Tennessee Adult Education 2011 Curriculum Math Level 3 Basic Operations Multiply and Divide Lesson 2

Multiplication

Multiplication 1. Always think of multiplication as just adding groups of numbers. 2. If you have 4 x 3, it simply means 4 groups of 3. Within these four groups, there are three triangles. 3 3 3 3 Count the triangles – how many? 3 + 3 + 3 + 3= 12 4 groups of 3 = 12 4 x 3= 12

Before solving multiplication problems, you must be able to identify them. There are 4 ways that you may find multiplication problems written: 3 x 4 is the traditional way 2. 3 4; a simple dot between two numbers 3. (3)(4) or 3(4) or (3)4 4. 3n= 12; anytime a number is connected to a letter it means multiply. Multiplication problems are found in vertical and sentence form. Sentence form: 12 x 4= If the problem is written in sentence form, rewrite the problem using vertical form. Vertical form: 1 2 x 4

Guided Practice Solve the multiplication problems using: Remember the first number in the multiplication problem is the number in each group and the second number is the number of groups. 4 x 4 = 16 5 x 2= 10 3 x 2 = 6 Solve the multiplication problems using: Smiley faces 2 x 8 = 16 Circles: 5 x 3 = 15 Squares: 9 x 2 = 18

The 1 is multiplied by the number in the tens column , which is 2 When multiplying two digits by three digits, multiply the 3 top numbers by the 2 bottom numbers. . STEP 1: Problem: 4 2 3 x 2 1 4 2 3 x 2 1 4 2 3 x 2 1 The 1 in the ones column is multiplied by the number in the ones column, which is 3 3 ones STEP 2: STEP 3: The 1 is multiplied by the number in the tens column , which is 2 4 2 3 x 2 1 3 The 1 is multiplied by the number in the hundreds column, which is 4 4 2 3 x 2 1 2 3 2 4

Multiply the 3 in the ones column by the 2 in the tens column 3 x 2= 6 After the numbers are multiplied by the digit in the ones column, move to the digit in the tens column and multiply. Don’t forget to line up the numbers and this set being multiplied begins in the tens column. Review STEP 3: Multiply the number in the tens column, which is 2 by each digit in the top number 4 2 3 4 2 3 x 2 1 4 2 3 X 1 2 STEP 4: tens Multiply the 3 in the ones column by the 2 in the tens column 3 x 2= 6 4 2 3 x 2 1 _____ Since the multiplier, which is 2, is in the tens column, the answer is placed in the tens column. Be sure and line up the digits according to place value. 6 tens

Multiply the 2 by the 2 in the tens column. Be sure and line up the digits according to place value. STEP 6: STEP 5: Multiply the 2 in the tens column by 4 in the hundreds column 4 2 3 x 2 1 _ 6__ 4 2 3 x 2 1 4 6__ 4 hundreds 4 2 3 x 2 1 4 6__ 4 2 3 x 2 1 8 4 6__ STEP 7: Add the numbers in the columns together. Begin on the right in the ones column. 8 8 8 8 3

Put it together! 4 2 3 x 2 1 4 2 3 8 4 6 8 8 8 3

Guided Practice- solve 1. 2 1 1 x 1 2 3. 4 5 4 x 1 1 4 2 2 2 1 1 2 5 3 2 2. 1 2 1 x 3 2 4. 4 2 1 x 2 3

2. 1 2 1 x 3 2 3. 4 5 4 x 1 1 4. 4 2 1 x 2 3 4 5 4 2 4 2 1 2 6 3 3 6 3 4 5 4 8 4 2 3 8 7 2 4 9 9 4 9 6 8 3

Carrying when Multiplying Multiply each digit in the top number by the bottom number. 2 x 6 2 x 7 2 x 3 3 7 6 x 2

Begin in the ones column If the answer when multiplying is two digits, the number in the tens column will have to be carried. Step 1: Begin in the ones column 3 7 6 x 2 Multiply 6 x 2 = 12 1 tens 3 7 6 x 2 ones 2 ones tens ones

The 2 stays in the ones column because there are 2 ones. 1 tens 3 7 6 x 2 Step 2: 2 ones The 2 stays in the ones column because there are 2 ones. The 1 from the tens column moves to the tens column because there is 1 set of ten to be carried.

