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Common Core: 5th Grade Math : Operations & Algebraic Thinking

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #141 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Find the product of $\displaystyle 6$ times the quotient of $\displaystyle 54$ divided by $\displaystyle 9$

Possible Answers:

$54\div(9\times6)$ $\displaystyle 54\div(9\times6)$

$54\times9\times6$ $\displaystyle 54\times9\times6$

$54\div9\times6$ $\displaystyle 54\div9\times6$

$54\div9+6$ $\displaystyle 54\div9+6$

$54\div9-6$ $\displaystyle 54\div9-6$

Correct answer:

$54\div9\times6$ $\displaystyle 54\div9\times6$

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.

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Example Question #142 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Subtract $\displaystyle 15$ from the quotient of $\displaystyle 60$ divided by $\displaystyle 2$

Possible Answers:

$60\div2\times15$ $\displaystyle 60\div2\times15$

$60\div2+15$ $\displaystyle 60\div2+15$

60-2-15 $\displaystyle 60-2-15$

60+2-15 $\displaystyle 60+2-15$

$60\div2-15$ $\displaystyle 60\div2-15$

Correct answer:

$60\div2-15$ $\displaystyle 60\div2-15$

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.

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Example Question #141 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

$\displaystyle 76$ divided by the product of $\displaystyle 19$ and $\displaystyle 4$

Possible Answers:

$76\div(19+4)$ $\displaystyle 76\div(19+4)$

$76\div(19-4)$ $\displaystyle 76\div(19-4)$

$76\div(19\times4)$ $\displaystyle 76\div(19\times4)$

$76\div19\times4$ $\displaystyle 76\div19\times4$

$76\div19+4$ $\displaystyle 76\div19+4$

Correct answer:

$76\div(19\times4)$ $\displaystyle 76\div(19\times4)$

Explanation:

$\displaystyle 76$ 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 $\displaystyle 76$, so we need to put the multiplication problem into parentheses.

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

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Example Question #143 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Add $\displaystyle 17$ to the difference between $\displaystyle 63$ and $\displaystyle 38$

Possible Answers:

$\displaystyle 63+38+17$

$63\div38+17$ $\displaystyle 63\div38+17$

$\displaystyle 63-38-17$

$\displaystyle 63-38+17$

$63-38\times17$ $\displaystyle 63-38\times17$

Correct answer:

$\displaystyle 63-38+17$

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.

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Example Question #144 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Add $\displaystyle 19$ to the product of $\displaystyle 5$ and $\displaystyle 9$

Possible Answers:

19+5+9 $\displaystyle 19+5+9$

$19-5\times9$ $\displaystyle 19-5\times9$

$19+5\times9$ $\displaystyle 19+5\times9$

$19+5\div9$ $\displaystyle 19+5\div9$

$(19+5)\times9$ $\displaystyle (19+5)\times9$

Correct answer:

$19+5\times9$ $\displaystyle 19+5\times9$

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.

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Example Question #145 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Find the sum of $\displaystyle 16$ and $\displaystyle 20$ and then divide $\displaystyle 6$

Possible Answers:

$(16\div20)\div6$ $\displaystyle (16\div20)\div6$

$16+20\div6$ $\displaystyle 16+20\div6$

$16\times20\div6$ $\displaystyle 16\times20\div6$

$(16-20)\div6$ $\displaystyle (16-20)\div6$

$(16+20)\div6$ $\displaystyle (16+20)\div6$

Correct answer:

$(16+20)\div6$ $\displaystyle (16+20)\div6$

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.

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Example Question #146 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Divide the product of $\displaystyle 12$ and $\displaystyle 6$ by $\displaystyle 3$

Possible Answers:

$12\times(6\div4)$ $\displaystyle 12\times(6\div4)$

$12\times6\times4$ $\displaystyle 12\times6\times4$

$12-6\div4$ $\displaystyle 12-6\div4$

$12\times6\div4$ $\displaystyle 12\times6\div4$

$12+6\div4$ $\displaystyle 12+6\div4$

Correct answer:

$12\times6\div4$ $\displaystyle 12\times6\div4$

Explanation:

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

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Example Question #781 : Concepts

Select the equation that reflects the phrase below.

Divide $\displaystyle 12$ by the quotient of $\displaystyle 18$ divided by $\displaystyle 6$

Possible Answers:

$12\div18\div6$ $\displaystyle 12\div18\div6$

$12\div(18\times6)$ $\displaystyle 12\div(18\times6)$

$12\div(18+6)$ $\displaystyle 12\div(18+6)$

$12\div(18\div6)$ $\displaystyle 12\div(18\div6)$

$12\div18\times6$ $\displaystyle 12\div18\times6$

Correct answer:

$12\div(18\div6)$ $\displaystyle 12\div(18\div6)$

Explanation:

Quotient means the answer to a division problem. Because we want to divide $\displaystyle 12$ by the answer of $18\div3$ $\displaystyle 18\div3$ 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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Example Question #148 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

Add $\displaystyle 15$ and $\displaystyle 7$ and then multiply $\displaystyle 3$ by the sum

Possible Answers:

$15+7\times3$ $\displaystyle 15+7\times3$

$(15-7)\times3$ $\displaystyle (15-7)\times3$

$15-7\times3$ $\displaystyle 15-7\times3$

$(15+7)\div3$ $\displaystyle (15+7)\div3$

$(15+7)\times3$ $\displaystyle (15+7)\times3$

Correct answer:

$(15+7)\times3$ $\displaystyle (15+7)\times3$

Explanation:

Because we are multiplying by the sum, which is the answer to an addition problem, we first need to add so we need to put the addition problem in parentheses, then we can do the multiplication.

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

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Example Question #149 : Common Core Math: Grade 5

Select the equation that reflects the phrase below.

$\displaystyle 28$ divided by the difference between $\displaystyle 14$ and $\displaystyle 7$

Possible Answers:

$28\div14-7$ $\displaystyle 28\div14-7$

$28\div(14\times7)$ $\displaystyle 28\div(14\times7)$

$28\div(14+7)$ $\displaystyle 28\div(14+7)$

$28\div(14-7)$ $\displaystyle 28\div(14-7)$

$28\div14+7$ $\displaystyle 28\div14+7$

Correct answer:

$28\div(14-7)$ $\displaystyle 28\div(14-7)$

Explanation:

Because we are dividing by the difference, or answer, from the subtraction problem, we first need to subtract. In order for the subtraction problem to go first, we need to put that in parentheses.

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

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Common Core: 5th Grade Math : Operations & Algebraic Thinking

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #141 : Common Core Math: Grade 5

Example Question #142 : Common Core Math: Grade 5

Example Question #141 : Common Core Math: Grade 5

Example Question #143 : Common Core Math: Grade 5

Example Question #144 : Common Core Math: Grade 5

Example Question #145 : Common Core Math: Grade 5

Example Question #146 : Common Core Math: Grade 5

Example Question #781 : Concepts

Example Question #148 : Common Core Math: Grade 5

Example Question #149 : Common Core Math: Grade 5

All Common Core: 5th Grade Math Resources

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