MT7 Test Notes

Working with Rationals

MT7: Working with Rationals

20 questions that cover Adding, Subtracting (like denominators and unlike denominators), Multiplying, and Dividing. This is a longer test that will be difficult! Study these two pages well.

Notes are provided at the bottom of each page.

Notes: Adding a subtracting Rational with like denominators is the easiest section of this test. The mistake that many students make is adding and subtracting the integers.

MT7: Working with RationalsTest Notes

Same denominator? Too Easy!

CLT: (5x + x) + (4y – y) 24y2

6x + 3y 24y2

Now decide: Can you GCF?Diamond?Diff of 2 Squares?

GCF!

3(2x + y) 24y2

Now reduce: (2x + y) 8y2

Remember: You can never, ever, ever cancel into parenthesis. That is why the 2 and 8 cannot be reduced.

CLT: (x + x) + (y + 6y) 25xy

2x + 7y 25xy

Now decide: Can you GCF?Diamond?Diff of 2 Squares?

No! All done.(Nothing goes into 2 and 7)

MT7: Working with Rationals

20 questions that cover Adding, Subtracting (like denominators and unlike denominators), Multiplying, and Dividing. This is a longer test that will be difficult! Study these two pages well.

Notes are provided at the bottom of each page.

Notes: Adding a subtracting Rational with like denominators is the easiest section of this test. The mistake that many students make is just adding and subtracting the integers.

MT7: Working with RationalsTest Notes

More of the same

CLT: (2v – 4v) + (2u) 10uv3

-2v + 2u 10uv3

Now decide: Can you GCF?Diamond?Diff of 2 Squares?

GCF!

-2(v - u) 10uv3

Now reduce: v – u 5uv3

Notice the sign change of the u? That happened because we pulled out a “-”.

CLT: (x + x) + (-6y + y) 4xy

2x – 5y 4xy

Now decide: Can you GCF?Diamond?Diff of 2 Squares?

No! All done.(Nothing goes into 2 and 5)

MT7: Working with Rationals

This section is the hardest part of the test. Make sure you can find a common denominator.

Notes: Must find common denominator first. A key is to take one of everything you see and take the largest of something if there is more than one.Making a box to put your extra numbers in can be helpful, but is not required.

MT7: Working with RationalsTest Notes

Not common Denominators!

(r+6)(r-2)

(r-2) (r+6)How do I know what goes here?

4r(r-2) + (r+6)(r+6)

(r+6)(r-2)

4r2-8r + r2+12r+36

(r+6)(r-2)

5r2+4r+36

(3n)(10n+2)

(10n+2) 3n

2n(10n+2) + 5(3n)

(3n)(10n+2)

20n2 + 4n + 15n

(3n)(10n+2)

20n2+19n

Now GCF and reduce (3n)(10n+2)

n(20n+19)

3(10n+2)

(20n+19)

MT7: Working with Rationals

This section is the hardest part of the test. Make sure you can find a common denominator.

Notes: Must find common denominator first. A key is to take one of everything you see and take the largest of something if there is more than one.Making a box to put your extra numbers in can be helpful, but is not required.

MT7: Working with RationalsTest Notes

(3x)(x+5)

(x+5) (3x)

(x-3)(x+5) - 3x(x-1)

(3x)(x+5)

x2+2x-15-3x2+3x

(3x)(x+5)

-2x2 + 5x – 15

(m+6)(m+5)

(m+5) (m+6)

3m(m+5) - 6(m+6)

(m+6)(m+5)

3m2+15m-6m-36

(m+6)(m+5)

3m2+9m-36

No GCF, Diamond, or Diff of 2 Squares! All Done.

Foil and DistributeWatch out distributing “-”

3, 9, 36? Time to GCF

(m+6)(m+5)

3(m2+3m-12)

MT7: Working with Rationals

This is from 7.3. Pretty easy as long as you can factor.

Notes: No need to find common denominator (not adding or subtracting). Just find the right method to factor and cancel your final results when possible.

MT7: Working with RationalsTest Notes

24

-11

Look at the pattern!Diamond Method

(b )(b )-8 -3

- 8 - 3

-27

69 -3

(b )(b )+ 9 - 3

Now just cancel.

(b - 8)

(b + 9)

-12

-1(v )(v ) -4 3- 4 + 3

-24

-5-8 3

(v )(v )- 8 + 3

Now just cancel.

(v - 4)

(v - 8)

MT7: Working with Rationals

This is from 7.3. Pretty easy as long as you can factor.

Notes: No need to find common denominator (not adding or subtracting). Just find the right method to factor and cancel your final results when possible.

MT7: Working with RationalsTest Notes

Look at the pattern!Difference of 2 Squares and Diamond

(n )(n )- 9 + 9

-36

-5-9 4

(n )(n )- 9 + 4

Now just cancel.

(n + 9)

(n + 4)

36

-13(x )(x ) -9 -4- 9 - 4

12

-7-4 -3

(x )(x )- 4 - 3

Now just cancel.

(x - 9)

(x - 3)

MT7: Working with Rationals

Similar to 7.3. Pretty easy as long as you can factor and reduce.

Notes: Almost like 7.3. Look for ways to factor then cancel. Watch out for ÷!

MT7: Working with RationalsTest Notes

Look for GCF, Diamond, or Diff of 2 Squares.

18m2

Now just cancel.

14

●2(m – 8) (m – 8)

GCF! 1

4

Divide means “Flip”

5r-35 4

●r + 45r - 35

Now just cancel.

r + 4 4

MT7: Working with Rationals

Similar to 7.3. Pretty easy as long as you can factor and reduce.

Notes: Almost like 7.3. Look for ways to factor then cancel. Watch out for ÷!

MT7: Working with RationalsTest Notes

Look for GCF, Diamond, or Diff of 2 Squares.

b+2b2 – 5b - 14

Now just cancel.

2b2

(b-7)

● 2b2

1

Divide means “Flip”

b+2(b – 7)(b + 2)

● 2b2

1 Now just cancel.

55(n – 2)

● (n + 4)(n – 2) 2

(n + 4) 2

MT7: Working with Rationals

The section on solving rationals is actually easier than adding them because you get to cancel the denominator after you find LCD.

Notes: Almost like 7.52 only after you find your LCD, you get to erase it. Don’t forget to solve your equations after you delete your denominator!

MT7: Working with RationalsTest Notes

3x2

Common denominator between x, 3x2, and 3x2?

Must find LCD first…

Now follow the process…

3x 1 1

3x = 1 + x + 1 Delete denominator

3x = 1 + x + 1 Solve for x

2x = 2

x = 1

6k

Common denominator between 3, 6, and 6k?

4k = k + k - 4

4k = k + k - 4

4k = 2k - 4

2k = -4

2k k 1

k = -2

MT7: Working with Rationals

The section on solving rationals is actually easier than adding them because you get to cancel the denominator after you find LCD.

Notes: Almost like 7.52 only after you find your LCD, you get to erase it. Don’t forget to solve your equations after you delete your denominator!

MT7: Working with RationalsTest Notes

6n2

Common denominator between 6n, n2, and 6n2?

Same thing…

Now follow the process…

n 6 1

n = 6 - n - 2 Watch for “-”!

n = 6 - n - 2 Solve for x

2n= 4

x = 2

4v2

Common denominator between 2v2, 4v2, and v2?

2 + v – 4 = 4

2 + v – 4 = 4

v – 2 = 4

v = 6

2 1 4

That’s your entire test. Make sure you don’t make the easy mistakes. The easy mistakes are usually messing up when you add, subtract, multiply and divide. Your precision is going to matter.