Multiply the number in the tens column, which is 7, by 2 Step 3: Multiply the number in the tens column, which is 7, by 2 2 x 7 = 14 1 3 7 6 x 2 2 1 Step 4: Add the number carried which was 1 5 Step 5: 14 + 1 = 15 The 5 is left in the column and the 1 is carried to the hundreds column

Place this product in the hundreds column in the answer Multiply the number in the hundreds column which is 3 by the multiplier 2. Step 6: 1 1 3 7 6 x 2 5 2 2 x 3 = 6 Step 7: Add to this 6 the number carried, which was 1, to the number in the hundreds column 6 + 1 = 7 1 1 3 7 6 x 2 5 2 Step 8: Place this product in the hundreds column in the answer 7

Guided Practice 1. 4 4 1 x 3 6 3. 3 7 5 x 2 2 2. 5 7 2 x 4 4 4. 1 8 1 x 9 2

Guided Practice 3. 3 7 5 x 2 2 2 1 2 2 2. 5 7 2 x 4 4 1. 4 4 1 x 3 6 7 5 0 7 5 0 1 1 2 6 4 6 2 2 8 8 8 2 5 0 1 3 2 3 2 2 8 8 2 5 1 6 8 1 5 8 7 6 4. 1 8 1 x 9 2 3 6 2 1 6 2 9 1 6 6 5 2

Multiplication: Word Problems Multiplication: key words to know Multiply Twice Product Per Total Times

Multiplication: Word Problems 1. Katie is on a diet so she can get better health insurance. Her goal is to lose 50 pounds by exercising and changing her diet. If she loses 5 pounds per month, how much will she lose in 6 months. 5 x 6 = 30 30 lbs.

If his lot measures 25ft x 35ft, what is area for his dogs? 2. Matt wants to fence a back lot for his dogs. But first he wants to know the area of the lot. If his lot measures 25ft x 35ft, what is area for his dogs? 35 35 x 25 = 875 sq. ft. 25 Note: to find the area multiply the length x width.

3. Matt wants to fence a back lot for his dogs 3. Matt wants to fence a back lot for his dogs. He knows the area of the lot is 875 sq. ft. If his lot measures 25 ft. x 35 ft., what is perimeter for the fence measurement? 35 ft. 35 x 2 = 70 ft. 25 x 2 = 50 ft. 25 ft. 70 + 50 = 120 sq. ft. Note: to find the perimeter 2L x 2W

Guided Practice 1. Frank works as a part-time cook at the local “Hamburger Hut”. During the lunch rush Frank fries up 150 hamburgers per hour. If the lunch rush lasts from 11:00 a.m. until 2:00 p.m., how many hamburgers does Frank fry?

If the lunch rush lasts from 11:00 a. m. until 2:00. p. m If the lunch rush lasts from 11:00 a.m. until 2:00 p.m., how many hamburgers does Frank fry? Answer the question: How many hamburgers during the lunch rush from 11a.m. – 2:00 p.m. does Frank fry? 150 burgers x 3 hours of lunch rush = 150 x 3 = 450

The price of gas in 2009 was $1. 83 per gallon The price of gas in 2009 was $1.83 per gallon. Today, May 11, 2011 the gas per gallon is at $4.87. If Mary’s car holds 17 gallons, how much will it cost her to fill her vehicle if it’s empty?

Answer the question: if Mary’s car holds 17 gallons of gas, how much will it cost to fill her vehicle at $4.87? $4.87 x 17 = $82.79 Oh, no! I think I’m having a heart attack! Call 911 !

3. Sally loves the new Organic Greek yogurt. If 3. Sally loves the new Organic Greek yogurt. If she eats 1 carton for breakfast, 1 carton for lunch and 1 carton for snack and continued this for 7 days, how much yogurt will she need to purchase to stock her refrigerator for the week?

