Answers for April 2022:
Questions:
(a) Find 30% of 750 g.
(b)Find 25% of $26.
(c) Find 6% of 300.
Answers:
(a) Our first step is to divide 30 by 100. 30 by 100 = 0.3. The next step would be to multiply 0.3 by 750. 0.3 x 750 = 225. Therefore, 30% of 750 g is 225 g.
(b) Our first step is to divide 25 by 100, which equals 0.25. The next step would be to multiply 0.25 by 26, which is 6.5. Therefore, 25% of $26 is $6.5.
(c) Our first step is to divide 6 by 100, which equals 0.06. The next step would be to multiply 0.06 by 300, which is 18. Therefore, 6% of 300 is 18.
Answers for January 2022:
Questions:
1. Is 299594912909526 divisible by 3?
2. Is 967324186932 divisible by 7?
3. Is 3719287654182345 divisible by 9?
Answers:
1. To see if a number is divisible by 3, calculate the sum of all the digits in the number. If the sum is a multiple of 3 or is divisible by 3, the original number is also divisible by 3. The sum of all of the digits in 299594912909526 is 81. 81 divided by 3 is 27. Therefore, 299594912909526 is divisible by 3.
2. To see if a number is divisible by 7, multiply the last digit of the number by 2. Subtract this number from the sum of the rest of the digits in the original number. If this number is 0 or is divisible by 7, the original number is also divisible by 7. For this question, the last digit of the number multiplied by 2 is 4. The sum of the rest of the digits from the original number is 58. Our next step is to subtract 4 from 58, which is 54. 54 is not divisible by 7. Therefore, 967324186932 is not divisible by 7.
3. To see if a number is divisible by 9, calculate the sum of all the digits in the number. If that sum is divisible by 9, then the original number is also divisible by 9. The sum of all of the digits in 3719287654182345 is 75. 75 is not divisible by 9. Therefore, 3719287654182345 is not divisible by 9.
Answers for July 2021:
Questions:
Find the value of x.
a) 5x=20
b) 12x-40=32
c )x/7 - 4 = -6
Answers:
a) Our first step is to divide both sides of the equation by x, to transform the left side of the equation from 5x to x. We are left with x=4
b) Our first step is to add 40 to both sides, leaving us with 12x=72. Then, we divide both sides of the equation by 12, leaving us with x=6.
c)Our first step is to add 4 to both sides of the equation, leaving us with x/7=-2. Then, we multiply both sides of the equation by 7, leaving us with x=-14.
Questions:
(a) Find 30% of 750 g.
(b)Find 25% of $26.
(c) Find 6% of 300.
Answers:
(a) Our first step is to divide 30 by 100. 30 by 100 = 0.3. The next step would be to multiply 0.3 by 750. 0.3 x 750 = 225. Therefore, 30% of 750 g is 225 g.
(b) Our first step is to divide 25 by 100, which equals 0.25. The next step would be to multiply 0.25 by 26, which is 6.5. Therefore, 25% of $26 is $6.5.
(c) Our first step is to divide 6 by 100, which equals 0.06. The next step would be to multiply 0.06 by 300, which is 18. Therefore, 6% of 300 is 18.
Answers for January 2022:
Questions:
1. Is 299594912909526 divisible by 3?
2. Is 967324186932 divisible by 7?
3. Is 3719287654182345 divisible by 9?
Answers:
1. To see if a number is divisible by 3, calculate the sum of all the digits in the number. If the sum is a multiple of 3 or is divisible by 3, the original number is also divisible by 3. The sum of all of the digits in 299594912909526 is 81. 81 divided by 3 is 27. Therefore, 299594912909526 is divisible by 3.
2. To see if a number is divisible by 7, multiply the last digit of the number by 2. Subtract this number from the sum of the rest of the digits in the original number. If this number is 0 or is divisible by 7, the original number is also divisible by 7. For this question, the last digit of the number multiplied by 2 is 4. The sum of the rest of the digits from the original number is 58. Our next step is to subtract 4 from 58, which is 54. 54 is not divisible by 7. Therefore, 967324186932 is not divisible by 7.
3. To see if a number is divisible by 9, calculate the sum of all the digits in the number. If that sum is divisible by 9, then the original number is also divisible by 9. The sum of all of the digits in 3719287654182345 is 75. 75 is not divisible by 9. Therefore, 3719287654182345 is not divisible by 9.
Answers for July 2021:
Questions:
Find the value of x.
a) 5x=20
b) 12x-40=32
c )x/7 - 4 = -6
Answers:
a) Our first step is to divide both sides of the equation by x, to transform the left side of the equation from 5x to x. We are left with x=4
b) Our first step is to add 40 to both sides, leaving us with 12x=72. Then, we divide both sides of the equation by 12, leaving us with x=6.
c)Our first step is to add 4 to both sides of the equation, leaving us with x/7=-2. Then, we multiply both sides of the equation by 7, leaving us with x=-14.
