Exponents/ Square Roots
Solve 62-52=?
62 (6 squared) is equal to 6×6=36
52 (5 squared) is equal to 5×5=25
Subtracting 25 from 62:
62−52=36−25=11
Find the LCM of 15 and 20.
Solution: To find the LCM, list the multiples of each number and identify the smallest multiple that they have in common.
Multiples of 15: 15, 30, 45, 60, ... Multiples of 20: 20, 40, 60, 80, ...
The smallest common multiple is 60. Therefore, the LCM of 15 and 20 is 60
Write the multiples fo 5 and 7.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...
Solve (6x2)+8-(40 -4x5)
(12) + 8 - (40 - 4X5)
(12) + 8 - (40 - 20)
(12) + 8 - (20)
20 -20
=0
Emily is planning a family reunion and wants to arrange transportation for her family members. She has 3 vans that leave the starting point at different intervals. The first van departs every 4 hours, the second van departs every 6 hours, and the third van departs every 8 hours. If all vans just left, how long will it take before they all depart at the same time again?
To find the time it takes for all the vans to depart at the same time again, we need to find the Least Common Multiple (LCM) of 4, 6, and 8.
Prime factorization:
LCM = 23×3=24.
Therefore, it will take 24 hours before all three vans depart at the same time again.
What is 7 cubed + 4 squared?
73 (7 cubed) is equal to 7×7×7=343
42 (4 squared) is equal to 4×4= 16.
Adding these two values together:359
Using Prime Factorization find the GCF of 16 and 42.
Prime factorization of 16: 16=24
Prime factorization of 42: 2×3×7
To find the GCF, we look for the common prime factors and take the lowest power of those factors:
Common prime factor: 2 (appears in both factorizations).
Lowest power of 2: 21=2x1=2.
Therefore, the GCF of 16 and 42 is 2.
State the factors of 64 and 40.
The factors of 64 are the numbers that can be multiplied together to give 64. The factors of 64 are:
1, 2, 4, 8, 16, 32, 64
The factors of 40 are the numbers that can be multiplied together to give 40. The factors of 40 are:
1, 2, 4, 5, 8, 10, 20, 40
Solve (13+21-7)+3+72
(13+21-7)+3+72
(34 -7)+3+72
(27)+3+72
(27)+3+49
= 79
79
Pencils come in packages of 10. Erasers come in packages of 12. Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil. How many packages of pencils and erasers should Phillip buy?
To have exactly 1 eraser for each pencil, the number of erasers should be the same as the number of pencils. Let's find the least common multiple (LCM) of 10 (packages of pencils) and 12 (packages of erasers).
Prime factorization of 10:2x5
Prime factorization of 12: 22×3
To find the LCM, we take the highest power of each prime factor:
LCM =22×3×5=60
Phillip should buy 60 pencils (6 packages of 10 pencils) and 60 erasers (5 packages of 12 erasers) to have exactly 1 eraser for each pencil.
Solve the following square roots:
- 25
- 144
- 36
- 81
- 36
- 49
Find the LCM and GCF of 24 and 36.
Prime factorization of 24: 24=23×31
Prime factorization of 36: 36=22×32
Now, to find the LCM, we need to take the highest power of each prime factor:
LCM=23×32=72.
To find the GCF, we take the lowest power of each prime factor:
GCF=22×31=12
Therefore, the LCM of 24 and 36 is 72, and the GCF is 12.
State the factors of 12 and 48.
The factors of 12 are the numbers that can be multiplied together to give 12. The factors of 12 are:
1, 2, 3, 4, 6, 12
The factors of 48 are the numbers that can be multiplied together to give 48. The factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Abby buys a bike for 400$ and gives a deposit of 50$. She pays the bike off in 7 equal payments. What is the amount of each payment?
To find the amount of each payment, we first need to subtract the deposit from the total cost of the bike to determine how much Abby needs to pay in installments.
Total cost of the bike = $400 Deposit = $50
Amount to be paid in installments = $400 - $50 = $350
Abby needs to pay $350 in 7 equal payments. To find the amount of each payment, divide the total amount by the number of payments:
Amount of each payment = $350 ÷ 7 = $50
So, Abby needs to make 7 equal payments of $50 each to pay off the bike.
Kiara baked 28 oatmeal cookies and 49 chocolate chip cookies to package in plastic containers for her teacher friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?
To find the greatest number of identical containers with an equal number of oatmeal and chocolate chip cookies, we need to find the greatest common factor (GCF) of 28 and 49.
