SAT Math : How to simplify an expression

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : How To Simplify An Expression

If x + y = 4, what is the value of x + y – 6?

Possible Answers:

0

2

–2

6

4

Correct answer:

–2

Explanation:

Substitute 4 for x + y in the expression given.

4 minus 6 equals –2.

Example Question #2 : How To Simplify An Expression

If 6 less than the product of 9 and a number is equal to 48, what is the number?

 

Possible Answers:

4

5

6

3

Correct answer:

6

Explanation:

Write an equation for the written expression: 9x – 6 = 48.  When we solve for x we get x = 6. 

 

 

Example Question #1 : Simplifying Expressions

If  x  Sat_math_164_01  y  = (5x - 4y)/y , find the value of y if 6  Sat_math_164_01  y = 2.

 

 

Possible Answers:

5

2

4

10

Correct answer:

5

Explanation:

If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 -->2y =30 -4y --> 6y =30 --> y=5.  We could also work from the answers and substitute each answer in and solve.

Example Question #3 : How To Simplify An Expression

Simplify the following expression: x3 - 4(x2 + 3) + 15

Possible Answers:

x3 – 12x2 + 15

x3 – 3x2 + 15

x3 – 4x2 + 3

x5 + 3

Correct answer:

x3 – 4x2 + 3

Explanation:

To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x2 and -4 by 3.

x3 - 4x2 -12 + 15

You can then add -12 and 15, which equals 3.

You now have x3 - 4x2 + 3 and are finished. Just a reminder that x3 and 4x2 are not like terms as the x’s have different exponents.

Example Question #4 : How To Simplify An Expression

Evaluate: (2x + 4)(x2 – 2x + 4)

 

Possible Answers:

2x3 + 16

2x3 – 8x2 + 16x + 16

2x3 + 8x2 – 16x – 16

2x3 – 4x2 + 8x

4x2 + 16x + 16

Correct answer:

2x3 + 16

Explanation:

Multiply each term of the first factor by each term of the second factor and then combine like terms.

(2x + 4)(x2 – 2x + 4) = 2x3 – 4x2 + 8x  +  4x2 – 8x + 16 = 2x3 + 16

Example Question #5 : Simplifying Expressions

Which of the following is equivalent to Satmath520_copy_2?

Possible Answers:

a2/(b5c)

abc

b5/(ac)

ab5c

ab/c

Correct answer:

b5/(ac)

Explanation:

First, we can use the property of exponents that xy/xz = xy–z

 

Satmath520_copy

Then we can use the property of exponents that states x–y = 1/xy

a–1b5c–1 = b5/ac

Example Question #5 : How To Simplify An Expression

Solve for x: 2y/3b = 5x/7a

Possible Answers:

15b/14ay

5by/3a

6ab/7y

14ay/15b

7ab/6y

Correct answer:

14ay/15b

Explanation:

Cross multiply to get 14ay = 15bx, then divide by 15b to get x by itself.

Example Question #74 : Expressions

Three consecutive positive integers are added together. If the largest of the three numbers is m, find the sum of the three numbers in terms of m.

Possible Answers:

3m – 6

3m

3m + 6

3m + 3

3m – 3

Correct answer:

3m – 3

Explanation:

Three consecutive positive integers are added together.  If the largest of the three numbers is m, find the sum of the three numbers in terms of m.

If m is the largest of three consecutive positive integers, then the integers must be:

m – 2, m – 1, and m, where m > 2.

The sum of these three numbers is:

m - 2 + m – 1 + m = 3m – 3

Example Question #2 : How To Do Distance Problems

Sophie travels f miles in g hours.  She must drive another 30 miles at the same rate.  Find the total number of hours, in terms of f and g, that the trip will take.

Possible Answers:

Ans3

Ans4

g + f

Ans5

g + f + 30

Correct answer:

Ans4

Explanation:

Using d = rt, we know that first part of the trip can be represented by f = rg.  The second part of the trip can be represented by 30 = rx, where x is some unknown number of hours.  Note that the rate r is in both equations because Sophie is traveling at the same rate as mentioned in the problem.

Solve each equation for the time (g in equation 1, x in equation 2).

g = f/r

x = 30/r

The total time is the sum of these two times

Exp1

Exp2

Note that, from equation 1, r = f/g, so 

Exp3

Exp4
=Ans4

Example Question #81 : Expressions

If ab = 10 and bc = 15, then what is the value of (c – a)/(a + 2b + c)?

Possible Answers:

150

1/5

3/2

2/3

5

Correct answer:

1/5

Explanation:

Add the two equations:

a + b = 10 

b + c = 15

------------

a + b + b + c = 10 + 15

a + 2b + c = 25 (this is the denominator of the answer)

Subtract the two equations:

b + c = 15

a + b = 10 

------------

b + c – (a + b) = 15 – 10

c – a = 5 (this is the numerator of the answer)

5/25 = 1/5

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