Multiplying and Dividing Whole Numbers
Piano Lessons: Your music lessons cost $45 per week. How much will you pay for 12 weeks of lessons?
*What do we need to find out?
*What method should we use to solve this problem?
1. We need to find out the total amount you will pay for lessons.
2. To do this, multiply $45 by 12.
45
x 12
90 Multiply 45 by the 1's digit, 2.
+ 45 Multiply 45 by the 10's digit, 1. Start in the 10's column.
540 Add the partial products together to find the total product.
* Try it a different way*
You can use mental math to solve this problem, also. We can use the Distributive Property and expand the number 12.
So, 45 x 12 can become
45 x (10 +2) and then one step further
45 x 10 + 45 x 2
450 + 90 = 540 *Mental Math*
MULTIPLICATION OF WHOLE NUMBERS DEFINITION: A product is the result when you multiply two or more numbers. To multiply two whole numbers, multiply the entire top number by the digit in each place value of the bottom number to obtain partial products. Then add the partial products. Then add the partial products.
DRIVING TIME:
You are traveling at a constant speed of 65 miles per hour. How long will it take to travel 2,210 miles?
*What do we need to find out?
*What method should we use to solve this problem?
1. We need to find out the how many hours you have to drive to travel the entire distance of 2,210 miles.
2. To do this, divide 2,210 by 65. In other words, find the quotient 2,210 / 65.
3 4
65 ) 2 , 2 1 0
1 9 5
2 6 0
2 6 0
0
STEP 1: Decide if 65 will go into 22. If not, see how many times it will go into 221. Therefore, the answer will be lined up with the ones place of the number you are dividing into (221), so place the answer above the 1.
STEP 2: Estimate to figure out how many times 65 goes into 221.
I estimated that 3 times 60 = 180 and 4 times 60 = 240, so the answer is between 3 and 4 times. We can't go over 221, so the answer will be 3 times. Write the 3 above the 1.
STEP 3: Then multiply 3 x65. It equals 195. Line the 195 up under 221.
STEP 4: Subtract to find the remainder of 26. Be sure the difference is less than the divisor (26 < 65)
STEP 5: Bring down the next digit, 0, to make 26 into 260 because 65 will not go into 26 so we need a larger number.
STEP 6: Estimate how many times 65 will go into 260. Again, 3 x 60 = 180 and 4 x 60 = 240 and 5 x 60 = 300. 4 will be the closest estimate without going over. Write the 4 above the 0.
STEP 7: Multiply 4 times 65 = 260.
STEP 8: Subtract 260 from 260 = 0. Since the remainder is zero, you are done your problem.
The answer is 34 hours.
Each hour you are traveling 65 miles (i.e. 65 miles per hour). So we can think of the size of each of our sets as 65. Our divisor is 65.
The total amount of miles traveled is 2,210. The dividend is 2,210.
This question is basically asking "How many groups of 65 will it take to equal 2,210?"
2,210 ¸ 65 = ?
Thus it will take 34 hours of driving at a constant rate of 65 miles per hours to travel 2,210 miles.
You could also think of this problem along with its solution as follows:
"If you travel for 34 hours at 65 miles per hour, you will cover 2,210 miles."
DIVISION OF WHOLE NUMBERS DEFINITION: The operation inverse to multiplication; the finding of a quantity, the quotient, that when multiplied by a given
quantity, the divisor, gives another given quantity, the dividend; the process of ascertaining how many times on
the number or quantity is contained in another.
Guided Practice:
1. Mark has $58,000. If he invests it and triples his money, how much will he have all together?
2. Mr. Smith needs to tile the floor in the school gymnasium. The gym is a rectangular and measures 50 feet wide by 65 feet long. Each tile is 1 square foot. How many tiles does he need to buy?
3. For Old Home Days, there is an ATV relay race. Each team needs to cover 75,000 feet of terrain. Each team must have 5 riders that evenly split the course. How many feet does each rider need to go?
4. Jake is a Cessna 150 airplane pilot. He plans to fly from Manchester, NH airport to the San Diego, CA airport. The plane flies an average of 110 miles per hour. The distance between airports is 2,530 miles. How many hours will it take him to get to San Diego?