Solving a 2 step equation Involving Rational Numbers

by Monica Marie
(Virginia)

2/3 = -1 5/9 + 5/8x

I'm getting stuck on finding the common denominator w/a mixed number to get this answer. Help!!

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Solving a 2 step equation Involving Rational Numbers

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May 16, 2012
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help on homework NEW
by: sierra

i need help on this equation 2/3 x + 3/9 = 5/9 find x?

May 16, 2012
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help on homework NEW
by: sierra

i need help on this equation 2/3 x + 3/9 = 5/9 find x?

Jan 16, 2012
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Solving a 2 Step Equation with Rational Numbers NEW
by: Karin

Sometimes you are given an equation with mixed numbers. In this case, you must always rewrite the mixed number as an improper fraction.

So, in this case, we must first rewrite 1 (5/9) as an improper fraction.

To do this: multiply the denominator by the whole number and add the numerator. This answer goes over the current denominator. So,

- 1 (5/9) = (9(-1)+5)/9
= -14/9

Now use -14/9 instead of the mixed number.

So, we have:

(2/3) = (-14/9) + (5/8)x

Your first job will be to find the least common multiple of all denominators. Start with your largest denominator and find the multiple that is also a multiple of the other denominators.

So, the multiples of 9 are: 9,18, 27, 36, 45, 54, 63, 72.

72 is a multiple of 8 and 3, so that is the least common multiple.

Now multiply all terms by 72.

72(2/3) = 72[(-14/9)+(5/8)x]

48 = -112 + 45x (You should have whole numbers at this point). Now solve as usual.

Add 112 to both sides

48 + 112 = -112 +112 +45x

160 = 45x

Divide by 45 on both sides
160/45 = 45x/45

160/45 = x

Simplify 160/45

32/9 = x

Check:

2/3 = -14/9 + (5/8)(32/9)

2/3 = 2/3

Hope this helps!

Karin

Jan 15, 2012
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helpful NEW
by: rakayla

this website was very helpful i am doing a little better in math and my teacher sees progress and a change in me and so will my parents

Nov 21, 2011
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Solving a 2 step equation Involving Rational Numbers NEW
by: Karin

For the equation, 1/3x - 5 = 30, I would start by adding five to both sides:

1/3x - 5+5 = 30+5
1/3x = 35

Now you can isolate x by multiplying both sides by 3.

3(1/3x) = 35(3)
x = 105

Hope this helps,
Karin

Nov 21, 2011
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Homework Help 7th grade NEW
by: Anonymous

What is 1/3x-5=30

Oct 04, 2011
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Solving a 2 step equation Involving Rational Numbers
by: Karin

5/9 + x = 2/3

In this problem, we have two fractions. We need to multiply all terms by the least common multiple (of the denominators), and this will get rid of the fractions.

The least common multiple of 9 and 3 is 9. Therefore, we will multiply all terms by 9.

9[5/9 + x] = 2/3(9)
5+ 9x = 6

Now solve the two step equation.

Subtract 5 from both sides.

5-5 +9x = 6-5

9x = 1

Divide by 9 on both sides

9x/9 = 1/9

x = 1/9.

Check your answer by substituting.

5/9 + 1/9 = 6/9

6/9 can be simplified to 2/3. Therefore, my answer is correct.

x = 1/9.

Hope this helps!!!

Oct 04, 2011
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math
by: Anonymous

5/9+x=2/3

Oct 02, 2011
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7th grade math
by: Anonymous

my teacher he explained a little bit but i still dont understand how to write the problem out and get the answer

Sep 20, 2011
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8TH GRADE MATH
by: Anonymous

im trying to do this egation with rational numbers but i just don't now how im in 8th grade

Sep 10, 2011
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Solving a 2 step equation Involving Rational Numbers
by: Karin

For the problem:

1.5d = 3/8

This problem seems more confusing because you have decimals and fractions. Decimals are a little easier to work with than fractions, so I would start by multiplying all terms by 8 to get rid of the fraction.

8(1.5d) = 3/8(8)
12d = 3 Now you don't have decimals or fractions!

To solve, subtract 12 from both sides:
12d/12 = 3/12

d = 1/4 (3/12 simplified is 1/4)

Check by substituting:
1.5(.25) = .375 which is 3/8
.375 = .375

The final answer is d = 1/4 or d = .25

Hope this helps,
Karin

Sep 10, 2011
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Solving a 2 step equation Involving Rational Numbers
by: Karin

For the problem:
3x/4 - 1/2 = 4

First get rid of the fraction by multiplying by 4.

4[3x/4-1/2] = 4(4) Notice that I multiply all terms by 4 on both sides!

3x - 2 = 16

Now solve as a two step equation by first adding 2 to both sides.

3x-2+2 = 16+2
3x = 18

Now divide by 3 on both sides.
3x/3 = 18/3

x = 6

Check by substituting 6 into the original equation:

(3*6/4) - 1/2 = 4
4=4

The final answer is x = 6.

The key is getting rid of the fraction first!!

Hope this helps,
Karin

Sep 09, 2011
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I'm stuck!!!!
by: Anonymous

Do u know what is 3x/4-1/2=4
what does x=?

Sep 01, 2011
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solving equations with rational numbers
by: Anonymous

1.5d=3/8

Jun 09, 2011
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Math iz hard
by: Anonymous

good very good

Sep 26, 2010
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Solving A 2 Step Equation Involving Rational Numbers
by: Karin

The first thing that you must do is convert the mixed number to an improper fraction.

-1 5/9 = -14/9 as an improper fraction.

Then you can begin solving by getting rid of the fraction. The least common multiple for 3, 9, and 8 is 72. Therefore, you must multiply all terms by 72.

72[2/3] = 72[-14/9 + 5/8x]

48 = -112 + 45x

Now that you don't have any fractions, it's much easier to solve this 2 step problem.

Step 1: Add 112 to both sides.

48 + 112 = -112 + 112 + 45x

160 = 45x

Step 2: Divide by 45 on both sides

160/45 = 45x/45

32/9 = x

Step 3: Then substitute to check your answer.

2/3 = -14/9 + 5/8(32/9)
2/3 = 2/3

I hope this helps,
Karin

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