The decimal .087 can be written as
Responses
A 8.7/10
B 87/10,000
C 87/1 , 000
D 87/100
The decimal .087 can be written as 87/100. Therefore, the answer is D) 87/100.
Find the product.
-10(-12)(5)
Responses
A -6000-6000
B -1200-1200
C -600-600
D 120120
E 600
The product of -10, -12, and 5 is determined by multiplying them together:
-10 * -12 * 5 = 600
Therefore, the answer is E) 600.
After being exposed to an incredible shrinking machine, Halley's height decreased by 108 cm over 6 seconds. Her height decreased by the same amount each second. How much did Halley's height change each second?
Responses
A 18 cm18 cm
B 108 cm108 cm
C −18 cm−18 cm
D −108 cm
To find out how much Halley's height changed each second, we need to divide the total height decrease by the number of seconds:
108 cm / 6 seconds = 18 cm
Therefore, the answer is A) 18 cm.
Which fraction is equal to 0.25?
Responses
A 1/4
B 1/5
C 2/5
D 3/4
To find the fraction that is equal to 0.25, we can convert 0.25 to a fraction.
0.25 can be written as 25/100, which can be simplified to 1/4.
Therefore, the answer is A) 1/4.
Over the last 6 months, Josh wrote 6 checks for a total of $702 to pay his phone bill. His phone bill is the same amount each month. What was the change in Josh’s bank account balance each month after paying his phone bill?
Responses
A $117$117
B $702$702
C −$117−$117
D −$702
To find the change in Josh's bank account balance each month, we need to divide the total amount paid over 6 months by the number of months:
$702 / 6 months = $117
Therefore, the answer is A) $117.
Divide −5/9 by 5/7.
To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 5/7 = 7/5
Therefore, -5/9 ÷ 5/7 is equivalent to -5/9 * 7/5.
When we multiply these fractions, we multiply the numerators and multiply the denominators:
(-5 * 7) / (9 * 5) = -35/45
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
(-35/5) / (45/5) = -7/9
Therefore, -5/9 ÷ 5/7 is equal to -7/9.
2 1/3÷2/5
To divide a mixed number by a fraction, we need to convert the mixed number to an improper fraction and then divide.
First, let's convert the mixed number 2 1/3 to an improper fraction.
2 × 3 = 6
6 + 1 = 7
Therefore, 2 1/3 is equal to 7/3.
Next, we can divide 7/3 by 2/5.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 2/5 is 5/2.
So, 7/3 ÷ 2/5 is equivalent to 7/3 * 5/2.
When we multiply these fractions, we multiply the numerators and multiply the denominators:
(7 * 5) / (3 * 2) = 35/6.
Therefore, 2 1/3 ÷ 2/5 is equal to 35/6.
9/15
B 4/5
C 14/15
D 5 5/6
To simplify the fraction 9/15, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3.
9 ÷ 3 = 3
15 ÷ 3 = 5
Therefore, 9/15 simplifies to 3/5.
The answer is not listed among the options provided.
Divide −5/9 by 5/7.
9/15
B 4/5
C 14/15
D 5 5/6
Apologies for the confusion earlier. Let's calculate the correct division: -5/9 ÷ 5/7.
To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 5/7 = 7/5.
Therefore, -5/9 ÷ 5/7 is equivalent to -5/9 * 7/5.
When we multiply these fractions, we multiply the numerators and multiply the denominators:
(-5 * 7) / (9 * 5) = -35/45.
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
(-35/5) / (45/5) = -7/9.
Therefore, -5/9 ÷ 5/7 is equal to -7/9.
The correct answer is not listed among the options provided.
2 1/3÷2/5
A 9/15
B 4/5
C 14/15
D 5 5/6
To divide a mixed number by a fraction, we need to convert the mixed number to an improper fraction and then divide.
First, let's convert the mixed number 2 1/3 to an improper fraction.
2 × 3 = 6
6 + 1 = 7
Therefore, 2 1/3 is equal to 7/3.
Next, we can divide 7/3 by 2/5.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 2/5 is 5/2.
So, 7/3 ÷ 2/5 is equivalent to 7/3 * 5/2.
When we multiply these fractions, we multiply the numerators and multiply the denominators:
(7 * 5) / (3 * 2) = 35/6.
To simplify this improper fraction, we can express it as a mixed number.
35 ÷ 6 = 5 remainder 5.
Thus, the fraction simplifies to 5 5/6.
Therefore, 2 1/3 ÷ 2/5 is equal to 5 5/6.
The correct answer is D) 5 5/6.