Answers for May 2021:
Questions:
1. What is the circumference of a circle with a diameter of 12 cm? Round your answer to two decimal places.
2. What is the circumference of a circle with a diameter of 8cm? Round your answer to two decimal places.
Answers:
1. The circumference of a circle is found by the equation 2𝛑r. Where 𝛑 = 3.14 and r = radius of the circle. The radius of a circle is the diameter divided by 2. For this question, the diameter is 12cm, so the radius is 6cm. Therefore the circumference is 2 x 3.14 x 6 = 37.68cm.
2. Using the equation 2𝛑r, the circumference is 2 x 3.14 x 4 = 25.12cm
Questions:
1. What is the circumference of a circle with a diameter of 12 cm? Round your answer to two decimal places.
2. What is the circumference of a circle with a diameter of 8cm? Round your answer to two decimal places.
Answers:
1. The circumference of a circle is found by the equation 2𝛑r. Where 𝛑 = 3.14 and r = radius of the circle. The radius of a circle is the diameter divided by 2. For this question, the diameter is 12cm, so the radius is 6cm. Therefore the circumference is 2 x 3.14 x 6 = 37.68cm.
2. Using the equation 2𝛑r, the circumference is 2 x 3.14 x 4 = 25.12cm
Answers for April 2021:
Questions:
1. What is the prime factorization of 30?
2. What is the prime factorization of 28?
3. What is the prime factorization of 45?
Answers:
30 = 2 x 2 x 2 x 5
28 = 2 x 2 x 7
45 = 3 x 3 x 5
Questions:
1. What is the prime factorization of 30?
2. What is the prime factorization of 28?
3. What is the prime factorization of 45?
Answers:
30 = 2 x 2 x 2 x 5
28 = 2 x 2 x 7
45 = 3 x 3 x 5
Answers for March 2021:
Question:
What is the smallest positive number that can be added to 280 so that the answer is a multiple of 45?
Answer:
First, find the multiple of 45 that's nearest to 280. That is 45 x 7 = 315 . Then take that and subtract 280 from it to find the difference. 315 - 280 = 35 this gives us our answer, 35.
Question:
What is the smallest positive number that can be added to 280 so that the answer is a multiple of 45?
Answer:
First, find the multiple of 45 that's nearest to 280. That is 45 x 7 = 315 . Then take that and subtract 280 from it to find the difference. 315 - 280 = 35 this gives us our answer, 35.
Answers for February 2021:
Question:
Find the value of x:
a) 3x +25 = 40
b) x/5 -17 = 10
c) 5x +10 = 17+23
Answers:
a) 3x +25 = 40, first move the 25 out of the left side of the equation by subtracting 20 from both sides of the equation. This gives us 3x=15. Then divide both sides by 3 to make the 3x into x. This gives us our answer, x=5.
b) x/5 - 17 = 10. First we add 17 to both sides. This gives us x/5 = 27. Then multiply both sides by 5. This gives us our answer, x=135.
c) 5x + 10 = 17 +23. Here we can start by combining our like terms on the right side of the equation, giving us
5x + 10 = 40. Now we subtract 10 from both sides of the equation, which gives us 5x = 30. Next we divide both sides by 5, which gives us our answer, x = 6.
Question:
Find the value of x:
a) 3x +25 = 40
b) x/5 -17 = 10
c) 5x +10 = 17+23
Answers:
a) 3x +25 = 40, first move the 25 out of the left side of the equation by subtracting 20 from both sides of the equation. This gives us 3x=15. Then divide both sides by 3 to make the 3x into x. This gives us our answer, x=5.
b) x/5 - 17 = 10. First we add 17 to both sides. This gives us x/5 = 27. Then multiply both sides by 5. This gives us our answer, x=135.
c) 5x + 10 = 17 +23. Here we can start by combining our like terms on the right side of the equation, giving us
5x + 10 = 40. Now we subtract 10 from both sides of the equation, which gives us 5x = 30. Next we divide both sides by 5, which gives us our answer, x = 6.
Answers for January 2021:
Question:
The length of one leg of a triangle is 5 cm. The other leg of the triangle is 7 cm long.
What is the length of the hypotenuse?
What is the area of this triangle?
Answer:
We can use Pythagorean theorem (a^2 +b^2 = c^2) to find the hypotenuse of this triangle. 5^2 + 7^2 = hypotenuse^2
which turns into 25+49=hypotenuse^2, which can be simplified into 64=hypotenuse^2. Now we take the square root of both sides to get 8=hypotenuse.
