HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #114 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Find \(\displaystyle 14\) more than \(\displaystyle 32\) and then find \(\displaystyle 7\) less than the sum. 

Possible Answers:

\(\displaystyle 14\times32-7\)

\(\displaystyle 14-32+7\)

\(\displaystyle 14-32-7\)

\(\displaystyle 14+32+7\)

\(\displaystyle 14+32-7\)

Correct answer:

\(\displaystyle 14+32-7\)

Explanation:

The phrase "more than" means to add. Because we are adding and subtracting in this question, we do not need to use parentheses because with addition and subtraction you work the problem out from left to right. So first we have the addition problem, then we subtract. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #115 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Find \(\displaystyle 17\) less than the product of \(\displaystyle 6\) and \(\displaystyle 8\)

Possible Answers:

\(\displaystyle 6\times8+17\)

\(\displaystyle 6\div8-17\)

\(\displaystyle 6\times(8+17)\)

\(\displaystyle 6\times8-17\)

\(\displaystyle 6\times(8-17)\)

Correct answer:

\(\displaystyle 6\times8-17\)

Explanation:

The phrase "less than the product" means that we are going to subtract \(\displaystyle 17\) from the answer of our multiplication problem. Because of our order of operations, multiplication will come beore subtraction so we do not need to use parentheses.

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #116 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Find the product of \(\displaystyle 6\) times the quotient of \(\displaystyle 72\) divided by \(\displaystyle 9\)

Possible Answers:

\(\displaystyle 72\div9\times6\)

\(\displaystyle 72-9\times6\)

\(\displaystyle 72+9\times6\)

\(\displaystyle 72\times9\times6\)

\(\displaystyle 9\times6\div72\)

Correct answer:

\(\displaystyle 72\div9\times6\)

Explanation:

When you are asked to find the product that means we are going to multiply. Because we are multiplying and dividing in this question, we do not need to use parentheses because with multiplication and division you work the problem out from left to right. So first we have the division problem, then we multiply because it says to find the product of the quotient (answer to a division problem), which means we need to divide first. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #117 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Subtract \(\displaystyle 5\) from the quotient of \(\displaystyle 100\) divided by \(\displaystyle 4\)

Possible Answers:

\(\displaystyle 100\div(4-5)\)

\(\displaystyle 100\div4-5\)

\(\displaystyle 100\times4-5\)

\(\displaystyle 100\div4+5\)

\(\displaystyle 100\div(5-4)\)

Correct answer:

\(\displaystyle 100\div4-5\)

Explanation:

Because of our order of operations, the division problem needs to come first. We list the subtraction  last because we are subtracting a number by the quotient, so the quotient needs to be listed first. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #118 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

\(\displaystyle 121\) divided by the product of \(\displaystyle 5\) and \(\displaystyle 2\)

Possible Answers:

\(\displaystyle 121\div(5+2)\)

\(\displaystyle 121\div(5\times2)\)

\(\displaystyle 121\div5\times2\)

\(\displaystyle 121\div5-2\)

\(\displaystyle 121\div5+2\)

Correct answer:

\(\displaystyle 121\div(5\times2)\)

Explanation:

\(\displaystyle 121\) needs to be listed first because that's the number that is getting divided. However, we need to do the multiplication problem first to find out what number we are dividing into \(\displaystyle 121\), so we need to put the multiplication problem into parentheses. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #119 : Common Core Math: Grade 5

Select the equation that reflects the phrase below. 

Add \(\displaystyle 42\) to the difference between \(\displaystyle 17\) and \(\displaystyle 8\)

Possible Answers:

\(\displaystyle 17-8+42\)

\(\displaystyle 8+42-17\)

\(\displaystyle 17\div8+42\)

\(\displaystyle 17+8+42\)

\(\displaystyle 17-8-42\)

Correct answer:

\(\displaystyle 17-8+42\)

Explanation:

Difference means the answer to a subtraction problem. Because we are adding a number to the difference, we need to do the subtraction problem first. Since we are adding and subtracting in this question, we do not need to use parentheses because with addition and subtraction you work the problem out from left to right. So first we have the subtraction problem, then we add

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #121 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Add \(\displaystyle 26\) to the product of \(\displaystyle 7\) and \(\displaystyle 7\)

Possible Answers:

\(\displaystyle 26+7-7\)

\(\displaystyle 26+7\times7\)

\(\displaystyle 23+7\times7\)

\(\displaystyle 26+7+7\)

\(\displaystyle 26+7\div7\)

Correct answer:

\(\displaystyle 26+7\times7\)

Explanation:

Product means the answer to a multiplication problem. Becuase of our order of operation rules, the multiplication problem will come first, regardless of if it's listed first or second. Then we add. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #121 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Find the sum of \(\displaystyle 15\) and \(\displaystyle 30\) and then divide \(\displaystyle 5\)

Possible Answers:

\(\displaystyle (15-30)\div5\)

\(\displaystyle 15-30\div5\)

\(\displaystyle (15+30)\div5\)

\(\displaystyle (15\times30)\div5\)

\(\displaystyle 15+30\div5\)

Correct answer:

\(\displaystyle (15+30)\div5\)

Explanation:

When you are asked to find the sum that means we are going to add. Because the phrase says "then divide" we need to put the addition problem in parentheses because of our order of operations. Then we can divide. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #122 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Divide the product of \(\displaystyle 4\) and \(\displaystyle 10\) by \(\displaystyle 8\)

Possible Answers:

\(\displaystyle 4\times(10\div8)\)

\(\displaystyle 4\times10-8\)

\(\displaystyle 4+10\div8\)

\(\displaystyle 4\times10\div8\)

\(\displaystyle 4+10-8\)

Correct answer:

\(\displaystyle 4\times10\div8\)

Explanation:

When you are asked to find the product that means we are going to multiply. Because we are multiplying and dividing in this question, we do not need to use parentheses because with multiplication and division you work the problem out from left to right. So first we have the multiplication problem, then we divide. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

Example Question #121 : Operations & Algebraic Thinking

Select the equation that reflects the phrase below.

Divide \(\displaystyle 30\) by the quotient of \(\displaystyle 12\) divided by \(\displaystyle 4\)

Possible Answers:

\(\displaystyle 30\div(12\div4)\)

\(\displaystyle 30\div(12-4)\)

\(\displaystyle 30\times(12\div4)\)

\(\displaystyle 30\div12\div4\)

\(\displaystyle 30\div(12\times4)\)

Correct answer:

\(\displaystyle 30\div(12\div4)\)

Explanation:

Quotient means the answer to a division problem. Because we want to divide \(\displaystyle 30\) by the answer of \(\displaystyle 12\div4\) we need to put that in parentheses so that it's done first. 

Remember, order of operations is PEMDAS= parentheses, exponents, multiplication/division, addition/subtraction.  

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