# GRADE FIVE MATHEMATICS

Hello Boys and Girls! Did you have an exciting week? I hope you challenged yourself to complete all your tasks. This week, our topics will be Multiples and Lowest Common Multiple. We will also add and subtract Fractions.

First, let us look at the answers for last week’s items.

Answers for last week Prime or Composite 1.12 –C, 2. 13 – P, 6. 24-C, 7. 25 – C , 11. 41- P, 12. 43 – P, 16. 60 –C, 17. 63 –C,

Prime Factors 1. 8= 2 x 2x 2 2. 10= 2 x 5 3. 15= 3 x 5 4. 16= 2 x 2 x 2 x 2 5. 20=2 x 2 x 5 6. 24=2 x 2 x 2 x 3 7. 28=2 x 2 x 7 8. 60= 2 x 2 x 3 x5 9. 72= 2 x 2 x 2 x 3 x 3 10.96=2 x 2 x 2 x 2 x 2 x 3

Common Factors 1. 6 and 9=3 2. 6 and 8=2 3. 12 and 16= 2 and 4 4. 9 and 12 = 3 5. 8 and 20 = 2and 4 6. 18 and 30= 3and 6 7. 25 and 40 =5 8. 15 and 20=5 9. 24 and 42=2,3,6 10.36 and 48=2,3,4,6,12

Let’s now move on to this week’s work.

Multiples When you learned your times tables in grammar school, you were learning multiples. For example, 2, 4, 6, 8, and 10 are multiples of 2. To get these numbers, you multiplied 2 by 1, 2, 3, 4, and 5, which are whole numbers. A multiple of a number is that number multiplied by a whole number.

Practice Activity Write down the first 5 multiples of the following 1.2 2. 3 3. 4 4. 5 5. 6 6. 7

Lowest Common Multiple The lowest common multiple of a group of numbers is their common multiple with the lowest or smallest value. We can find the lowest common multiple by either listing them or doing repeated division by prime numbers. We did repeated division by prime numbers when we found the square root of numbers. Remember: When doing repeated division:

- If the number does not divide exactly, we bring it down - We divide until we get 1.

e.g. What is the Lowest Common Multiple of 2 and 3? 2 2, 3 Please insert vertical line to show repeated division. 3 1, 3 1, 1 LCM= 2x3= 6

Practice Exercise Use any method that you are comfortable with, to find the L.C.M of the following numbers. 1. 2,3 2. 2,4 3. 3,4 4. 3,7 5. 3,18 6. 2,3,6 7. 6,8,12 8. 3,4,8 9. 4,6,9 10.4,5,10

Solve the following problems. 1. Write down any common multiple of the denominators of the follow ing fractions.

2. What is the least number of boys that can be placed in rows of 6,8 or 12 without any being left out? 3. Today, both the soccer team and the basketball team had games. The soccer team plays every 3 days and the basketball team plays every 5 days. When will both teams have games on the same day again? 4. A manager at a restaurant can buy hamburger buns in packages of 8 and hamburger patties in packages of 6. Suppose the manager cannot buy part of a packages. What is the least number of packages of each product he can buy to have an equal number of hamburger patties and buns? 5. A man smiles at his wife every 3 seconds while the wife smiles back every 6 seconds. When will both husband and wife smile at each other at the same time? 6. Steve can save 9 dollars every day while Maria can save 12 dollars. What is the least number of days it will take each person to save the same amount of money? 7. Boxes that are 12 centimetres tall are being piled next to boxes that are 10 centimetres tall. What is the least height at which the two piles will be the same height? 8. A radio station plays “yesterday” by the Beatles once every 2 days. Another station plays the same song once every 3 days. How many times in 30 days will both radio stations play the same song on the same day? 9. Two men running a marathon took a sip of water at the same time 72 minutes after they started the race. If the first man took a sip of water every 9 minutes, how often did the other man take a sip of water? 10. A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the station together?

Remember : Always ask yourself the following questions when you want to solve a word problem: - What is the sum telling me? - What is the sum asking me?

Can you remember how to add and subtract fractions? Use the skills that you have mastered, to work the following fraction sums. You will be supplied with all the answers for this week’s work, next week.