To find the area of the triangle, multiply the length of the two legs together and then divide by 2. 5x7=35,
35 divided by 2 = 17.5. Remember to put the units on your answer. 17.5cm^2
Question:
The length of one leg of a triangle is 5 cm. The other leg of the triangle is 7 cm long.
What is the length of the hypotenuse?
What is the area of this triangle?
Answer:
We can use Pythagorean theorem (a^2 +b^2 = c^2) to find the hypotenuse of this triangle. 5^2 + 7^2 = hypotenuse^2
which turns into 25+49=hypotenuse^2, which can be simplified into 64=hypotenuse^2. Now we take the square root of both sides to get 8=hypotenuse.
To find the area of the triangle, multiply the length of the two legs together and then divide by 2. 5x7=35,
35 divided by 2 = 17.5. Remember to put the units on your answer. 17.5cm^2
Answers for August 2020:
Questions:
What is the prime factorization of 45?
What is the prime factorization of 90?
What is the prime factorization of 84?
Answers:
Prime numbers are numbers that can only be divided by itself and 1 (for example, 2, 3, 7). Prime factorization is when you find what prime numbers multiply to make the given number. To find the prime factorization of 45, you can break down 45 into 9 x 5, and then 9 can be broken down into 3 x 3, which makes 3 x 3 x 5 the prime factorization of 45. To find the prime factorization of 90, you can break 90 down into 9 x 10, and break 9 into 3 x 3 and 10 into 2 x 5, which makes 2 x 3 x 3 x 5 the prime factorization of 90. To find the prime factorization of 84, you can break 84 into 12 x 7, which can break down into 2 x 6 x 7, and then into 2 x 2 x 3 x 7. There is no right way to know what you want to break the number down into first, any way you like to break the number down will eventually lead you to the prime factorization, where all the numbers being multiplied to give you your number are prime.
Questions:
What is the prime factorization of 45?
What is the prime factorization of 90?
What is the prime factorization of 84?
Answers:
Prime numbers are numbers that can only be divided by itself and 1 (for example, 2, 3, 7). Prime factorization is when you find what prime numbers multiply to make the given number. To find the prime factorization of 45, you can break down 45 into 9 x 5, and then 9 can be broken down into 3 x 3, which makes 3 x 3 x 5 the prime factorization of 45. To find the prime factorization of 90, you can break 90 down into 9 x 10, and break 9 into 3 x 3 and 10 into 2 x 5, which makes 2 x 3 x 3 x 5 the prime factorization of 90. To find the prime factorization of 84, you can break 84 into 12 x 7, which can break down into 2 x 6 x 7, and then into 2 x 2 x 3 x 7. There is no right way to know what you want to break the number down into first, any way you like to break the number down will eventually lead you to the prime factorization, where all the numbers being multiplied to give you your number are prime.
Answers for July 2020:
Question:
(Hint- You do not need to divide each of these numbers. There is a trick!)
Is 20983765 divisible by 3?
Is 93092857812 divisible by 2?
Is 10298928374 divisible by 9?
Answer:
You do not need to divide these numbers. Here are some tricks to find out if a number is divisible by 3,2, or 9. To find out if a number is divisible by 3, add up all the digits in the number. If the sum of all the digits is divisible by 3, then the whole number is too. This trick can be also used to find out if a number is divisible by 9.
Is 20983765 divisible by 3? 2+0+9+8+3+7+6+5=40. 40 is not divisible by 3. Therefore, 20983765 is not divisible by 3.
Is 10298928374 divisible by 9? 1+0+2+9+8+9+2+8+3+7+4=53. 53 is not divisible by 9. Therefore, 10298928374 is not divisible by 9.
To find out if a number is divisible by 2, just check the number made by the last two digits. If the number made by the last two digits is divisible by 2, then the whole number is divisible by 2.
Is 93092857812 divisible by 2? The last two digits make the number 12. Since 12 is divisible by 2, 93092857812 is divisible by 2.
Question:
(Hint- You do not need to divide each of these numbers. There is a trick!)
Is 20983765 divisible by 3?
Is 93092857812 divisible by 2?
Is 10298928374 divisible by 9?
Answer:
You do not need to divide these numbers. Here are some tricks to find out if a number is divisible by 3,2, or 9. To find out if a number is divisible by 3, add up all the digits in the number. If the sum of all the digits is divisible by 3, then the whole number is too. This trick can be also used to find out if a number is divisible by 9.
Is 20983765 divisible by 3? 2+0+9+8+3+7+6+5=40. 40 is not divisible by 3. Therefore, 20983765 is not divisible by 3.
Is 10298928374 divisible by 9? 1+0+2+9+8+9+2+8+3+7+4=53. 53 is not divisible by 9. Therefore, 10298928374 is not divisible by 9.
