiply 2-Digit Numbers Multiply. Use mental math.

1. 4 x 30 = 2. 5 x 90 =

3. 9 x 200 4. 6 x 500 =

5. 3 x 600 = 6. 0 x 600 =

7. 90 x 70 = 8. 70 x 400

9. 50 x 800 = 10. 30 x 800 =

11. 90 x 500 == 12. 30 x 4,000 =

13. Number Sense How many zeros are in the product of 60 x 900? Explain how you know.

Truck A can haul 400 Ib in one trip. Truck B can haul 300 Ib in one trip.

14. How many pounds can Truck A haul in 9 trips?

15. How many pounds can Truck B haul in 50 trips?

16. How many pounds can Truck A haul in 70 trips?

A 280 B 2,800 C 28,000 o 280,000

17. Writing to Explain There are 9 players on each basketball team in a league. Explain how you can find the total number of players in the league if there are 30 teams.

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Name ___~__~_~~~ ______~_____~______~______~_____~_ Reteaching

6-2Estimating Products

Estimate 11 x 94.

Using rounding Using compatible numbers

Round 11 to 10. Replace 11 with 10.

Round 94 to 90. Replace 94 with 100.

10 x 90 = 900 10 x 100 = 1,000

11 x 94 is about 900. 11 x 94 is about 1,000.

Use rounding to estimate each product.

1. 62 x 82 2. 59 x 48 3. 74 x 302

---_.._--­

4. 47 x 790 5. 498 x 63 6. 687 x 38

7.18x412 8. 385 x 75 9. 62 x 147

Use compatible numbers to estimate each product.

10. 32 x 83 11. 37 x 22 12. 51 x 296

13. 65 x 34 14. 108 x 81 15. 43 x 620

16. 426 x 71 17. 59 x 701 18. 87 x 87

19. Number Sense To estimate the product of 37 x 99, Chris multiplied 40 x 100. Tell how you know if this is an

<I" underestimate or an overestimate. .; E

~ v -" c 9 ~ V

Co..

77

Norne Practice .~.~--.~~-

6-2 Estimating Products l J Use rounding to estimate each product.

1. 38 x 29 2. 71 x 47 ~.---~-~-

3. 54 x 76 4. 121 x 62

5. 548 x 28 6. 823 x 83 __.

7. 67 x 289 8. 183 x 34

Use compatible numbers to estimate each product.

9. 28 x 87 10. 673 x 85

---_._----------­

11. 54 x 347 ______ 12. 65 x 724 ----.-..-.~.-.--

13. 81 x 643 14. 44 x 444

15. 72 x 285 16. 61 x 761

17. Vera has 8 boxes of paper clips. Each box has 275 paper clips. About how many paper clips does Vera have?

A 240 B 1,600 C 2,400 D 24,000

18. Writing to Explain A wind farm generates 550 kilowatts of electricity each day. About how many kilowatts does the wind farm produce in a week? Explain.

.----.~------

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Name ________~_._._._________________________ Reteaching

Arrays and an 6-3

Expanded Algorithm

Here is how to find the product of 12 x 24 using an array.

Draw a rectangle 24 units long by 12 units wide.

Divide the rectangle by tens and ones for each factor. Find the number of squares in each smaller square.

!

