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z+(-3 2/5)=-4 1/10

I need help solving this step by step, please


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Suresh P. | Friendly, patient tutor with experience in many subjects!Friendly, patient tutor with experience ...
4.9 4.9 (182 lesson ratings) (182)

Hey Hillary,

To solve this, there are several things to do to simplify the way this equation looks. First off, we need to make it so that the fractions can be added and subtracted across the equal sign as in any other equation. In order to do that, we need to find a common denominator - preferably the lowest one. 

Even before we get to that step, it would be even more handy to convert the mixed numbers into simple fractions. 

SO, starting with -4 1/10: We want to make this into a fraction that's easy to work with, such as 3/4 or 1/2. We know that 4 is equal to forty tenths, or 40/10 (ten tenths = 10/10 = 1, so 40/10 = 4), and there is 1/10 left over from the given equation. We simply add that 1/10 to 40/10. Therefore, 4 1/10 becomes 41/10, and we throw on the negative sign that they gave.

Now we have z + (-3 2/5) = -41/10.

So let's convert -3 2/5 into a simple fraction with a denominator of 10 -- combining the first two steps I mentioned way above. That way we can add or subtract the two fraction across the equal sign, leaving z all by itself and solving the equation. Starting with the 2/5 part, we can multiply the whole thing by 2 to give us 4/10, which is still reducible to 2/5 (meaning we haven't changed anything about the value of the mixed number). We know that thirty tens make up 3 (30/10 = 3), and we had the 4/10 from just before, so 30/10 + 4/10 = 34/10. Therefore, 3 2/5 = 34/10. And we'll throw on the negative sign they gave once again.

After all that, we now have z + (-34/10) = -41/10, which now is simple algebra.

To isolate the z, we have to add positive (34/10) to both sides and cancel it out on the left. Also note that we can add the fractions now because they have the same denominator: 10.

-41/10 + 34/10 = -7/10

Hope this helped! Remember that whenever you are performing operations with mixed numbers or fractions with different denominators, it is important to convert one or both so that they share a common denominator (e.g. 2/5 + 3/4 becomes 8/20 + 15/20).

Tina P. | Willing to try any concept to ensure students learn the materialWilling to try any concept to ensure stu...
4.5 4.5 (4 lesson ratings) (4)

This is a pretty straightforward problem.

z + (-3 2/5) = -4 1/10

You are trying to solve for z, so the first thing you need to do is get z alone. You would do this by subtracting -3 2/5 from both sides of the equation.


z + (-3 2/5) = -4 1/10

- (-3 2/5)       -(-3 2/5)

Because you subtract the -3 2/5 it becomes a positive number.  This is because a negative times a negative yields a positive. This is what your result would be.

z= -4 1/10 + 3 2/5

Next, you need to add the two numbers together. In order to do this you must first convert each number into an improper fraction.

We get these fractions by first multiplying the whole number in from of the fraction by the denominator of the fraction. After multiplying, you then add the result to the number of the fraction's numerator.

z = -41/10 + 17/5

Now you are ready to find a common denominator.

-41/10 and 17/5 have a common denominator of 10. this is the lowest common denominator for both fractions. Because -41/10 already has 10 as the denominator you do not have to do anything with this fraction. For the 17/5 you must multiply both the numerator and denominator by 2.

your equation should now look like this:

z = -41/10 + 34/10

Now all you have to do is solve the equation by adding 34 to -41.

In this case, the resulting numerator would be -7.

So, your solution would be:

z = -7/10