The access code to a houses security system consists of 6 digits. How many different codes are available if each digit can be repeated? Please show work.

1,000,000

Step-by-step explanation: Since there are 10 possible digits, we know that there is a 1/10 chance for any possible digit in any slot. So, since there are 6 slots we can do 1/10^6, or 1 in 1 million.

It depends, well, 5.. but there’s another way if you want to get a fraction. 2 1/3 + 1 1/2 + 2/3 + 1/2 = 5

But, if you use pemdas and kind of switch the problem up a bit,

Conversion a mixed number 2 1/

2

to a improper fraction: 2 1/2 = 2 1/

2

= 2 · 2 + 1/

2

= 4 + 1/

2

= 5/

2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/

2

= 4/

2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs

Conversion a mixed number 1 1/

3

to a improper fraction: 1 1/3 = 1 1/

3

= 1 · 3 + 1/

3

= 3 + 1/

3

= 4/

3

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/

3

= 3/

3

b) Add the answer from previous step 3 to the numerator 1. New numerator is 3 + 1 = 4

c) Write a previous answer (new numerator 4) over the denominator 3.

One and one third is four thirds

Subtract: 5/

2

- 4/

3

= 5 · 3/

2 · 3

- 4 · 2/

3 · 2

= 15/

6

- 8/

6

= 15 - 8/

6

= 7/

6

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five halfs minus four thirds = seven sixths.