Please explain the steps towards solving these 5 math problmes?

Question

Break it down as much as you can plz.. they are for an online class and i can't ask the professor as there is no professor to ask... I know some but i'm a bit lost...

These are examples, i'm not even sure if they'll work.. thnx

1. Write the decimal as a fraction or mixed number: 0.345

2. Solve for x: 0.4x + 2.6 = 1.4

3. Add 763.7651 + 22.001 + 43.89

4. Simplify 4/15 + b/5

5. Find the difference in length of two scarves if one scarf is 5/12 of a yard and the other is 2/3 of a yard long.

Answer 1

1.  Since 0.345 has 3 decimals, multiply by 1000, so

     345/1000 now factor down.  Both are divisible by 5 so

     69/200.

2.  get the numbers on one side by subtracting 2.6 from each side:

     0.4X = - 1.2

     Now divide both sides by 0.4

     X = - 1.2/.4 = -3

3.  Just add them vertically, put the decimals in line and add. If there

     is nothing in the column, it's a zero.

     763.7651

       22.001

       43.89

------------------

     829.6561

4.  They are both factors of 5, but the 4/15 ths also has a 3 in the denominator, so multiply the b/5 by 3/3 and get

4/15 + 3b/15 = (4 + 3b)/15

5.  You are looking for a common denominator between the 12 and the 3.  The common denominator is 12, so multiply the 2/3 by 4/4 to get

8/12 then subtract 8/12-5/12 = 3/12.  Since 12 can be divided by 3, reduce this to 1/4 yard.

Answer 2

1. 345/1000 divide all by 5 = 69/200

2. 0.4x+2.6=1.4

   0.4x+2.6-2.6=1.4-2.6

   0.4x=-1.2

   0.4x/0.4= -1.2/0.4

   x = -3

3. 829.6561

4. 4/15 + 3b/15

   (4+3b)/15

5. 5/12 - 2/3

    5/12 - 8/12

    difference is 3/12 or 1/4 of a yard

Answer 3

1. with decimals the first digit (to the right of the zero) is called the tenths column. the second is called the hundredths, the third is called the thousandths and so on.

so for example 0.3 - the digit is in the tenths column so it is three tenths or 3/10

for 0.34 the digits extend into the hundredths column so it is thirty four hundredths or 34/100

in your example the digits extend into the thousandths column so it would be 345/1000

Answer 4

1.  345 over 1000.  You can then reduce, by dividing both top and bottom by 5, for example.

2.

0.4x + 2.6 = 1.4

subtract 2.6 from both sides:

0.4 x = - 1.2

divide both sides by 0.4 (or multiply both by 2.5) to get x = -3

3.  829.6561  by hand.

4.  (4+3b)/15

5.   2/3 - 5/12 .  Multiply 2/3 by 4/4 to get 8/12.  8/12 - 5/12 = 3/12 = 1/4.

Answer 5

1)

Divide it by one to turn it into a fraction

0.345 = 0.345 / 1

Multiple the denominator (bottom number) and numerator (top number) by 100

0.345 / 1 = 345 / 100

divide both parts of the fraction by 5

345 / 100 = 69/20

so 69/20 is the answer!!!!

2)

0.4x + 2.6 = 1.4

take away 2.6 from both sides of the equation...

0.4x + 2.6 - 2.6 = 1.4 - 2.6

0.4x = 1.4 - 2.6

its like moving the 2.6 to the other side except it changes from positive to negative.

0.4x = 1.4 - 2.6 = -1.2

0.4x = -1.2

multiply both sides of the equation by 10

4x = -12

divide both sides of the equation by 4

x = -3

and the is the answer!!!!!!!!!!!!!!!

3)

use a method for adding numbers.

I go from right to left, adding the columns, carrying the 10's to the left.

763.7651+

022.0010 +

043.8900

---------------

829.6561

1  1 1

so 829.6561 is the answer!!!!!!!!!!!!

4)

Simplify 4/15 + b/5

to add fractions you need a common denominator (bottom number)

Times both sides of b/5 by 3 so it becomes 3b/15 but its still the same fraction.

Now we have:

3b/15 + 4/15

Now the denominators are the same, we can add the numerators (top numbers)

We end up with:

(3b + 4)/15

And thats the answer!!!!!!!!!!!!!!

5)

Find the difference in length of two scarves if one scarf is 5/12 of a yard and the other is 2/3 of a yard long

The question is asking you  2/3 - 5/12

Again we must find common denominators.

we can multiply both sides of 2/3 by 4 to get 8/12

We can now subtract the numerators:

8 - 5 = 3

8/12 - 5/12 = 3/12

3/12 can be reduced by dividing both sides of the fraction by 3

3/12 = 1/4

so 1/4 of a yard is the answer!!!!!!!!!!!!

Answer 6

PROBLEM NUMBER 2

First of all think of an equation as a balancing scale.  If the scale is balanced and you change one side of it, it is now unbalanced.  In order to keep it balanced you have to make the exact same change to the other side. (other side of the equal sign)  That is why whenver you change the value of one side, you have to change the value of the other side in the same manner.

Read the problem as a word sentence; not a numeric one.

for instance

5x +3 =6, You are solving for "x"

This reads as Five "x" plus three equals six.

You want to work the equation so that the sentence will read

Ex equals three fifths. which, of course, you will not know the answer up front.

You want to get the variable "x" all alone. Therefore take away any other elements that are not "x" variables.   In this case there is a 3 with the 5x and you want to get rid of the 3.

Since you're taking 3 from one side, you have to take three from the other side.

5x +3 -3 = 6-3  TAKE THREE FROM BOTH SIDES

5x = 3 DIVIDE BOTH SIDES BY 5 TO GET THE "X" ALONE

5x/5 = 3/5

x = 3/5

PROBLEM 3

Line up the problems so that the decimals are in line

763.7651

+22.001

Since there is nothing under the one "1" at the end, that is the same as a "0" being there.  Add 1 + 0 = 1.  GIVING YOU

763.7651

+22.0010

PROBLEM 4

Denominators have to be the same in order to add or subtract fractions.  

multiply the "b" and the "5" by 3 and you will have

3b/15.  I choose "3" because i wanted the denominators to be the same.

Now add the numerators (top number) and leave the denominator the same(bottom number)

PROBLEM 5

Once again you need  common denominators.

Multiply the "2" and the "3" by "4".  You will get 8/12.  Now subtract the numerators and you'll have your answer.

HOPE THIS HELPS