Grade 7 Pre Algebra Math Problems

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Questions and Answers

How much money does Jared have left if he buys 5 packs of trading cards at $3 each and a display book for $7?

10

How much money does David spend on 3 movie tickets for $6 each and 2 bags of popcorn for $2 each?

22

What is the result of simplifying the expression $4 \times 9 \times 50$?

1800

What is the result of $(33 + 45) + 7$?

<p>85</p> Signup and view all the answers

What property is demonstrated by the equation $1 + (6 + 7) = (1 + 6) + 7$?

<p>Associative property of addition</p> Signup and view all the answers

What is the identity property illustrated by the equation $1 \times 10 = 10$?

<p>Identity property</p> Signup and view all the answers

Which property is shown by $3 \times 5 = 5 \times 3$?

<p>Commutative property</p> Signup and view all the answers

What does the expression $4 \times (4 \times 2) = (4 \times 4) \times 2$ demonstrate?

<p>Associative property</p> Signup and view all the answers

If $K=5$, what is the value of $K + 9$?

<p>14</p> Signup and view all the answers

If $K=2$, what is the value of $K + 9$?

<p>11</p> Signup and view all the answers

What is the expression for 'w increased by 5'?

<p>w + 5</p> Signup and view all the answers

What is the expression for the difference of 3 times a number and 7?

<p>3n - 7</p> Signup and view all the answers

What property is illustrated by $9 + 8 = 8 + 9$?

<p>Commutative property of addition</p> Signup and view all the answers

What does the equation $5 + 0 = 5$ demonstrate?

<p>Identity property of addition</p> Signup and view all the answers

What is the identity property illustrated by $27 \times 1 = 27$?

<p>Identity property of multiplication</p> Signup and view all the answers

What property is shown by $8 \times (6 \times 2) = (8 \times 6) \times 2$?

<p>Associative property of multiplication</p> Signup and view all the answers

What is the expression for $3n$ when $n=4$?

<p>12</p> Signup and view all the answers

What is the value of $X + 8$ for $x=8$?

<p>16</p> Signup and view all the answers

If $w=20$, how many days are there in 20 weeks using the expression $7w$?

<p>140</p> Signup and view all the answers

How many hours does Tyrone work in 5 days if he works 8 hours a day?

<p>40 hours</p> Signup and view all the answers

What is the value of $c-9$ when $c=11$?

<p>2</p> Signup and view all the answers

What is the value of $7q$ for $q=10$?

<p>70</p> Signup and view all the answers

What is the result of $2y + 9$ when $y=8$?

<p>25</p> Signup and view all the answers

What is the value of $a - 4$ for $a=9$?

<p>5</p> Signup and view all the answers

What does $a + 7$ yield if $a=3$?

<p>10</p> Signup and view all the answers

What is the value of $12 + m$ when $m=9$?

<p>29</p> Signup and view all the answers

Evaluate $2x - 5y$ for $x=33$ and $y=9$.

<p>21</p> Signup and view all the answers

What expression represents 26 increased by 12 times a number?

<p>26 + 12n</p> Signup and view all the answers

What is the expression for the difference of 2 times a number and 6?

<p>2n - 6</p> Signup and view all the answers

What is the expression for 18 less than the product of a number and 4?

<p>4n - 18</p> Signup and view all the answers

What is the product of 3 and n?

<p>3n</p> Signup and view all the answers

What does a number decreased by 9 represent mathematically?

<p>n - 9</p> Signup and view all the answers

What is the expression for 48 more than the product of a number and 64?

<p>64n + 48</p> Signup and view all the answers

What does the expression $y + 5y$ simplify to?

<p>6y</p> Signup and view all the answers

What does $9x - 4x$ simplify to?

<p>5x</p> Signup and view all the answers

What is the result of $5s - 2s$?

<p>3s</p> Signup and view all the answers

What is the absolute value of -18?

<p>18</p> Signup and view all the answers

What is the absolute value of -10?

<p>10</p> Signup and view all the answers

What integer represents Christy's depth of 12 feet below the surface of the water?

<p>-12</p> Signup and view all the answers

What is the result of $7 - 11$?

<p>-4</p> Signup and view all the answers

What is the value of $-7 - 6$?

<p>-13</p> Signup and view all the answers

What is the result of $8.67 - 6.87$?

<p>1.80</p> Signup and view all the answers

What is $28.94 - 9.48$?

<p>19.46</p> Signup and view all the answers

What does $6.14 + 8.91$ equal?

<p>15.05</p> Signup and view all the answers

What is the sum of $4.51 + 13.08$?

<p>17.59</p> Signup and view all the answers

What is the result of $6 \times 0.3$?

<p>1.8</p> Signup and view all the answers

What is $3 \times 0.05$ equal to?

<p>0.15</p> Signup and view all the answers

What is the result of $-3 \times 0.03$?

<p>-0.90</p> Signup and view all the answers

What is the result of $5.34 - 2.08$?

<p>3.26</p> Signup and view all the answers

What is the result of $-8 + (-5)$?

<p>-13</p> Signup and view all the answers

What is the result of $-7 + (-4)$?

<p>-11</p> Signup and view all the answers

What expression represents the perimeter of an equilateral triangle with side length $4x-5$?

<p>12x - 5</p> Signup and view all the answers

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Study Notes

Money and Cost Problems

  • Jared has $32, spends on trading cards ($3 each for 5 packs) and a display book ($7). Left with $10 after purchases.
  • David spends on movies ($6 each for 3 tickets) and popcorn ($2 each for 2 bags). Total expenditure is $22.

Mathematical Calculations

  • Multiplication of constants: 4 x 9 x 50 equals 1800.
  • Addition of two numbers: (33 + 45) + 7 results in 85.

Properties of Operations

  • Associative Property: 1 + (6 + 7) equals (1 + 6) + 7.
  • Identity Property: 1 x 10 equals 10, and 5 + 0 equals 5.
  • Commutative Property: 3 x 5 equals 5 x 3 and 9 + 8 equals 8 + 9.

Expressions and Evaluations

  • Variable expressions include K + 9 for K = 5 resulting in 14, and for K = 2 resulting in 11.
  • General expression for 'w' increased by 5 is w + 5; difference expressed as 3n - 7 for a number n.
  • Evaluating expressions: 3n for n = 4 gives 12, X + 8 for x = 8 gives 16.
  • 7w for w = 20 calculates to 140 (days in weeks).

Algebraic Operations

  • Tyrone's work calculation for 5 days: 8 x d gives 40 hours worked.
  • Expressions in standard form: c - 9 for c = 11 results in 2, while 7q for q = 10 computes to 70.

Simplifying Expressions

  • Various terms simplifications include 2y + 9 for y = 8 resulting in 25, and a - 4 for a = 9 equaling 5.

Absolute Values and Integers

  • Absolute values are defined: | -18 | equals 18, and | -10 | equals 10.
  • Christy's depth is expressed as -12 feet; subtraction examples include 7 - 11 resulting in -4, and -7 - 6 equating to -13.

Decimal Operations

  • Arithmetic operations on decimals yield results: 8.67 - 6.87 gives 1.80, 28.94 - 9.48 results in 19.46.
  • Addition of decimals: 6.14 + 8.91 equals 15.05, while 4.51 + 13.08 results in 17.59.

Multiplication Facts

  • Multipling decimals yields: 6 x 0.3 equals 1.8, and 3 x 0.05 equals 0.15.
  • Negative multiplication gives -3 x 0.03 equaling -0.90.

Perimeter of Shapes

  • For an equilateral triangle with side length represented as 4x - 5, the perimeter is expressed as 12x - 5.

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