Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
Green – Equivalent Fractions and LCM
Solve each problem. List all pairs of numbers that fit each description.
1. Commuter trains depart from a train station every 10 minutes. Subway trains
depart every 3 minutes. A subway train and a commuter train both leave the station
at 5:00 PM. What is the next time a subway train and a commuter train will depart
at the same time?
2. A school hallway has a long row of lockers. Every sixth locker contains a package of
chewing gum, every eight locker contains a hockey stick, and every ninth locker
contains a mirror. Which is the first locker to contain all three items?
3. You and a friend are playing basketball. You only make 3-point baskets, while your
friend only makes 2-point baskets.
a. List 6 different scores at which you and your friend could be tied.
b. How many baskets would it take for each of you to have each of those
scores?
4. Mr. Rutherford needs to buy some rope for a trolley system he is designing. He
buys rope of 3 different colors. The turquoise colored rope is sold in 12-meter
lengths, the hazel colored rope is sold in 18-meter lengths, and the pink rope is sold
in 42-meter lengths. How many pieces of each color must he buy so that he has the
same overall length of each color?
5. Three bells ring at intervals of 4, 6, and 9 seconds respectively. If they start to
ring at the same time instant, how long will it take before they will again ring
together?
6. Cans of soft drink come in two different sized packs: 4 and 6. For some number of
cans, packs of either size would give you the same number of cans. What is the
smallest number of cans you could buy this way?
7. A bank sells travelers’ checks in two different denominations: $20 and $50. What
is the smallest amount in dollars where either kind of travelers’ checks would give
you the amount you wanted?
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
8. A hairdresser works from home. She has two prices: $15 for adults and $9 for
children. This table shows the money she makes in one week. One of the figures is
wrong
Earnings ($)
Monday
$20
Tuesday
$18
Wednesday
$24
Thursday
$45
Friday
$30
a. Which day has the wrong figure?
b. Explain what type of haircuts she must have done on Tuesdays and
Thursdays.
c. The lowest common multiple of 15 and 9 is 45. Explain what information that
gives you about the haircuts on Thursdays.
9. One lighthouse flashes every 6 seconds. Another lighthouse flashes every 14
seconds. They have both just flashed at the same time. How many seconds will it
take for them to both flash again at the same time?
10. Allie, Brian, Cait and Duncan each own a dog. All of them are exercising their dogs
today.
•
•
•
•
Allie exercises her dog every day.
Brian exercises his dog every second day.
Cait exercises her dog every third day.
Duncan exercises his dog every fourth day.
In how many days’ time will they all be exercising their dogs on the same day?
11. In the first pattern shown below, the triangle repeats every 6 figures. In the
second pattern, the triangle repeats every 9 figures. How many figures after the
first figure will both patterns have a triangle?
12. Noreen runs a lap around a track in 70 seconds while Elnora runs a lap around the
same track in 80 seconds. The girls start their laps at the same time from the same
place on the track and maintain their pace. When will they both be at their starting
place at the same time again?
13. The planet Ezon has three moons. The biggest moon is full every 45 days. The
smallest moon is full every 15 days. The middle moon is full every 30 days. How
often is there a night with a triple full moon?
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
14. Clarence has pizza for lunch every four days. He has piano lessons every eight days.
Clarence’s friend, Percival, spends the night every twelve days when his parents go
to their Parents of Nerds Support Group. How often does Clarence have pizza,
piano, and Percy all in one day?
15. There are three fourth grades at PIE. Room 4A contains 12 children, room 4B
contains 18 and room 4C contains 24 children. The fourth graders get together
each Friday to play a game. The teachers want the children on teams with their own
classmates but all teams need to be of equal size. What is the size of the teams
that the teachers decide to make so that every one plays and each team contains
children from the same room?
16. Three different arcade games cost 3, 4 and 5 tokens respectively. Three brothers
each play one of the games and spend the same amount. How many tokens will they
each need?
17. Four students accompanied by a pianist have a special bar of music to play. The
recorder player repeats her piece every 4th bar, the saxophone player every 5th
bar, the drummer every 6th bar and the xylophone player every 10th bar. If the
piece of music is 100 bars long, at what stages will they all be playing together?
18. Ms. Davies has to have her car’s oil, battery, and radiator checked every 5000 km,
her tires rotated every 15 000 km, and her engine tuned every 20 000 km. At what
stage will all three services happen together?
19. A census is a survey that counts people. In the United States, a census is taken
every 10 years. Presidential elections are held every 4 years. The year 2000 was
both a census year and a presidential election year.
a. What is the next year that there will be presidential election and a census?
b. How many times in the next 90 years will both occur in the same year?
c. When was the last time both the census and the presidential election
occurred in the same year prior to 2000?
d. Will 2030 be a census year? Will it be a presidential election year.
20. Three long distance runners train to rest at 3, 5, and 6-kilometer intervals
respectively. At what distance will they all rest together?
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
Solutions
1. 5:30 pm
2. The 72nd locker
3.
a.
Point total
6
12
18
24
30
36
to
to
to
to
to
to
6
12
18
24
30
36
b.
2 point
shots
3
6
9
12
15
18
3 point
shots
2
4
6
8
10
12
4. The GCF is 252, so he needs 21 pieces of turquoise, 14 pieces of hazel, and 6 pieces
of pink rope.
5. 36 seconds
6. 3 packs of 4
12 cans total
2 packs of 6
7. $100
8. a. Monday
b. Tuesday – 2 children | Thursday – 3 adults or 5 children
c. She could have done 5 children or 3 adults
9. 42 seconds
10. 12 days
11. 18th figure
12. After 560 seconds, 9 min 20 seconds
13. Every 90 days
14. Every 24 days
15. Teams of 6 children
16. 60 tokens
17. 60th bar
18. At 60,000 km
19. a. 2020
b. 4
c. 1980
d. It will be a census year but not a presidential year
20. At 30 km
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
Bibliography Information
Teachers attempted to cite the sources for the problems included in this problem set. In some cases,
sources may not have been known.
Problems
Bibliography Information
9-10, 12-13
Barton, David. Alpha Mathematics.
Auckland: Longman.
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