Translating into Expressions and Equations From words to

Translating into Expressions and Equations From words to math symbols

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

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

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

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

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

Look for OPERATION words tell you to: ADD (+) SUBTRACT (–) MULTIPLY ( • ) DIVIDE (÷) use EXPONENTS (x 2)

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

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

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

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

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

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

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 ( -41 + 6 ) ( -4 – 17 ) 2 – 11 ( 30 ÷ 5 ) the sum of negative forty-one and six eleven subtracted from two the quotient of thirty and five

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

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

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

Translate Equations & Inequalities five more than a number c equals twice c c +5 = 2 c negative z quantity squared is at least twelve ( -z )2 ≥ 12 twenty minus ten is less than two less than w 20 – 10 < n divided by four is at most n÷ 4 ≤ w– 2 seven times sixteen 7 • 16

Now You Try! seven is greater than or equal to three minus p 7≥ 3–p 5–q=2+6 a number q subtracted from five equals two plus six thirty divided by f is 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 quantity negative two plus h is no less than the difference of h and eight

Now You Try! three times a number x decreased by fourteen 3 x – 14 4 ÷ (-2 + 2 k) 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 4 y 2 = 100 four times y squared equals one hundred the difference of j and nineteen is at most fifty (j – 19) ≤ 50 (4 y)2 = 64 four times y quantity squared equals sixty-four