! o

j

I

I

I

-r ii,

,--+-,...-+--r-lO X 20

: IIII : ! I

1

~~~~~~t-:-;-:i~71-r i

:-rl~~1 I . \ ! 1 I j

x 26 -r-:-I

, I

Then add the numbers of the squares in the four rectangles:

200 + 40 + 40 + 8 = 288

So, 12 x 24 288.

Divide the rectangle by tens and ones for each factor. Then complete the calculation.

1.

79

22

Name Practice J 6-3

, ;Arrays and an Expanded Algorithm Use the grid to draw a rectangle. Then complete the calculation.

1. ~~'-r-r--r-T~~, i i T"--'---;

! J i

~-l

..L

23

3. 26 4. 33 x 22 x 1 4

2.

-.-..-.~- ---~

+

5. 24 x 57 6. 44 x 48 = ~..___._~.__..__._

7. A red kangaroo can cover 40 ft in 1 jump. How many feet can the red kangaroo cover in 12 jumps?

8. Barb exercises for 14 hours in 1 week. How many hours does she exercise in 32 weeks?

A 496 t-Ir B 448 hr C 420 hr o 324 hr .,. u

9. Writing to Explain Explain how the product of 16 x 34 is c

~.

Ci u ~like the product of 6 x 34 plus 10 x 34. u :...;J

~ n c "­

80

Name ______________________________________________ Reteaching

6-4Multiplying 2-Digit: Numbers and Multiples of lf~n

To find the product of 60 and 26, you can use breaking apart.

Mark off a section of a grid to show 60 x 26.

Count the number of rows. Count the number of squares In each row.

There are 60 rows. There are 26 squares per row.

Draw a line to separate the factor :26 into the tens place and the ones place. Show 26 as 20 -+- 6. 20

I

I

Into how many sections have you divided the larger section? IIT I 20 .. 60 = 1 .200 d ,.

There are 2 sections. Mark one section 660 360 II I'

60 x 20 and the other section 60 x 6. 60

Multiply to find the products. 11 II II

60 rows of 20 1,200 Add. IIII I .60 rows of 6 x 360

---- i: I I1,560 ---.-LJ11.-1__

Use grid models to break apart each product and solve.

1. 23 x 40

2. 16 >< 30

3. 34 x 50 -----------------------------------.----------------­

4. 60 x 47

5. 17 x 80

"<t

6. 70 x 31 -----.------------.----------------------------------­

'.:

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PracticeName 6-4

Multiplying 2-Digit Numbers and Multiples of Ten Use the grid to show the partial products. Multiply to find the product.

1. 23 x 50 2. 30 x 82 80 2

20 x 50 1,000 30 ;< 80 2.40030

30 x 2 = 60

3. 14 x 40 4. 20 x 63 60 3

~

40

1 0 >~ 40 = 400 20i I 20 x 60 1.2001jl 41 4 x 40 == 160 II ;fT

20 x 3 = 60 7

...--~....------- ­

5. Martika works as a legal secretary. She earns $20 an hour. How much

does Martika earn if she works 32 hours? ------ ­

6. Which numbers are the partial products of 77 x 30?

A 210 and 700 B 2,100 and 210 C 511 and 2,100 0 4,900 and 210

7. Writing to Explain Explain how you can find the product of 40 x 16 by breaking apart the numbers.

---....--~....-----------~

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Name __~ Reteaching

6-5 Multiplying 2-Digit Numbers by 2-Digit Numbers

There are 24 cars in a race. Each car has a 13-person crew in the pit area. How many pit-area workers are at the race?

Step 1

Multiply the ones.

Regroup as necessary,

1

24 x13

72

Step 2

Multiply the tens.

Regroup as necessary.

1

24 x13

72 240

Step 3

Add the partial products.

1

24 x13

72 240 312

24 13 == 312, so there are 312 pit-area workers at the race.

1. 38 2. 67 3. 47 4. 88 X 26 X 27 X 85 X 32

5. Writing to Explain Corina multiplied 62 X 22 and got a product of 1,042. Explain why Corina's answer is not reasonable.

83

l I

jName _______________ Practice

6-5 Multiplying 2-Digit Numbers by 2-Digit Numbers 1. 54 2. 36 3. 53 4. 48

>( 17 x 20 x 12 x 46

5. 37 6. 62 7. 91 8. 28 >< 83 x 17 x 49 x 56

9. 70 10. 58 11. 97 12. 64 x 39 x 90 x 42 x 88

13. A carton holds 24 bo-:tles of juice. How many juice bottles are in 15 cartons?

14. How much do 21 bushels of [ Vegetable Weight of 1 Bushel sweet corn weigh? I Asparagus 241b

Beets 521b -------{

Carrots 50 Ib

Sweet corn 35 Ib15. How much do 18 bushels of aspara~lus weigh?

16. How much more do 13 bushels of beets weigh than 13 bushels of carrots?

17. Which of the following is a reasonable answer for 92 x 98?

A 1,800 B 9,000 C 10,000 o 90,000

".18. Writing to Explain Garth is multiplying 29 x 16. He has ~

174 after multiplying the ones and 290 after multiplying g

the tens. Explain how Garth can find the final product. ] () "l

