Different Operations, Same Answer
How can you use two different operations and still reach the same answer?
Goal:
Goal:
When operations are related, like multiplication and division, it is possible to reach the same answer using either operation. After all, both operations are working with equal groups or quantities. Consider the problem below.
Krista and Kim have \(\mathsf{ \frac{1}{3} }\) of a box of crackers to share. If they want to share the crackers equally, what fraction of the crackers will they each get to eat?
Work through the steps below to solve this problem. As you complete each step, click the row to check your work.
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\(\mathsf{ \frac{1}{3} }\) could be represented by a circle cut into three pieces. 
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The visual model would look like the original circle, where each piece is cut into two pieces. 
This leaves each piece with a value of \(\mathsf{ \frac{1}{6} }\). \(\mathsf{\frac{1}{3} \div 2 = \frac{1}{6} }\) |
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The visual model would look the same as the division problem.
This time, you are multiplying by the fraction \(\mathsf{ \frac{1}{2} }\). \(\mathsf{ \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} }\) |
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Whether you choose to solve this problem using multiplication or division, your answer is that Krista and Kim will each get \(\mathsf{ \frac{1}{6} }\) of the box of crackers. |
Keep practicing! Follow the same steps to complete the problems that follow. After you have finished each problem, click the Answer button to check your work.
Anushka and her friends are running a relay race at school. The race is \(\mathsf{ \frac{1}{2} }\) of a mile long, in total. There are 4 runners on a team. What fraction of a mile will each runner on a team run in the race?
Create a division sentence and visual model to represent this problem.
\(\mathbf{\hspace{10px} \div \hspace{10px} 4 =
\hspace{10px}}\)
\(\mathbf{ \frac{1}{2} \div 4 = \frac{1}{8} }\)
Create a multiplication sentence and visual model to represent this problem.
\(\mathbf{\hspace{10px} \times \hspace{10px}
\frac{1}{4} = \hspace{10px}}\)
\(\mathbf{ \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} }\)
Final Answer
Each runner will run \(\mathsf{ \frac{1}{8} }\) of a mile.
Brayden has \(\mathsf{ \frac{1}{3} }\) of barrel of grain to feed his 8 cows. What fraction of a barrel will each cow receive?
Create a division sentence and visual model to represent this problem.
\(\mathbf{ \frac{1}{3} \div 8 = }\)
\(\mathbf{\hspace{10px} \div \hspace{10px} 8 =
\hspace{10px}}\)
\(\mathbf{ \frac{1}{3} \div 8 = \frac{1}{24} }\)
Create a multiplication sentence and visual model to represent this problem.
\(\mathbf{ \frac{1}{3} \times \frac{1}{8} = }\)
\(\mathbf{\hspace{10px} \times \hspace{10px}
\frac{1}{8} = \hspace{10px}}\)
\(\mathbf{ \frac{1}{3} \times \frac{1}{8} = \frac{1}{24} }\)
Final Answer
Each cow will receive \(\mathsf{ \frac{1}{24} }\) of a barrel of grain.