The Snake Eyes Roller Coaster climbs 125 feet from ground level then drops 60 feet before climbing another 135 feet. How far does the coaster need to drop or climb to be back at ground level? (Hint: Draw a picture or use a number line.)
To solve this problem, we can use a number line. Let's assume that ground level is represented by the number 0 on the number line.
The roller coaster starts at ground level, then climbs 125 feet. This takes it to a height of +125 on the number line.
Next, the roller coaster drops 60 feet. This takes it down to a height of +125 - 60 = +65 on the number line.
Finally, the roller coaster climbs another 135 feet. This takes it to a height of +65 + 135 = +200 on the number line.
To find out how much the coaster needs to either drop or climb to be back at ground level, we need to determine how far the coaster is from 0 on the number line.
The coaster is currently at +200, which is 200 feet above ground level. Therefore, it needs to drop 200 feet to be back at ground level.
Simplify |-7| + |6|.
:)
|-7| + |6| simplifies to 7 + 6, which equals 13.
Before it started to rain, Amnar cut 1/6 of the grass and Aayush cut 1/3 of the grass. Which statement is true?
(1 point)
Responses
a. Together the boys didn’t even cut half of the yard.
b. The boys cut almost the whole yard.
c. The boys cut exactly half of the yard.
d. Together the boys cut three-fourths of the yard.
To find the total amount of grass cut by both boys, we need to add the fractions 1/6 and 1/3.
First, we find a common denominator for 1/6 and 1/3, which is 6.
Next, we convert the fractions to have the same denominator:
1/6 = 1/6 * 1/1 = 1/6 * 2/2 = 2/12
1/3 = 1/3 * 2/2 = 2/6
Now, we can add the fractions:
2/12 + 2/6 = 4/12 + 8/12 = 12/12
The boys together cut 12/12, which is equivalent to the whole yard (1 whole).
Therefore, the statement "The boys cut almost the whole yard." (b) is true.
The Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4
chocolate cakes, 2 1/2
red velvet cakes, 3/4
of a carrot cake and 3 1/2
sugar cream cakes.
Which statement tells the total number of cakes they sold and explains how the total can be calculated?
(1 point)
-
To calculate the total number of cakes sold, we need to add the number of each type of cake sold together.
2 1/4 chocolate cakes can be represented as a mixed number: 2 + 1/4 = 2 1/4 (or 9/4)
2 1/2 red velvet cakes can also be represented as a mixed number: 2 + 1/2 = 2 1/2 (or 5/2)
3/4 of a carrot cake can be represented as a fraction: 3/4
3 1/2 sugar cream cakes can be represented as a mixed number: 3 + 1/2 = 3 1/2 (or 7/2)
To find the total number of cakes sold, we add these quantities together:
2 1/4 + 2 1/2 + 3/4 + 3 1/2 = 9 + 5/4 + 3/4 + 7/2
We can convert the mixed numbers to improper fractions:
9 + 5/4 + 3/4 + 7/2 = 9 + 5/4 + 3/4 + 14/4
Next, we add the fractions with a common denominator:
9 + 5/4 + 3/4 + 14/4 = 9 + (5 + 3 + 14)/4 = 9 + 22/4
Finally, we simplify the fraction:
9 + 22/4 = 9 + 11/2 = 18/2 + 11/2 = 29/2
So, the total number of cakes sold is 29/2, which can also be expressed as 14 1/2.
Therefore, the statement that tells the total number of cakes sold is: "They sold a total of 14 1/2 cakes, which can be calculated by adding the quantities of each type of cake sold."
The Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4
chocolate cakes, 2 1/2
red velvet cakes, 3/4
of a carrot cake and 3 1/2
sugar cream cakes.
Which statement tells the total number of cakes they sold and explains how the total can be calculated?
(1 point)
A. First, find the least common multiple and change only the denominators: 2 1/4 + 2 1/4 + 3/4 + 3 1/4 = 764
. Next, simplify: 7 6/4 = 8 1/2
.
B. First, change the fractions to make denominators common, and then add: 2 1/4 + 2 2/4 + 3/4 + 3 2/4 = 7 8/4
. Next, simplify: 7 8/4 = 9
.
C. First, add across the numerators and denominators: 1/4 + 1/2 + 3/4 + 1/2 = 6 1/2
. Next, add whole numbers: 2 + 2 + 3 = 7. Then combine, 7 6/12= 7/12
.
D. First, change the numerators to 3 to make them common, and then add: 2 3/4 + 2 3/2 + 3/4 + 3 3/4= 7 12/14
. Next, simplify: 7 12/14=7 6/7
.
.
. . . . . .
. [ a n s w e r ] . . .
.
The correct statement that tells the total number of cakes they sold and explains how the total can be calculated is:
B. First, change the fractions to make denominators common, and then add: 2 1/4 + 2 2/4 + 3/4 + 3 2/4 = 7 8/4. Next, simplify: 7 8/4 = 9.
Explanation:
In this statement, we correctly add the quantities of each type of cake sold after adjusting the fractions to have a common denominator of 4. By doing so, we can add the whole numbers (2 + 2 + 3) and the fractions (1/4 + 2/4 + 3/4 + 2/4) separately. This yields 9 as the total number of cakes sold.
Mrs. Taylor is crocheting a blanket for her daughter. She made 3/8
of the blanket green, 1/4
of the blanket blue, and the rest of the blanket was yellow. Which fraction represents the yellow part of the blanket?
A. 5/8
B. 3/4
C. 1/2
D. 3/8
. . . [ a n s w e r ] . . .