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Convert 6/32

to a decimal using long division.(1 point)
Responses

0.1875
0.1875

1.875
1.875

0.2
0.2

6.32

11 answers

To convert \( \frac{6}{32} \) to a decimal using long division, follow these steps:

  1. Set up the division: Divide 6 by 32. Since 6 is less than 32, we know the whole number part of the quotient is 0. So we'll proceed with decimal division.

  2. Add decimal point and zeros: We write 6.000 as the dividend to perform long division.

  3. Start the division:

    • 32 goes into 60 (the first two digits of 6000) 1 time (because \( 32 \times 1 = 32 \)).
    • Subtract \( 32 \) from \( 60 \): \( 60 - 32 = 28 \).
    • Bring down the next 0 (making it 280).

  4. Continue with the division:

    • 32 goes into 280 8 times (because \( 32 \times 8 = 256 \)).
    • Subtract \( 256 \) from \( 280 \): \( 280 - 256 = 24 \).
    • Bring down the next 0 (making it 240).

  5. Continue with the division:

    • 32 goes into 240 7 times (because \( 32 \times 7 = 224 \)).
    • Subtract \( 224 \) from \( 240 \): \( 240 - 224 = 16 \).
    • Bring down the next 0 (making it 160).

  6. Continue with the division:

    • 32 goes into 160 5 times (because \( 32 \times 5 = 160 \)).
    • Subtract \( 160 \) from \( 160 \): \( 160 - 160 = 0 \).

Now, we can combine the results from our long division:

  • 1 from the first step,
  • 8 from the second,
  • 7 from the third,
  • 5 from the last step.

Putting it all together, the decimal representation of \( \frac{6}{32} \) is \( 0.1875 \).

Therefore, the correct response is:

0.1875

The decimal 0.037 can be written as which fraction?(1 point)
Responses

37/1000
37 over 1000

37/10
37 tenths

3.7/10
3 point 7 over 10

37/100

To convert the decimal \( 0.037 \) into a fraction, we can analyze it as follows:

  1. The decimal \( 0.037 \) can be read as \( 37 \) in the thousandths place. This means that it can be expressed as \( \frac{37}{1000} \).

Thus, the correct response is:

37/1000

What is 0.32 expressed as a simplified fraction?(1 point)
Responses

8/25
8 over 25

32/100
32 over 100

16/100
16 over 100

16/5

To convert the decimal \( 0.32 \) into a fraction, we can follow these steps:

  1. Write it as a fraction: Since \( 0.32 \) is in the hundredths place, we can express it as: \[ 0.32 = \frac{32}{100} \]

  2. Simplify the fraction: To simplify \( \frac{32}{100} \), we need to find the greatest common divisor (GCD) of 32 and 100. The GCD is 4.

  3. Divide both the numerator and the denominator by the GCD: \[ \frac{32 \div 4}{100 \div 4} = \frac{8}{25} \]

Thus, the simplified fraction for \( 0.32 \) is:

8/25

Find the product.

(-2)(6)(-5)(-4)

(1 point)
Responses

-30
-30

-5
-5

240
240

-240

To find the product \((-2)(6)(-5)(-4)\), we can follow these steps:

  1. Multiply the first two numbers: \[ (-2) \times 6 = -12 \]

  2. Multiply the next number: \[ -12 \times (-5) = 60 \quad \text{(multiplying two negative numbers results in a positive number)} \]

  3. Multiply the last number: \[ 60 \times (-4) = -240 \]

Putting it all together, the product of \((-2)(6)(-5)(-4)\) is:

\(-240\)

Therefore, the correct response is:

-240

Find the product:

−6(−4/3)(10)
(1 point)
Responses

-45
-45

60
60

-120
-120

80

To find the product \( -6 \left(-\frac{4}{3}\right)(10) \), we can follow these steps:

  1. Multiply the first two numbers: \[ -6 \times \left(-\frac{4}{3}\right) = \frac{24}{3} = 8 \quad \text{(because multiplying two negative numbers gives a positive result)} \]

  2. Now multiply the result by 10: \[ 8 \times 10 = 80 \]

Therefore, the product \( -6 \left(-\frac{4}{3}\right)(10) \) is:

80

Each issue of a magazine costs $6.95 at the supermarket. A 6-month digital subscription costs $30.99. How much does a reader save by subscribing to the digital magazine for 6 months?(1 point)
Responses

10.71
10.71

1.79
1.79

41.70
41.70

24.04

To determine how much a reader saves by subscribing to the digital magazine for 6 months, we first need to calculate the total cost of buying the magazine issues individually for 6 months.

  1. Calculate the cost of individual issues: \[ \text{Cost per issue} = 6.95 \] \[ \text{Number of months} = 6 \] \[ \text{Total cost for 6 months} = 6.95 \times 6 = 41.70 \]

  2. Compare with the cost of the digital subscription: \[ \text{Cost of digital subscription} = 30.99 \]

  3. Calculate the savings: \[ \text{Savings} = \text{Total cost for 6 months} - \text{Cost of digital subscription} = 41.70 - 30.99 = 10.71 \]

Thus, a reader saves $10.71 by subscribing to the digital magazine for 6 months.

The correct response is:

10.71