Translating into Expressions and Equations

1. Translating into Expressions and Equations From words to math symbols

2. Look for EQUALITY words • EQUALITY words mean you will write an EQUATION(=)or INEQUALITY(<,>,≤,≥,≠) • NO EQUALITY words means you will write an EXPRESSION

3. = OR ≠ • IS • equals • IS equal to • IS the same as • is NOT equal to • does NOT equal • is NOT the same as other verbs might be used instead of IS: was, were, are, has, have, etc.

4. < OR > • IS less than • IS smaller than • IS lower than • IS younger than • IS greater than • IS more than • IS larger than • IS bigger than • IS higher than • IS older than

5. ≤ OR ≥ • IS less than or equal to • IS at most • IS no more than • IS no bigger than • IS greater than or equal to • IS at least • IS no less than • IS no younger than

6. Which symbol would you use? ≠ < > ≤ ≥ = equals is less than or equal to is at least is no more than is no less than is less than IS is greater than or equal to is more than does NOT equal is at most is greater than

7. Look for OPERATIONwords OPERATIONwords tell you to: ADD (+) SUBTRACT (–) MULTIPLY (•) DIVIDE (÷) use EXPONENTS (x2)

8. + OR – • plus • increased by • added to • more than • sum of • minus • decreased by • subtracted from • less than • difference of

9. • OR ÷ • times • multiplied by • product of • out of • divided by • quotient of

10. Some translate directly… six increased by three plus + 6 3 negative two seven minus decreased by – -2 7 negative five times nine multiplied by • -5 9 four eight out of divided by ÷ 4 8

11. Now You Try! negative eight increased by twenty-two -8 + 22 thirteen multiplied by nine 13 •9 four out of five 4 ÷5 negative fifteen minus negative six -15 –-6

12. Some are tricky… sum of four negative ten and + 4 -10 ( ) difference of five eleven and ) ( – 5 11 product of ten twelve and ( ) • 10 12 quotient of nine negative three and ( ) ÷ 9 -3

13. More tricky ones… 16 six more than sixteen 11 + 6 twenty added to eleven + 20 -4 five less than negative four 9 –5 two subtracted from nine –2

14. Now You Try! the difference of seventeen and negative four negative three added to nineteen the product of negative one and eight ( -1 •8 ) 19 +-3 ( -4 –17 ) ( -41 +6 ) 2–11 ( 30 ÷ 5 ) the sum of negativeforty-one and six eleven subtracted from two the quotient of thirty and five

15. Words that signal EXPONENTS fifth six ten raised to the third power 10 5 3 6 five squared four cubed 2 3 5 4 You Try! nine cubed twelve squared 93 122 two raised to the fourth power 24 68 six raised to the eighth power

16. More signal words… Word(s) Meaning a number variable, such as norx Example: three plusa number y 3 + y twice 2 times Example: twicea number m 2m quantity use parentheses ( ) Example: quantity seven minus one (7 – 1) (–6)2 negative six quantity squared

17. Combine for complex expressions eight times the quotient of three andn ) ) ÷ + ( ( n • 3 8 3 n ( ) 8 negative six minusthe sum of x and two -6 – – x -6 2 ( x + 2 )

18. Translate Equations & Inequalities five more than a number c equals twicec c+5 = 2c negative z quantitysquared twelve is at least ( -z)2 ≥ 12 twoless than w twenty minus ten is less than 20 –10 < w –2 n divided by four seven timessixteen is at most n ÷ 4 ≤ 7•16

19. Now You Try! seven is greater than or equal to three minus p 7 ≥ 3 – p 5 – q = 2 +6 a number qsubtracted from five equals two plussix thirty divided by fis three more than negative four 30 ÷f= -4 +3 v – 12< 43 twelve less than v is less than four cubed ( 9 • (-2+h) ) ≥ (h –8 ) the product of nine and the quantitynegative two plus his no less than the difference of h and eight

20. Now You Try! three times a number x decreased by fourteen 3x – 14 4 ÷ (-2 + 2k) four divided by the sum of negative two and twice k thirty-one is greater than a number t divided by six 31 > t ÷ 6 4y2 = 100 four times y squared equals one hundred the difference of j and nineteen is at most fifty (j – 19) ≤ 50 (4y)2 = 64 four times y quantity squared equals sixty-four