Stumped with a math problem?

Question

No, I'm not a student trying to cheat on my math paper. Rather, I'm a mother who is having difficulty helping my child.
4 and z/8 is a mixed numeral. So, 4 is the whole number and z/8 is the fraction that is beside it.
I need to know how to solve this problem in order to do more just like it.
4 z/8 + z/6

Answer 1

Assuming 4z/8 means multiply 4*(z/8)

4*(z/8) +z/6=
extract the z from both fractions.
=z*(4/8) + z*(1/6)=
z* ( 4/8 + 1/6)= ......."same as z*(4/8) + z*(1/6) "
get common denominator,
8 and 6 have a common denominator of 24
8*3=24=6*4, or you can cross multiply 6*8, and 8*6 both equal 48. I will use 48 by cross multiplying, then show you the common denominator as a second example.
Get 48 on the bottem of both sides, by multiplying 6*8, or 8 * 6, but to be fair, you must multiply the top of the fraction by the same number.
Multiply by 6 over 6 =1, or 8/8 which is also 1. Multiplying by 1 doesnt change the fraction. By multiplying by 6/6, you didnt change the fraction, but changed the lower number from 8 to 48, and 6 to 48 ( hence common denominator).

z* ( 4/8 + 1/6)= ....multiplying the 4 over 8 by 6 over 6 and the 1 over 6 by 8 over 8.....

z*[ (6*4)/6*8) + (8*1)/8*6)]=
z*[24/48 + 8/48]=
Now that the bottom number of the fraction is the same, you can add the top part of the fraction.
z*[32/48]=
reduce the fraction, by dividing the top and bottem by 16.
z*[2/3]=2/3*z
Answer= 2/3 * z or (2*z)/3

You could have solved by using the common deminator.
(4*z)/8 + z/6=
extract the z
z(4/8) + 1/6)=
get the common denominator of 24 3*3=24, and 6*4=24
So to get the same number 24 on the bottom of both fractions,
z* [ (3/3)*(4/8) + (4/4)*(1/6) ]=
z* [ 12/24 + 4/24 ]=
now the bottom number of the fraction is the same, so you can add the top number of the fraction.
z*[ 16/24]=
reduce the fraction
z*(2/3)= which agrees with the first finding.


I think the other answers are incorrect.

Austin Semiconductor

Answer 2

Well, you can't actually solve the problem, but you can simplify it. That's probably what your daughter's being asked to do.
If you could solve the problem, you'd be solving for what z equals, and so there'd have to be an equals sign in the problem. It'd look something like this:
4 z/8 + z/6 = 24 (or another number besides 24, whatever the teacher chose)

but to simplify it, this is what you'd do:
Before I explain, in case you don't remember, the top number on a fraction is called the numerator and the bottom number is the denominator. Anyway...
First, convert any mixed numerals into improper fractions. An improper fraction is something like 3/2, since the numerator is larger than the denominator. 3/2 in mixed number form, for example, is 1 and 1/2. 4 and z/8 is a mixed numeral, so convert that to an improper fraction. This is how you do it: 4 and z/8 is really the same thing as 4 + z/8, which can also be written as 4/1 + z/8. You want to get 4/1 to have the same denominator as z/8 does, so you can combine the two into one big improper fraction. The way you do this is, since 8 is the denominator of z/8, multiply both the numerator and the denominator of 4/1 by 8:
4/1 + z/8 = (4*8)/(1*8) + z/8 = 32/8 + z/8
Now you can combine the two to get (32+z)/8 as the whole improper fraction.
Now put this back into your original problem, and you have
(32+z)/8 + z/6
Again, you have fractions with two different denominators, so you want to make them have the same denominator so you can combine them. The way to do this is to think of a common multiple of 6 and 8, or a number that both 8 and 6 divide into evenly. Ideally, you want to find the smallest number, and there are smaller numbers you can use, but since it's simple I'll use 48. The reason I picked 48 is because no matter what, you can always find a common multiple by multiplying the two numbers together, and 6*8=48.

