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Thread: Could use a bit of help, just want to make sure I'm doing this right.

  1. #1
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    Could use a bit of help, just want to make sure I'm doing this right.

    Hey all, just joined up. Long story short I took a break from college for personal reasons and now that I feel I'm ready to return after 2 years I must retake my entry exams. I'm thrilled this time because instead of just gauging what you know from your test scores they're actually encouraging people to study and do as best as possible on the test. I'm going through my study sheets right now and I'm in the fractions section. Yes I know very simple, however I am 27 and high school was 10 years ago, let alone fractions which must have been introduced when I was about 7 or 8 years old.

    I was initially in shock at how much I've forgotten but thanks to youtube and google I'm getting my chops back so to speak. I still have a few questions those two websites can't answer, so here I am.

    First off I'm being asked to simply the expresion (which pretty much has gone over my head as far as deciphering what they mean).

    For example, the problem is as such:

    Simplify the expression:

    3/4 minus 2/5 multiplied by 7/12. Since the first two fractions have unlike denominators I turned it into: 3/20 minus 2/20 multiplied by 7/12. 1/20 multiplied by 7/12 is 7/240 which is in it's simplest form. Once again still confused, I'm not sure if they want me to solve the problem or write the equation in another form, so any help on that will be appreciated.

    Now I'm getting into word problems (oh, what a mind **** these things are) and the first one seemed simple enough but coming from someone who is finishing out the their Automotive Technology certificate the answer doesn't seem to fit logically for this one:

    The depth of tread on a new tire is 9/32 of an inch. In two months time, 1/16 of an inch has been worn off. What is the remaining tread depth of the tire?

    Well lets see... once again unlike denominator, so instead of 9/32 minus 1/16 it's 9/64 minus 1/64 which is 8/64 or 1/8 simplified. However I'm not the best at being able to "imagine" the size of a fraction in my head so I just wanna makes sure I solved it right.

    Thanks in advance.
    Last edited by Hemispheres; Jun 8th 2015 at 10:06 PM.
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Well first of all, 3/4 is not the same as 3/20, it's actually 15/20.

    Now is it written as 3/4 - 2/5 x 7/12, or (3/4 - 2/5) x 7/12? Because it affects which order you have to do the operations in...
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Appreciate it, some of the website I was looking at just said to change the denominator and leave the numerator the same if trying to add/subtract/multiply/divide fractions with unlike denoms.

    However when I did this with the other problems and went behind myself and checked with a fractions calculator it was saying my answers were right. Let me re-work the problem with your advice and see what I get. Thanks again.
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Derp moment, For some reason I thought 64 was the lowest number both 32 and 16 went into... had a few sleepless nights so I'm a bit burnt out right now.

    9/32 - 1/16 = 9/32 - 1/32 = 7/32nds.... I'm a bit lost now. How does 9 - 1 = 7? I'm completely missing a step somewhere here.
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Ok didn't turn them into equivalent fractions. I should be good from here on out. Found a fraction calculator that not only shows step-by-step how to work things out, but allows you to add/subtract/multiply/divide at least 10 fractions together at once.
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    1/16 is NOT the same as 1/32, it's 2/32. Then 9/32 - 1/16 = 9/32 - 2/32 = 7/32...
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Quote Originally Posted by Hemispheres View Post
    3/4 minus 2/5 multiplied by 7/12.
    3/4 - 2/5 * 7/12 means 3/4 - 14/60 = 3/4 - 7/30

    (3/4 - 2/5) * 7/12 means (15/20 - 8/20) * 7/12 = 7/20 * 7/12

    Make sure you understand above before keeping on...else you'll swear lots !
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Quote Originally Posted by DenisB View Post
    3/4 - 2/5 * 7/12 means 3/4 - 14/60 = 3/4 - 7/30

    (3/4 - 2/5) * 7/12 means (15/20 - 8/20) * 7/12 = 7/20 * 7/12

    Make sure you understand above before keeping on...else you'll swear lots !
    Been quite a while since my fraction days in elementary school. I'll be studying my butt off today.... Here in a few hours I'll have the Fire Department knocking at my door due to the amount of smoke pouring from my ears.
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    Cool Re: Could use a bit of help, just want to make sure I'm doing this right.

