Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
Blue – Equivalent Fractions and LCM
Fraction Mysteries
Here is a set of mysteries that will help you sharpen your thinking skills. In each
exercise, use the clues to discover the identity of the mystery fraction.
1. My numerator is 6 less than my denominator.
I am equivalent to 3 .
4
2. My denominator is 5 more than twice my numerator.
I am equivalent to 1 .
3
3. The GCF of my numerator and denominator is 3.
I am equivalent to 2 .
5
4. The GCF of my numerator and denominator is 5.
I am equivalent to 4 .
6
5. My numerator and denominator are prime numbers.
My numerator is one less than my denominator.
6. My numerator and denominator are prime numbers.
The sum of my numerator and denominator is 24.
7. My numerator is divisible by 3.
My denominator is divisible by 5.
My denominator is 4 less than twice my numerator.
8. My numerator is divisible by 3.
My denominator is divisible by 5.
My denominator is 3 more than twice my numerator.
9. My numerator is a one-digit prime number.
My denominator is a one-digit composite number.
I am equivalent to 8 .
32
10. My numerator is a prime number.
The GCF of my numerator and denominator is 2.
I am equivalent to 1 .
5
11. Challenge. Make up your own mystery like the ones above. Be sure that there is only
one solution. To check, have a classmate solve your mystery.
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
Solve each problem. List all pairs of numbers that fit each description.
Relatively prime numbers have a greatest common factor (GCF) of 1
12. The numbers are relatively prime. Each number is a prime number. Their sum is 56.
13. The numbers are relatively prime. One number is composite. Their product is 90.
14. In an orchestra there are 4 piano players, 8 drummers, 16 trumpeters, and 12
saxophone players. Each row of the orchestra must have the same number of players
without mixing the instruments. How many instruments will be in each row? How many
rows of each type of instrument will be in the orchestra?
15. A piece of fabric is in the shape of a rectangle measuring 96 cm x 64 cm. It is to be
cut into square pieces. All the pieces have to be equal in size. What is the largest
possible size for these square pieces?
16. Two friends live out of town and come back to town periodically for business. The
judge comes for one day every 15 days, while the accountant comes for one day every
66 days. They were together in town this year on January 11. On what day will they
next be together in town?
17. Marble Mayhem
Fred, Ginger, Julio and Dawn decided to play marbles. Fred emptied his bag of
marbles and divided them equally among the four players. Everyone got at least one
marble. There was one marble left over.
At that moment Jake arrived and asked to play. They gathered up all Fred’s marbles
and divided them equally among the five kids. There was still one marble left over.
Just then Maria joined them, so they gathered all the marbles again and divided
them equally six ways. There was still one marble left over.
What is the fewest number of marbles that Fred could have had in his bag?
Extra: What is the fewest number of marbles Fred could have had in his bag if Dawn
had not been there at all? How did your answer compare with your original answer?
Why do you think that is so?
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
18. Moons, by Jove!
Galileo first used his telescope in 1609 to look at the Earth's Moon. In the following
year he discovered the 4 largest moons of Jupiter – Io, Europa, Ganymede, and
Callisto. Since then astronomers have identified more
than 60 moons orbiting the giant planet.
Imagine a planet with 3 moons. Moon A completes its
revolution around the planet in just 7 hours. Moon B
takes 12 hours to orbit the planet, and Moon C takes 16
hours. Suppose that at noon on May 13 they are aligned
as in the diagram. When will they next all be lined up in
that position?
Extra: Imagine another planet with 3 moons, each with a
different orbital period. It takes exactly 15 days for those moons to return to a
position of alignment. Find 3 possible orbital periods that would produce that result.
19. Sharing Birthdays
Alana and her mother share the same birthday. On Alana's 8th birthday her mother
turned 32. Alana noticed that her mother's age was exactly 4 times her own age.
Alana wondered if it were ever possible for her mother's age to be 3 times her own
age.
Is that possible? If not, how do you know? If so, how old would Alana and her mother
be at that time?
Be sure to explain how you solved the problem and how you know you are correct.
Extra: Alana then wondered if it would ever be possible for her mother's age to be
twice her own age. If so, she wants to know how old she and her mother would be at
that time.
Tell us your answers to her questions. Then write an explanation telling Alana how to
solve the problem.
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
Solutions
1.
18
24
2.
5
15
3.
6
15
4.
10
15
5.
2
3
6.
5
7 11
or or
19 17 13
7.
27
12
20 or 50
8.
21
6
15 or 45
9.
2
8
10.
2
10
11. 12.19 & 37 or 13 & 43 or 53 & 3
13.2 & 45 or 5 & 18
14. 1 row of 4 piano, 2 rows of 4 drummers, 4 rows of 4 trumpets, 3 rows of 4 sax
15.32 x 32 cm
16.330 LCM
Dec. 7 (or Dec. 6 on a Leap Year J)
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Unit 4 – Number Patterns and Fractions
Lesson 3 – Equivalent Fractions and LCM
17.I decided that finding the least common multiple would give me the correct answer. So
I tried to find the LCM of 4,5,and 6.
I knew that the answer had to end with a zero because multiples of 5 can only end with 5
and 0, but since we also have a 4 and a 6 it has to be 0 because 4 and 6 are even numbers.
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
60 ends with a zero so that means it's also a multiple of 5.
Finally, I had to add 1 because every time someone came to Fred's
house, they had 1 marble left over.
60 + 1 = 61
My final answer is 61.
18.First I wrote down the multiples of 16
16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304,
320, 336.
12; 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228,
240, 252, 264, 276, 288, 300, 312, 324, 336.
7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119.
Instead of continuing with all the multiples of 7, I multiplied 7 x 16 and got 112, 112 is not
common to 12. Then I multiplied 112 x 2 = 224.224 is not common to 12. Then I multiplied
by 112 by 3 = 336.336 is common to 12, 16,a nd 7 since(7 x 16) x 3= 336.
So 336 hours /24 = 14 days since 24 hours = 1 day.
So May 13th + 14 days = May 27.
19.Alana's mom must be 24 years older than Alana (32-8=24). If you are looking for a
number that is 24 more than another number and 3 times as more at the same time, you
must find a number that is a multiple of 3. I made a chart of the ages of Alana and her
mother starting when Alana was 1 and her mother was 25 to when Alana was 25 and her
mother was 49 (I did not think going further was necessary). I crossed out the numbers
that weren't a multiple of three. Then I looked at Alana's age and her mother's age. I
multiplied Alana's age by three and looked to see if it equaled her mother's age. Then I
came to when Alana is 12 and her mother is 36. 36 is a multiple of 3 and it was 24 away
from 12! So my answer is that when Alana is 12 and her mother is 36, Alana's mother's age
is exactly 3 times Alana's age.
EXTRA: When Alana is 24 and her mother is 48 Alana's mother's age will be exactly twice
of Alana's age. The two ages are 24 years apart and 48 is a multiple of both 2 and 24.
5
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
17-19
The Math Forum @ Drexel
(http://mathforum.org/)
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