Fractions
I have 24 pieces of candy. If I eat 2/3 of them, how many are left?
8.
1/3 of 24=8
Explain why 0.4 x 10 = 4. Explain why 3.4 x 10 = 34.
When multiplying by ten, you move the decimal point one place to the right.
If we take a circle and make 3 cuts through the center we will have 6 sections. If we make 3 cuts that do not have to go through the center, what is the most number of sections we can make (the sections do not have to be the same shape).
7.
Jenny is 3 times as old as David right now. In 8 years she will be twice as old as David. How old is each person now?
Jenny is 24, David is 8.
I have a certain number of pieces of candy. I ate half on the first day, two-thirds of the remaining pieces on the second day and three-fourths of the remaining pieces on the third day. On the fourth day I ate the remaining 2 pieces. How many pieces did I start with?
Going backward: 2 was ¼ of what remained before eating ¾ so there were 8 before eating ¾. 8 was 1/3 remaining after eating 2/3 so before eating 2/3 there were 24. 24 was ½ of what was there before eating ½ so originally there were 48 pieces of candy.
We know that 1/2 is equivalent to 2/4 and 3/6 and 4/8. What other decimals are equivalent to .5?
.50, .500, etc.
There are 12 numbers, 1-12, on a standard clock. There are 60 minutes in an hour. How many minutes does each number represent? If there are 360 degrees in a full circle, how many degrees does each number represent? If the clock moves 12 degrees, how many minutes is that? 8 degrees? 1 degree?
Each number represents 5 minutes, 360/12= 30 degrees, 12/360 is 1/30, 1/30 of 60minutes is 2 minutes. 1 degree is 1/360 of the full circle, 8/360 is 1/45 of the circle and 1/45 of 60 is 4/3 so 1 and 1/3 of a minute or 1 minute 20 seconds. 1/360 of 60 is 1/6 so 1/6 of a minute is 10 seconds.
Jeff is 50 and Sarah is 10. In how many years will Jeff be twice as old as Sarah?
30 years.
Find a number between ½ and 1/3. Find a number between 1/x and 1/y.
2/5 is between ½ and 1/3 so 2/(x+y) is between 1/x and 1/y.
Another solution is to take the average. (½+1/3)/2= (3/6+2/6)/2 which is 5/12. So y/(xy)+x/(xy)= (y+x)/(xy)
Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why?
72 grams. Each digit's place value will be multiplied by a factor of 10: 10 x (7 + 0.2) = (10 x 7) + (10 x 0.2) = 70 + 2 = 72.
We have seen that square numbers add the next odd number: 1, 1+3=4, 4+5=9 . . . and that these numbers can form a square. There are also triangular numbers that form a triangle and these numbers add the next integer: 1, 1+2=3, 3+3=6, 6+4=10. So the first 4 triangular numbers are 1, 3, 6, 10. After 1 what is the next number that is both a square number and a triangular number. The third number is in the thousands and the fourth number is more than 41,000.
36, 1225, 41616
3 and 5 are both prime. 5 and 7 are both prime. 11 and 13 are both prime. Find the next 3 sets of primes that differ by 2.
17,19 and 29,31, and 41,43
To create equivalent fractions you can multiply both the numerator and the denominator by the same number and the new fraction is equal to the original. What is the only number that you cannot multiply both the numerator and denominator by and have the fraction remain the same value?
0 because the fraction would now be undefined since it would have 0 in the denominator.
Between any two different numbers on a number line there is a different number that is between them. Find a number between .4 and .5 (it doesn’t have to be exactly between). There isn’t a number between .4 and 2/5 because they are the same. Are 1 and .999... the same? (a decimal with the bar above it means that number repeats forever).
.45 is between .4 and .5 but there are an infinite number of correct answers that start .4 and have other numbers after it.
As we know the area of a rectangle is length times width. How does the area of the rectangle change if both the length and the width are doubled? What if the length triples and the width is multiplied by 4?
Area is multiplied by 4, area is multiplied by 12.
A prime has exactly 2 factors. 6 has 4 factors. What numbers have an odd number of different factors?
perfect squares, 1,4,9,16,25 . . .
If you take a fraction and add one to both the numerator and the denominator does the fraction get bigger, smaller, or stay the same? (Assume the numerator and denominator are positive)
If the fraction is less than 1 then it gets bigger, if it equals 1 then it stays the same and if it is greater than 1 then it gets smaller.
Convert 23/5 to a decimal.
23/5 = 4r3, so 4 3/5 = 4 6/10 = 4.6.
The angles of a triangle add to 180 degrees. If the smallest angle is ½ of another angle and 1/3 of the third angle. What are the angles of this triangle?
30, 60, and 90 degrees.
If it is 8am right now, what time will it be in 50 hours? 100 hours? 500 hours? Explain how you are arriving at your answer.
50 hours- 10am, 100 hours, 12pm, 4am, find the remainder when you divide the number of hours by 24 and add that to 8am.