Unit 4, Lesson 7
What Fraction of a Group?
Grade 6
7.1
Warm-up
What do you notice? What do you wonder?
Tuesday
Thursday
7.2
Activity
One batch of a soup recipe uses 9 cups of milk. A chef makes different amounts of soup on different days. Here are the amounts of milk she used:
- Monday: 12 cups
- Tuesday: cups
- Thursday: 6 cups
- Friday: cups
For each question:
- Write a multiplication equation and a division equation that represent it. Use the “?” symbol for the unknown value.
- Answer the question. Use the partially started tape diagram to show your reasoning. The shaded region represents the cups of milk in 1 batch.
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How many batches of soup did she make on Monday?
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Multiplication equation:
Division equation:
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Answer:
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How many batches of soup did she make on Tuesday?
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Multiplication equation:
Division equation:
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Answer:
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What fraction of a batch of soup did she make on Thursday?
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Multiplication equation:
Division equation:
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Answer:
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What fraction of a batch of soup did she make on Friday?
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Multiplication equation:
Division equation:
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Answer:
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7.4
Activity
For each question, write a multiplication equation and a division equation. Then answer the question. You can draw a tape diagram if you find it helpful.
- What fraction of 9 is 3?
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Multiplication equation:
Division equation:
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Answer:
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- What fraction of 5 is ?
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Multiplication equation:
Division equation:
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Answer:
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Student Lesson Summary
It is natural to think about groups when we have more than one group, but we can also have a fraction of a group.
Sometimes an amount is less than the size of 1 group, and we want to know what fraction of a group that amount is.
Suppose a full bag of flour weighs 6 kg. A chef used 3 kg of flour. What fraction of a full bag was used? In other words, what fraction of 6 kg is 3 kg?
We can still write equations and draw a diagram to represent the situation.
A tape diagram of 2 equal parts. Above the diagram, a brace from the beginning of the diagram to the end of the diagram is labeled 6 kilograms. Below the diagram, a brace from the beginning of the diagram to the end of the diagram is labeled 1 bag. The first part is labeled three kilograms. Below the diagram, a third brace which also contains the first part is labeled question mark bag.
We can see from the diagram that 3 is of 6, so . We can check this quotient by multiplying: .
In any situation where we want to know what fraction one number is of another number, we can write a multiplication equation and a division equation to help us find the answer.
For example, “What fraction of 3 is ?” can be expressed as:
The value of is also the answer to the original question.
Fraction bar diagram. 12 equal parts. 9 parts shaded. Total labled "1 group" and "3 cups." 9 parts labeled "unknown quantity group" and "2 and the fraction 1 over 4 or the fraction 9 over 4."
We can use a diagram to reason that there are 12 fourths in 3 and 9 fourths in , so is , or , of 3. If we multiply and 3, we get .
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