c 5?

ID ----.----------.------~-~-.----------.----.----.--.--.---_.__._----- CL "

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Name __~~_~~___~ Reteaching

6-6 Multiplying Greater Numbers by 2-Digit Numbers

You multiply a 3- or 4-digit number the same way you multiply a 2-digit number.

Find 457 x 32.

Step 1 Multiply by Step 2 Write a zero Step 3 Add the the ones. Regroup as in the ones place. products. needed. Multiply by the tens 1 2

1 1

1 1 digit. Regroup as 457 457 needed. x 32

L32 1 2 914 914

1 1

457 + 13,710 14,6242:: 32

914 13,710

Here's WHY it Works:

457 x 32 = 457 x (30 + 2)

= (457 x 30) + (457 x 2)

= 13,710 + 914

:::: 14,624

Check by estimating. 500 x 30 = 15,000; The answer is reasonable because 15,000 is close to 14.624.

135 4. 3,2661. 442 2. 3. 5,371 x 7~ x 27 ~~ x 15

5. 512 6. 936 7. 7,386 8. 7,923 ~

x 73 X 78 2LAi x~ ~ 5 3

~ 0.

85

Name __________ Practice

6-6 Multiplying Greater Numbers by 2-Digit Numbers

5341. 263 2. 3. 3,357 x-86x 17 X- 32

8554. 237 5. 6. 9,362 x 5Ax 53 LJ_l

7. 421 x 45 8. 357 x 74 9. 64 x 848

10. 93 x 4,247 11.9,989X57 12. 81 x 2,777

13. Algebra Find the value of 78 x n when n 3,237. _____________________ _

14. Laura addresses 127 envelopes every week. Each envelope contains 4 pieces of paper. How many envelopes does Laura address in one year? Remember that there are 52 weeks in a year.

15. There are 36 large fish tanks at a zoo. Each tank holds 215 gallons of water. How many gallons of water would it take to fill all the tanks?

A 7,740 B 7,613 C 7,610 o 251

16. Writing to Explain Is the product of 686 and 50 greater than or less than 30,000? Explain.

"

86

ReteachingName 6·7

Problem Solving: Two-Question Problems

Read and Understand Problem 1: Gina gave 3 sheets of paper to each of the 12 students in her class. How many sheets of paper did she give out?

Problem 2: Each sheet of paper had 3 paperclips attached to it. How many paperclips did she give out?

Answer Problem 1 first. I-? Sheets of paper--;

[ 12 I 12 I 12 I 12 students x 3 sheets of paper = 36 sheets of paper Gina gave out 36 sheets of paper.

Plan and Solve Use the answer from Problem 1 to solve Problem 2. 1-- ? Paper clips ---;

[ 36 I 36 I 36 I 36 sheets of paper x 3 paperclips = 108 paperclips Gina gave out 118 paperclips.

Solve. Use the answer from Problem 1 to solve Problem 2.

1. Problem 1: April made 16 baskets and glued 5 flowers on each one. How many flowers did she use altogether?

Problem 2: Each flower April used had 8 petals. How many petals were there on all the flowers she used?

2. Problem 1: Jorge washed cars for four hours on Saturday. In the first hour, he washed 2 cars. In the second hour, he washed 1 car. In the third hour, he washed 3 cars. How many cars did he wash all together in the first three hours?

" Problem 2: Jorge washed the same number of cars in the

~ fourth hour as he did in the first three hours combined. How many cars did he wash all together in four hours?

~ ~

::L

-----~.~-.~.-.-..--~~

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Name __.. Practice J 6·7

Problem Solving: " Two-Question Problems Use the answer from the first problem to solve the second problem.

1. Problem 1: Francisco reads 75 pages every week for a summer reading program. There are about 4 weeks in a month. How many pages can Francisco read in a month?

-------.---~~------~.~-.-.-.-.------~

Problem 2: How many pages will Francisco read in the three months of summer?

2. Problem 1: Mr. Dunn drives 15 miles every day to work. Mr. Dunn works five days a week. How many miles does he drive?

Problem 2: Mr. Dunn estimates he uses 3 gallons of gas over the course of a week. How many miles per gallon does his car get?

3. A company buys printer paper in a box which contains 8 packages. Each package of paper costs 3 dollars. Which number sentence shows how much 12 boxes will cost?

A 8 + 3 x 12 B 24 -;.- 12 C 24 -i- 12 D 24 x 12

4. Writing to Explain There are 12 plots in a community garden. Each plot is the same size. What information would you need to know if you wanted to know how much area can be farmed in the community garden? Explain.

"

9 B c ~

"0

~ Q " n.

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