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## Phrases to Algebraic Expressions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

 1 the quotient of b and g 2 21 added to -19

### Complexity=1, Mode=equation

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

 1 the product of 27 and negative twenty-seven is greater than f divided by -38 2 g plus 4 is greater than or equal to z divided by twenty-three

### Complexity=2

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

 1 negative thirty-nine times (nine subtracted from forty-one) 2 the product of 31 and (e added to (the product of -1 and b))

### Complexity=2, Mode=equation

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

 1 a plus g times x is equal to the product of twenty-nine and (b increased by r) 2 fifteen added to the product of negative one and d plus fifteen is less than or equal to 6 added to the product of g and z

### Complexity=3, Mode=equation

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

 1 u times (x subtracted from (the product of h and p)) is greater than 13 subtracted from (the product of twelve, -32, and t) 2 the product of -45 and ((the sum of c and m) subtracted by q) is less than or equal to the product of (the quotient of (one added to (the product of negative one and p)) and z) and x

### Complexity=1

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

1the quotient of b and g
Solution
For the phrase "21 added to -19", - 19 is being modified by 21, so we get "- 19 + 21"

### Complexity=1, Mode=equation

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

1the product of 27 and negative twenty-seven is greater than f divided by -38
2g plus 4 is greater than or equal to z divided by twenty-three
Solution
For the phrase "g plus 4", g is being modified by 4, so we get "g + 4"

### Complexity=2

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

1negative thirty-nine times (nine subtracted from forty-one)
Solution
For the phrase "(nine subtracted from forty-one)", 41 is being modified by 9, so we get "41 - 9"
2the product of 31 and (e added to (the product of -1 and b))
Solution
For the phrase "(e added to (the product of -1 and b))", -b is being modified by e, so we get "-b + e"

### Complexity=2, Mode=equation

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.

1a plus g times x is equal to the product of twenty-nine and (b increased by r)
Solution
For the phrase "a plus (g times x)", a is being modified by gx, so we get "a + gx"
For the phrase "(b increased by r)", b is being modified by r, so we get "b + r"
2fifteen added to the product of negative one and d plus fifteen is less than or equal to 6 added to the product of g and z
Solution
For the phrase "((the product of negative one and d) plus fifteen)", -d is being modified by 15, so we get "-d + 15"
For the phrase "fifteen added to ((the product of negative one and d) plus fifteen)", -d + 15 is being modified by 15, so we get "-d + 15 + 15"
For the phrase "6 added to (the product of g and z)", gz is being modified by 6, so we get "gz + 6"

### Complexity=3, Mode=equation

Convert to an algebraic expression. Use / for division (write as fraction, not ÷).
When multiplying 2 numbers, use ( ). Example: write   28 × -14   as   28(-14).
Do NOT include leading 1's, example: write   -1x   as   -x.