To find out if a number is divisible by 2, just check the number made by the last two digits. If the number made by the last two digits is divisible by 2, then the whole number is divisible by 2.
Is 93092857812 divisible by 2? The last two digits make the number 12. Since 12 is divisible by 2, 93092857812 is divisible by 2.
Answers for June 2020:
Question:
If the legs of a triangle are 3cm, and 4 cm, what is the length of the hypotenuse?
Answer:
Use the Pythagorean theorem. 3 squared is 9. 4 squared is 16. 9+16=25. The square root of 25 is 5. The length of the hypotenuse is 5 cm.
Question:
If the legs of a triangle are 3cm, and 4 cm, what is the length of the hypotenuse?
Answer:
Use the Pythagorean theorem. 3 squared is 9. 4 squared is 16. 9+16=25. The square root of 25 is 5. The length of the hypotenuse is 5 cm.
Answers for April 2020:
Question 1:
Express the fraction 5/50 as a decimal.
Answer: Make the fraction 5/50 into 1/10 by multiplying both the numerator and denominator by 5. One tenth is 0.10 , or 0.1 .
Question 2:
Express the mixed number 3 7/100 as a decimal.
Answer: 3 7/100 is 3 and 7 hundredths is 3.07.
Question 3:
Express the fraction 100/1000 as a decimal.
Answer: 100/1000 can be reduced to 1/10 which is one tenth. One tenth is 0.1
Question 1:
Express the fraction 5/50 as a decimal.
Answer: Make the fraction 5/50 into 1/10 by multiplying both the numerator and denominator by 5. One tenth is 0.10 , or 0.1 .
Question 2:
Express the mixed number 3 7/100 as a decimal.
Answer: 3 7/100 is 3 and 7 hundredths is 3.07.
Question 3:
Express the fraction 100/1000 as a decimal.
Answer: 100/1000 can be reduced to 1/10 which is one tenth. One tenth is 0.1
Answers for March 2020:
Question:
What is the sum of all the numbers from 1 to 100?
Answer:
There is a shortcut. To answer this question, think of it as 50 pairs of sums. Pair up 1+100, 2+99, 3+98,4+97, etc. You get 50 pairs of 101. 50 times 101 is 5050. 5050 is your answer!
February 16th - February 29th 2020:
Question:
What is the smallest positive number that can be added to 153 so that the answer is a multiple of 35?
Answer:
The closest multiple of 35 is 175. 175 minus 153 is 22. The answer is 22.
Question:
What is the smallest positive number that can be added to 153 so that the answer is a multiple of 35?
Answer:
The closest multiple of 35 is 175. 175 minus 153 is 22. The answer is 22.
February 9th - February 15th 2020:
Question:
The length of one leg of a triangle is 4 cm. The other leg of the triangle is 6 cm long. What is the length of the hypotenuse?
Answer:
Use Pythagoreas theorem to find the answer to this question. Pythagoreas theorem says that if you square each leg of the triangle, and then add the squares together, it equals the square of the hypotenuse, or the diagonal side. For this problem:
4 squared = 16
6 squared = 36
16 + 36 is equal to 52. To find the answer, you must now square root 52. Since 52 is not a perfect square, you can leave your answer as the square root of 52.
Question:
The length of one leg of a triangle is 4 cm. The other leg of the triangle is 6 cm long. What is the length of the hypotenuse?
Answer:
Use Pythagoreas theorem to find the answer to this question. Pythagoreas theorem says that if you square each leg of the triangle, and then add the squares together, it equals the square of the hypotenuse, or the diagonal side. For this problem:
4 squared = 16
6 squared = 36
16 + 36 is equal to 52. To find the answer, you must now square root 52. Since 52 is not a perfect square, you can leave your answer as the square root of 52.
January 5th - January 18th 2020:
Question:
Is the number 358019811 divisible by 3?
Is the number 209387088 divisible by 4?
Is the number 98357855 divisible by 9?
Answer: A short cut to find out if a number is divisible by three or by nine, add all the digits together and see if the sum is divisible by three or nine. To find out if a number is divisible by four, see if the number formed by the last two digits is divisible by four.
December 29th - January 4th 2020:
Question: What is the circumference of a circle with a diameter of 14cm?
Answer: The formula for finding the circumference of the circle using radius is 2∏r. R stands for the radius. The radius is 1/2 of the diameter. Given that pi is approximately equal to 3.14, the circumference of the circle is approximately equal to 43.98
Question: What is the circumference of a circle with a diameter of 14cm?
Answer: The formula for finding the circumference of the circle using radius is 2∏r. R stands for the radius. The radius is 1/2 of the diameter. Given that pi is approximately equal to 3.14, the circumference of the circle is approximately equal to 43.98