Next, what you want to do is make each of the individual fractions you're adding have that common multiple as the denominator. Do this by multiplying both sides (numerator & denominator) of the fraction by whatever number will make the denominator equal the common multiple that you found. So,

(32+z)/8 = ((32+z)*6)/(8*6) = (192+6z)/48

And

z/6 = (z*8)/(6*8) = 8z/48

Now, plug both of these back intot he problem and you have:

(192+6z)/48 + 8z/48

Which equals

(192+6z)+8z/48

combine the z's to get:

(192+14z)/48

Now, you can simplify the fraction even further by finding numbers that go in evenly into both the numerator and denominator. 2 goes into the numerator and denominator (in order for a number to go into a number like (192 + 14z), it has to go into both 192 and 14, which 2 does). So you can divide both sides of the fraction by 2, to get:

(96+7z)/24

This is your final simplification of the fraction. It seems like a long, difficult process, but once you get the hang of it it's not that bad. Hope I helped. And by the way, I think it's really nice that you're helping your daughter with your math, but from my personal experience, it's pretty stressful when a parent tries to help their kid with homework- and unfortunately, the math problems only get harder. Your daughter should go in for extra help from her teacher, if your school offers it. It's free, and can be really helpful.

Answer 3

To add fractions, the denominators need to be the same. To find the LCD, lowest common denominator, you 1st need to factor the denominators. (* is multiplication)

8 = 2*2*2
6=2*3

There are 2's and 3's. Use the greatest number of both to find the LCD. That would be three 2's and one 3.

2*2*2*3=24

Both denominators need to be 24. Change both denominators to 24 by multiplying. You also need to multiply the corresponding numerators by the same thing so that the value of each fraction doesn't change.

z/8 * 3/3 = 3z/24
z/6 * 4/4 = 4z/24

Now add the two numbers.

4 3z/24 + 4z/24 = 4 7z/24
No reduction needed, so this is the answer.

Good luck!

Answer 4

u gotta find the common denominator: 8 and 6 have 24 in common. also, w/ a mixed numeral, it is easier to turn it into a regular fraction.

multiply the whole # by the demoninator, and add it to the numerator:

4 z/8 = (4*8 + z )/8 = (32 + z)/8

now u can find the common denominator, which is 24. multiply the 1st # by 3/3, the 2nd one by 4/4 in order to make them have the same denominator:

3(32+z)/24 + 4(z)/24 =

96 + 3z + 4z
___________
24

= 96 + 7z
_________
24

hope that makes sense :)

Answer 5

4 z/8 + z/6 = 4 3z/24 + 4z/24= 4 7z/24
You must find a common denominator in order to add the fractions.

Answer 6

4 z/8 =(4*8+z)/8 = (32+z)/8 (This is how you convert mixed numerals to fractions.)
So 4 z/8 + z/6 = (32+z)/8 +z/6
= (3(32+z)+4z)/24
= (96+7z)/24

Answer 7

solve for a common denominator:

8 = 2*2*2
6=3*2

The common denominator is 24 so it can be expressed as 4 3z/24 +4z/24 = 4 7z/24

Answer 8

First you need to find a common denominator.

4 z/8 =4 3z/24
z/6 = 4z/24

4 7z/24 would be my answer.

Answer 9

start up by using dispensing the three into the x-4. To distribute, you're taking the form on the exterior of the parentheses (3) and multiply it by using the separate values on the interior (x) (-4). three times x equals 3x. three times -4 is -12. combine the values. you're actually left with 3x-12. Your equation now sounds like this: x + 8 = 3x - 12 Now you are going to be able to desire to get all the x values on the comparable section: x + 8 = 3x - 12 -1x -1x 8 = 2x - 12 (From here i assume you comprehend a thank you to clean up it, yet nonetheless) +12 + 12 20 = 2x /2 /2 10=x properly, it somewhat is the respond. Sorry if I perplexed you.