Basic Arithmetic Operations and When to Use Them - II
Multiplication is often used as a shortcut to repetitious addition problems. Usually you have a situation where you have 1 (one) of something and want the total of many.
You will divide when you have a situation where you are given a whole quantity and are asked to determine how many portions, pieces, parts, of a given size can be obtained from it.
Part-Whole Model for Multiplication and Division
Example 1 Aaron has 3 baskets of oranges.There are 5 oranges in each basket.How many oranges does Aaron have? (15)
Example 2 Devi saves $8 each week. How many weeks will ittake her to save $40? (5)
Example 3 There are 9 white flowers. There are 3 times asmany red flowers as white flowers. How many redflowers are there? (27)
Practice 1 There are 27 red flowers. There are 3 times asmany red flowers as white flowers. Howmany white flowers are there? (9)
Practice 2 Jenny has 64 jellybeans. This is 8 times as many jellybeans as Carl has. How many morejellybeans does Jenny have than Carl? (56)
Practice 3 Jim and Dan have $24 altogether. If Jim gives $6 to Dan, he will have three times as muchmoney as Dan. How much money does Jim have? ($24)
Example 4 Ellen, Giselle, and Brenda bake 111 muffins. Giselle bakes twice as manymuffins as Brenda. Ellen bakes 9 fewer muffins than Giselle. How many muffinsdoes Ellen bake? (39)
(111 + 9) ÷ 5 = 24
(2 × 24) – 9 = 39
Practice 4 A number is divided by 4. The result is the same as 63 divided by 3.What is the number? (84)
63 ÷ 3 × 4 = 84
Practice 5 A pear costs 50¢ and an apple costs 35¢. Mary bought some pears and apples for $10.50. The amount she paid for the pears was twice that of the apples. How many pears did she buy? (14)
10.5 ÷ 3 = 3.5; Apple price = 3.5 ÷ .35 = 10; Pears = 2 × 3.5 ÷ .5 = 14
Practice 6 Candice, Kerry, and Nathan sold a total of 85 tickets to the school’s production.Candice sold three times as many tickets as Nathan. Kerry sold 4 more tickets than half of what Nathan sold. How many tickets did Kerry sell? (13)
(85 – 4) ÷ 9 = 9; Kerry sells 9 + 4 = 13
Practice 7 Joe knows that a pen costs 1 dollar more than a pencil. His friendbought 2 pens and 3 pencils for17 dollars. How many dollars will Joeneed to buy 1 pen and 2 pencils? (10)
(17 – 2) ÷ 5 = 3 – pencil
3 + 1 = 4 - pen
1 pen and 2 pencils = 4 + 2 × 3 = 10
Practice 8 The length of a rectangle is 6 cm, and itsperimeter is 16 cm. What is the area of therectangle in square centimeters? (12)
16 ÷ 2 = 8 – sum of length and width;8 – 6 = 2 – width
6 × 2 = 12 – area = length × width
Practice 9 Two apples and a mango cost $4.Two apples and three mangos cost $9.Find the cost of a mango. (2.5)
9 – 4 = 5 – costs of two (3 – 1) mangos; 5 ÷ 2 = 2.5 – cost of one mango
Practice 10 The number of cattle on a ranch was four times the number of horses. After 280 heads of cattle were sold, there were twice as many horses as cattle. What was the total number of cattle and horses in the beginning? (400)
Practice 11 72 is subtracted from 3 times a number.The result is 3 times the difference of the number and 72.What is the number? (48)
Practice 12 Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years? (23)
Practice 13 Vito has made 504 cookies and wants to distribute them evenly among his 12 friends. He wrote the following: 504 ÷ 12 = 42
Which expression should Vito use to check if his number sentence is correct?
- 42 × 12
- 42 + 12
- 42 + 12
- 42 – 12
Practice 14 Vito plans to work seven days a week and make four cookies a day. He uses the expression 7 × 4 to figure out how many cookies he'll make every week.
Which expression is not equivalent to 7 × 4?
- 4+4+4+4+4+4+4
- 7+7+7+7
- 4×7
- 7×7×7×7
Practice 15 At a garage sale, Thea found an old grocery store sign that reads as shown.
A.What is the least expensive way to buy 4 loaves of bread according to the sign? $1
B.What is the least amount of money you would need to buy exactly 10 loaves of bread according to the sign? $1 × 2 + $0.32 × 2 = $2.64
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