Common Core: 3rd Grade Math : Representing and Solving Problems Involving Multiplication and Division

Study concepts, example questions & explanations for Common Core: 3rd Grade Math

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Example Questions

Example Question #211 : Operations & Algebraic Thinking

\(\displaystyle 72\div6=\)

Possible Answers:

\(\displaystyle 12\)

\(\displaystyle 10\)

\(\displaystyle 9\)

\(\displaystyle 11\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 12\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 72\) items and we want to split them up equally into \(\displaystyle 6\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 6\) circles and start putting the \(\displaystyle 72\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 3.42.10 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 12\) triangles in each of the groups so our answer is \(\displaystyle 12\)

Example Question #212 : Operations & Algebraic Thinking

\(\displaystyle 45\div5=\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 10\)

\(\displaystyle 6\)

\(\displaystyle 9\)

\(\displaystyle 7\)

Correct answer:

\(\displaystyle 9\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 45\) items and we want to split them up equally into \(\displaystyle 5\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 5\) circles and start putting the \(\displaystyle 45\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 3.36.33 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 9\) triangles in each of the groups so our answer is \(\displaystyle 9\)

Example Question #213 : Operations & Algebraic Thinking

\(\displaystyle 40\div4=\)

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 8\)

\(\displaystyle 10\)

\(\displaystyle 11\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 10\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 40\) items and we want to split them up equally into \(\displaystyle 4\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 4\) circles and start putting the \(\displaystyle 40\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 3.31.50 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 10\) triangles in each of the groups so our answer is \(\displaystyle 10\)

Example Question #214 : Operations & Algebraic Thinking

\(\displaystyle 21\div3=\)

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 8\)

\(\displaystyle 5\)

\(\displaystyle 4\)

\(\displaystyle 7\)

Correct answer:

\(\displaystyle 7\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 21\) items and we want to split them up equally into \(\displaystyle 3\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 3\) circles and start putting the \(\displaystyle 21\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 3.28.33 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 7\) triangles in each of the groups so our answer is \(\displaystyle 7\)

Example Question #215 : Operations & Algebraic Thinking

\(\displaystyle 22\div2=\)

Possible Answers:

\(\displaystyle 11\)

\(\displaystyle 9\)

\(\displaystyle 7\)

\(\displaystyle 8\)

\(\displaystyle 10\)

Correct answer:

\(\displaystyle 11\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 22\) items and we want to split them up equally into \(\displaystyle 2\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 2\) circles and start putting the \(\displaystyle 22\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 3.25.31 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 11\) triangles in each of the groups so our answer is \(\displaystyle 11\)

Example Question #216 : Operations & Algebraic Thinking

\(\displaystyle 84\div12=\)

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 10\)

\(\displaystyle 9\)

\(\displaystyle 8\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 7\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 84\) items and we want to split them up equally into \(\displaystyle 12\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 12\) circles and start putting the \(\displaystyle 84\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 4.53.14 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 7\) triangles in each of the groups so our answer is \(\displaystyle 7\)

Example Question #141 : How To Divide

\(\displaystyle 66\div11=\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 7\)

\(\displaystyle 5\)

\(\displaystyle 6\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 6\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 66\) items and we want to split them up equally into \(\displaystyle 11\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 11\) circles and start putting the \(\displaystyle 66\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 4.52.23 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 6\) triangles in each of the groups so our answer is \(\displaystyle 6\)

Example Question #151 : How To Divide

\(\displaystyle 20\div10=\)

Possible Answers:

\(\displaystyle 3\)

\(\displaystyle 4\)

\(\displaystyle 5\)

\(\displaystyle 1\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle 2\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 20\) items and we want to split them up equally into \(\displaystyle 10\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 10\) circles and start putting the \(\displaystyle 20\) items, in this case triangles, into each circle equally. 

Screen shot 2015 09 03 at 12.13.26 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 2\) triangles in each of the groups so our answer is \(\displaystyle 2\)

Example Question #219 : Operations & Algebraic Thinking

\(\displaystyle 45\div9=\)

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 8\)

\(\displaystyle 5\)

\(\displaystyle 6\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 5\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 45\) items and we want to split them up equally into \(\displaystyle 9\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 9\) circles and start putting the \(\displaystyle 45\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 4.49.51 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 5\) triangles in each of the groups so our answer is \(\displaystyle 5\)

Example Question #152 : How To Divide

\(\displaystyle 80\div8=\)

Possible Answers:

\(\displaystyle 11\)

\(\displaystyle 9\)

\(\displaystyle 7\)

\(\displaystyle 10\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 10\)

Explanation:

When we are dividing, we are splitting things up into groups. For this problem, we can think of this as we have \(\displaystyle 80\) items and we want to split them up equally into \(\displaystyle 8\) groups. We are solving for the number of items in each group. 

We can draw \(\displaystyle 8\) circles and start putting the \(\displaystyle 80\) items, in this case triangles, into each circle equally. 

Screen shot 2015 08 18 at 4.48.35 pm

Our answer is the number of items in \(\displaystyle 1\) group. In this case, there are \(\displaystyle 10\) triangles in each of the groups so our answer is \(\displaystyle 10\)

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