translate sentences into equations

Question

Seven more than a number is 15.

2) Five less than a number is 3.

3) Four times a number is 24.

4) A number decreased by 6 is 1.

5) A number divided by 5 is 7.

6) If 12 is subtracted from a number, the result is 88.

7) Twice a number increased by 3 is 23.

8) One half a number decreased by 2 is 5.

9) The sum of four times a number and 3 equals 35.

10) 40 increased by a number is less than 80.

11) A number decreased by 9 is greater than 11.

12) The product of 7 and 4 is not equal to 21.

13) If 6 is subtracted from 8 times a number, the result is less than 26.

14) 3 less than two times a number is more than 11.

15) Twice a number decreased by 9 is 7.

16) A number increased by 11 is 33.

17) Three times a number is 54.

18) The sum of three times a number and 4 is 19.

19) A number divided by 5 is 11 more than the number.

20) Four times a number decreased by 9 is less than 31.

21) The product of 10 and 3 is not equal to 32.

22) Twice a number increased by 3 is more than 9.

23) A number decreased by 2 is greater than 7.

24) If 17 is subtracted from 4 times a number, the result is less than 3.

 

Answer 1

Jenna,  after you review the above definitions #'s 1-5 are :  1) x+7; 2)x-5. 3) 4x=24. 4)  x-6=1. 5)x/5=7.  Try practicing on the rest.  Good luck!

Answer 2

Hi, Jenna!

 

First of all, since this forum is designed as a place for tutors to provide academic support to students, I am not going to answer all of the questions that you posted.  However, I will do a couple to help you get an idea of how to translate english sentences into equations.

 

Before I get to the questions, I want to review some key words that are helpful to remember:

 

Words that mean addition (+):

sum

more than (<--switch the order of the numbers/variables)

added to

increased by

 

Words that mean subtraction (-):

difference

decreased by

subtracted from (<--switch the order of the numbers/variables)

less than (<--switch the order of the numbers/variables)

 

Words that mean multiply (•):

product

times

of <-- this can mean other things too! or nothing at all.  Think about the context of the sentence.

multiplied by

twice (<--multiply by 2)

 

Words that mean divide:

half (<--divide by 2)

divided by

 

Words that mean equals (=):

result

is

equals

 

"is less than" means <

"is greater than" means >

"is less than or equal to" means ≤

"is greater than or equal to" means ≥

"is not equal to" means ≠

 

Let's look at some examples!

2. Five      less than            a number  is    3.

     (5)   (- & switch order*)        (x)     (=) (3)

*When switching the order of two numbers/variables (terms), only switch the order of the numbers/variables on that side of the equation.

      x - 5 = 3

 

13. If 6 is subtracted from      8 times a number, the result is less than 26.

        (6) (- & switch order**)  (8)  (•)     (x)                           (<)        (26)

**8x is considered one term, so the 6 and 8x need to switch places.

      8x - 6 < 26

 

9. The sum of^∇ four times a number and 3           equals 35.

           (+)-->(4)   (•)         x              (3)<--       (=)  (35)

^∇In this case, the word "of" does not mean to multiply.  Instead, it indicates that a list of numbers is coming up in the sentence that are supposed to be added together (summed).

      4x + 3 = 35

 

Good luck!

 

Patty

 

 

Answer 3

When translating words into mathematical expressions or equations, there are some major key words you must be aware of.  These keywords determine which operations to use to replace those keywords.

 

Here some keywords to know.  Once you know them, apply them to answer the questions.

 

For addition:

 

1) "more than"

2) "plus"

3) "increased by"

4) "added to"

5) "sum"

 

For subtraction:

 

1) "less than"

2) "minus"

3) "decreased by"

4) "subtracted from" or "subtract"

5) "difference"

 

 

For multiplication:

 

1) "times"

2) "double", "triple", "quadruple", etc

3) "product"

 

For division:

 

1) "divided by"

2) "half", "third", "quartered", etc

3) "quotient"

4) "over"

 

 

For exponents:

 

"square" means power of 2

"cubed" means power of 3

"raised to the nth power", where n is a number

 

 

For equal (indicates equation):

 

1) "equal" or "equal to"  (=)

2) "is"  (=)

 

 

For inequalities (indicates comparison):

 

1) "less than" and "less than or equal to"  (<  and  ≤)

2) "greater than" and "greater than or equal to"  (>  and   ≥)