| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
The __________ is the greatest factor that divides two integers.
absolute value |
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greatest common multiple |
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least common multiple |
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greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 48,000 seats in a stadium are filled, how many home fans are in attendance?
| 30,400 | |
| 35,200 | |
| 32,000 | |
| 24,000 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
48,000 fans x \( \frac{2}{3} \) = \( \frac{96000}{3} \) = 32,000 fans.
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 154.6 | |
| 144.8 | |
| 117.2 | |
| 165.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 7 = \( \frac{7 \times 7}{100} \) = \( \frac{49}{100} \) = 0.49 errors per hour
So, in an average hour, the machine will produce 7 - 0.49 = 6.51 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 6.51 = 117.2 error free parts were produced yesterday.
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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commutative property for division |
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distributive property for division |
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distributive property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Bob buys two shirts, each with a regular price of $48, how much will he pay for both shirts?
| $79.20 | |
| $72.00 | |
| $16.80 | |
| $52.80 |
By buying two shirts, Bob will save $48 x \( \frac{35}{100} \) = \( \frac{$48 x 35}{100} \) = \( \frac{$1680}{100} \) = $16.80 on the second shirt.
So, his total cost will be
$48.00 + ($48.00 - $16.80)
$48.00 + $31.20
$79.20