The prime factorization of 28 is = 22 x 7
The prime factorization of 49 is = 72
The common prime factor is 7, and it's the highest power of 7 that both numbers share.
Therefore, Kiara can pack the cookies into containers of 7 x 7 cookies each (7 oatmeal and 7 chocolate chip).
To find out how many containers she needs, she can divide the total number of cookies by the number of cookies in each container:
Since Kiara cannot have a fraction of a container, she needs 2 containers to pack the cookies for her teacher friends.
What is the square root of 169 + the square root of 121?
The square root of 169 is 13 (169=13), and the square root of 121 is 11 (121==11).
Adding these two values together:
169+121=13+11=24
Using Prime Factorization, find the GCF and LCM of the following: 32 and 48
Prime factorization of 32: 32=2532=25
Prime factorization of 48: 48=24×348=24×3
Now, to find the GCF, we look for the common prime factors and take the lowest power of those factors:
GCF = 24=1624=16
To find the LCM, we take all the prime factors with their highest power:
LCM = 25×3=9625×3=96
So, the GCF of 32 and 48 is 16, and the LCM is 96.
State the factors of 52 and 30. Do they share a common factor?
The factors of 52 are the numbers that can be multiplied together to give 52. The factors of 52 are:
1, 2, 4, 13, 26, 52
The factors of 35 are the numbers that can be multiplied together to give 35. The factors of 35 are:
1, 5, 7, 35
Clara and Judy rent a scouter for 1 hour. The scouter costs 55$ to rent. Judy paid 5$ more than Clara. How much did they each pay?
Judy paid 30$ and Clara paid 55$
At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in this table. i.
Items in the Gift Bags
Hat
Every 2nd visitors
T-shirt
Every 7th visitor
Backpack
Every 10th visitor
How often will a bag contain all three items?
A. Every 14th bag B. Every 19th bag C. Every 70th bag D. Every 140th bag
C. Every 70th bag
Sarah is building a square garden. She knows that the area of the garden is 64 m2. What is the length of one side of the square garden?
The area (A) of a square can be calculated using the formula A=side×side
In this problem, we are given that the area (A) is 64m2. Let's represent the length of one side of the square as side x side.
So, A=side×side=64 m2
To find the length of one side, we need to take the square root of 64 because side×side=64
The square root of 64 is 8.
Therefore, the length of one side of Sarah's square garden is 8 meters x 8 meters.
A school is forming teams for a competition. There are 24 students interested in joining. The school wants to create teams where each team has the same number of students, and no student is left out. What is the largest number of students the school can have in each team, ensuring all students are included?
To find the largest number of students per team, we need to find the greatest common factor (GCF) of the total number of students (24). Let's find the factors of 24:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Since we want to divide the students into teams, we need to find a factor that divides 24 evenly. The largest factor that allows us to form teams without leaving any students out is 8. Therefore, the school can have 8 students in each team, and there will be 24/8=3 teams in total.
What are the multiples of 3,5, and 10?
What are the factors of 3,5, and 10?
The factors of 3 are 1 and 3 because these are the numbers that can be multiplied to give 3 (1 × 3 = 3).
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
The factors of 5 are 1 and 5 because these are the numbers that can be multiplied to give 5 (1 × 5 = 5).
The factors of 10 are 1, 2, 5, and 10 because these are the numbers that can be multiplied to give 10 (1 × 10 = 10 and 2 × 5 = 10).
A gardening club planted 72 flowers in their garden. They divided the flowers equally into 6 rows. Each row was further divided into 4 small plots. If they want to put a decorative stone in every other small plot, how many stones will they need in total?
First, find out how many small plots are there in total:
Number of small plots=6 rows×4 plots per row=24 small plots. Number of small plots=6 rows×4 plots per row=24 small plots
Since they want to put a stone in every other small plot, divide the total number of small plots by 2:
Number of small plots with stones=24 small plots÷2=12 small plots.
Therefore, they will need 12 decorative stones in total
Tom and Sarah both have gardens. Tom planted 15 apple trees, and Sarah planted 20 orange trees. They want to arrange the trees in rows, with each row having the same number of trees. What is the largest number of trees they can put in each row so that all trees are used?
Prime factorization:
The common factor is 5, and it's the largest factor they both share. Therefore, Tom and Sarah can plant 5 trees in each row, and they will have 3 rows of apple trees and 4 rows of orange trees.