3. If she eats 1 carton for breakfast, 1 carton for 3. If she eats 1 carton for breakfast, 1 carton for lunch and 1 carton for snack and continued this for 7 days, how much yogurt will she need to purchase to stock her refrigerator for the week? Cartons per day: 1+1+1=3 Cartons per week = (cartons per day) x (days per week) 1 + 1 + 1 x = 3 7 = 21

4. Barney’s Department Store had a sale on women’s sandals for $19.90. If the store sold 199 pairs at this price, how much did the store take in from the shoe sale?

store sold 199 pairs, how much did the store take in? …..sandals for $19.90. store sold 199 pairs, how much did the store take in? 19.90 x 199 = $3,960.10

5. Chris plans to begin a Christmas club. account in June 5. Chris plans to begin a Christmas club account in June. He wants to have the money to spend on his family in December. If Chris puts $200 in the Christmas Club account each month, how much will he have in December to spend ?

5. Chris plans to begin a Christmas club. account in June 5. Chris plans to begin a Christmas club account in June. If Chris puts $200 in the account each month, how much will he have in December to spend? June – December = 7 months 7 x $200 = $1,400 1400

There are 3 ways you may find a division problem written: Is the process of separating an amount into equal parts. You divide to find out how many equal groups can be made or to find out the number in each group. There are 3 ways you may find a division problem written: all three are read the same way.

• “Sixty-eight divided by two.” Quotient Divisor • “Sixty-eight divided by two.” Dividend • Frame Form: 2)68 • Equation Form: 68 ÷ 2 = 34   ...........................................................................................................................................................................................

The order of the numbers in a division problem is important. 18 ÷ 3 ≠ 3 ÷ 18 If you divide a number by 1, the value does not change. 125 ÷ 1 = 125 or 251 ÷ 1= 251 Any number divided by itself, other than zero, will have a quotient of 1.     Any number divided by zero, the answer is zero. 18 ÷ 0 = 0

The opposite operation of division is multiplication. For each division fact, there is another division fact. For example: 72÷9=8 and 72÷8=9 For each of those division facts, there is a related multiplication fact. For example: 8 x 9 = 72 and 9 x 8 = 72

 

Divide Division – Key words to know Average Each Cut Split Finding a part Share Quotient

The stack of 24 books were shared equally among 4 people. 2 4 How many equal groups of 3 can be made from 15? 3 1 5 There are 15 chairs and 3 tables. Each table gets the same number of chairs. How many chairs for each table? 3 15

Guided Practice: word problems 1. Chris plans to begin a Christmas club account in March. He wants to have the money to spend on his family in December. If Chris wants to have $2,500 to spend, how much will he need to save each month?

1. Christmas club account in March…. spend in December. wants to have 1. Christmas club account in March…... spend in December. ..wants to have $2,500 to spend, how much will he need to save each month? March - December = 10 months 2500 / 10 = 250

2. The Career Center needed a new. microwave for the staff to use. The 2. The Career Center needed a new microwave for the staff to use. The staff agreed to divide the cost. The total purchase for the new microwave is $175.00. If there are 20 people working in the Career Center, how much will each employee pay for the purchase?

2. The Career Center needed a new. microwave. for the staff to use 2. The Career Center needed a new microwave for the staff to use. The staff agreed to divide the cost. The total purchase for the new microwave is $175.00. If there are 20 people working in the Career Center, how much will each employee pay for the purchase? 8 7 5 $8.75 20 1 7 5.0 0 1 6 0 1 5 0 1 4 0 1 0 0 1 0 0

3. Shelby works at the local cell. phone store. She makes $35 3. Shelby works at the local cell phone store. She makes $35 commission on each cell phone she sells. If she made $1,365 in commissions last month, how many cell phones did she cell?

3. Shelby works at the local cell phone. store 3. Shelby works at the local cell phone store. She makes $35 commission on each cell phone she sells. If she made $1,365 in commissions last month, how many cell phones did she cell? 3 9 35 1 3 6 5 1 0 5 3 1 5 3 1 5