    I think we need to start at the very beginning.

    If you need to add or subtract two fractions with different denominators, you must first change one or both FRACTIONS to make the denominators equal. To change the denominator of a fraction, you must also make a corresponding change to the numerator. You make a corresponding change by multiplying (or dividing) both numerator and denominator by the SAME number.

    $\dfrac{3}{7} = \dfrac{4 \times 3}{4 \times 7} = \dfrac{12}{28}.$

    I suspect where you were getting off track was that you heard "change the denominator" without realizing that you also had to make the corresponding change to the numerator. What people SHOULD say is to change the fraction by multiplying or dividing both numerator and denominator by the same number.

    You with me on this?

    Now you may have to change both fractions to make the denominators equal, in which case you will be changing one fraction by multiplying that fraction's numerator and denominator by some number and changing the other fraction by multiplying that fraction's numerator and denominator by a different number. SAME number for numerator and denominator of the same fraction, but DIFFERENT numbers for different fractions.

    $\dfrac{3}{16} + \dfrac{2}{3} =$

    $\dfrac{3 \times 3}{3 \times 16} + \dfrac{16 \times 2}{16 \times 3} =$

    $\dfrac{9}{48} + \dfrac{32}{48} =$

    $\dfrac{41}{48}.$
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Quote Originally Posted by JeffM View Post
    I think we need to start at the very beginning.

    If you need to add or subtract two fractions with different denominators, you must first change one or both FRACTIONS to make the denominators equal. To change the denominator of a fraction, you must also make a corresponding change to the numerator. You make a corresponding change by multiplying (or dividing) both numerator and denominator by the SAME number.

    $\dfrac{3}{7} = \dfrac{4 \times 3}{4 \times 7} = \dfrac{12}{28}.$

    I suspect where you were getting off track was that you heard "change the denominator" without realizing that you also had to make the corresponding change to the numerator. What people SHOULD say is to change the fraction by multiplying or dividing both numerator and denominator by the same number.

    You with me on this?

    Now you may have to change both fractions to make the denominators equal, in which case you will be changing one fraction by multiplying that fraction's numerator and denominator by some number and changing the other fraction by multiplying that fraction's numerator and denominator by a different number. SAME number for numerator and denominator of the same fraction, but DIFFERENT numbers for different fractions.

    $\dfrac{3}{16} + \dfrac{2}{3} =$

    $\dfrac{3 \times 3}{3 \times 16} + \dfrac{16 \times 2}{16 \times 3} =$

    $\dfrac{9}{48} + \dfrac{32}{48} =$

    $\dfrac{41}{48}.$
    Thank you very much sir, This is exactly what I was looking for.
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    Re: Could use a bit of help, just want to make sure I'm doing this right.

    Now about simplifying.

    Remember that I said you can change a fraction into an equivalent fraction by multiplying OR DIVIDING both numerator and denominator by the same number. Simplifying fractions usually involves dividing numerator and denominator by the same number. (The exception will just confuse the basic idea at this point so we shall ignore the exception.)

    The purpose of simplifying a fraction in arithmetic is to make it easier to understand and to work with by finding the equivalent fraction with the smallest whole numbers in numerator and denominator. Suppose both the numerator and denominator can be divided evenly by the same number. Do so and you will have an equivalent fraction with a smaller numerator and a smaller denominator. For example

    $\dfrac{39}{52}.$ It's difficult to have a mental vision of this, but both 39 and 52 can be divided by 13 so we can simplify.

    $\dfrac{39}{52} = \dfrac{39 \div 13}{52 \div 13} = \dfrac{3}{4}.$

    Unfortunately not all fractions can be simplified. Example $\dfrac{33}{52}.$

    Good tutorials on many math topics can be found at Khan Academy. I personally have not looked at any on arithmetic, but the general quality of those I have looked at has been good. Another site you might try is purplemath.
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