−4/7(−13/2)
A −43/14− 43 14
B −26/7− 26 7
C 26/7
D 43/14
To multiply fractions, we simply multiply the numerators and multiply the denominators.
For the expression -4/7 * -13/2, we have:
(-4 * -13) / (7 * 2) = 52 / 14
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
52/2 / 14/2 = 26/7
Therefore, -4/7 * -13/2 is equal to 26/7.
The answer is C) 26/7.
Divide −4/17 by −3/4.
Responses
A −16/51−
B −3/17
C 16/51
D 3/17
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of -3/4 is -4/3.
So, -4/17 ÷ -3/4 is equivalent to -4/17 * -4/3.
When we multiply these fractions, we multiply the numerators and multiply the denominators:
(-4 * -4) / (17 * 3) = 16/51.
Therefore, -4/17 ÷ -3/4 is equal to 16/51.
The answer is C) 16/51.
Multiply: −1/3 · −5/6
Responses
A −2/3
B -5 /18
C 2/3
D 5/18
To multiply fractions, we simply multiply their numerators and denominators.
For the expression -1/3 * -5/6, we have:
(-1 * -5) / (3 * 6) = 5/18
Therefore, -1/3 * -5/6 is equal to 5/18.
The answer is D) 5/18.
A local coffee shop serves 2/9 as many customers as a shop run by a national coffee chain. The shop run by the chain serves 502 customers a day. About how many customers does the local shop serve in a day (round to the nearest whole number)?
Responses
A 45
D 112
C 390
D 645
To find out how many customers the local coffee shop serves in a day, we need to calculate 2/9 of the number of customers served by the national coffee chain.
2/9 * 502 = 111.33
Rounding this to the nearest whole number, the local coffee shop serves about 111 customers in a day.
Note: None of the given options matches the calculated value exactly.
Landscape Services
Service Price
Mowing Lawn $22.00
Weed-eating $5.00
Edging $5.00
Leaf Blowing $5.00
Planting Flowers $10.00 per flower bed
Ms. Davis hires Kyle to mow the grass, edge the lawn, clean up the leaves, and plant 2 flower beds. Kyle spends 3.2 hours completing the work. What is Kyle's average hourly earnings for the job?
Responses
A $15.00$15.00
B $16.25$16.25
C $17.50$17.50
D $18.75$18.75
E $20.25
To calculate Kyle's average hourly earnings for the job, we need to divide the total amount he earned by the number of hours he worked.
The total amount Kyle earned can be calculated by summing up the prices for the services he provided:
Mowing Lawn: $22.00
Edging: $5.00
Leaf Blowing: $5.00
Planting Flowers (2 flower beds): $10.00 * 2 = $20.00
Total earnings: $22.00 + $5.00 + $5.00 + $20.00 = $52.00
Next, we divide the total earnings by the number of hours worked:
$52.00 / 3.2 hours ≈ $16.25
Therefore, Kyle's average hourly earnings for the job is $16.25.
The answer is B) $16.25.
Henry did 56 of his math problems. The next day, he checked 23 of the homework problems he did the night before. What fraction of the homework problems did he check?
Responses
A 161 6
B 131 3
C 595 9
D 54
To find the fraction of the homework problems that Henry checked, we divide the number of problems he checked (23) by the total number of problems (56).
The fraction would be 23/56.
Therefore, the answer is not listed among the options provided.
Henry did 5/6 of his math problems. The next day, he checked 2/3 of the homework problems he did the night before. What fraction of the homework problems did he check?
Responses
A 1/6
B 1/3
C 5/9
D 5/4
To find the fraction of the homework problems that Henry checked, we multiply the fraction of problems he did (5/6) by the fraction of problems he checked the next day (2/3).
(5/6) * (2/3) = 10/18.
The fraction of homework problems he checked is 10/18, which can be simplified to 5/9.
Therefore, the answer is C) 5/9.
Over the course of four weeks Mia spent 35 1/2 hours training for a race. Michael spent 1 1/2 times that amount training for the same race. How many hours did Michael spend training?
Responses
A 49 1/2
B 53 1/4
C 71
D 73 1/4
E 93 1/2
To find out how many hours Michael spent training, we need to calculate 1 1/2 times the amount Mia spent training.
1 1/2 times 35 1/2 can be calculated as follows:
1 1/2 = 3/2 (improper fraction)
35 1/2 = 71/2 (improper fraction)
Now, we multiply the two fractions:
(3/2) * (71/2) = (3*71) / (2*2) = 213/4.
The fraction 213/4 can be simplified to 53 1/4.
Therefore, Michael spent 53 1/4 hours training.
The answer is B) 53 1/4.