Visual Model 1
Question: A number line shows where a product lands. What point represents \(0.5 \times 8\)?
- A. \(2\)
- B. \(3\)
- C. \(4\)
- D. \(5\)
How the model helps: \(0.5 \times 8 = 4\), so the point belongs exactly at \(4\) on the number line.
CH03-04 lesson
Dividing Decimals by Decimals Learning Activity
A focused Grade 5 learning session for Dividing Decimals by Decimals using visual models, worked examples, strategy guidance, and a short mastery check.
- 18
- minutes
- 6
- lesson parts
- 11
- practice items
Students will divide decimals by decimals using equivalent expressions and place-value reasoning.
Student goal: I can divide decimals by decimals.
Helpful first:
Dividing Decimals by Whole Numbers
Learn the Idea
Dividing Decimals by Decimals is the Grade 5 skill of students divide decimals by decimals using strategies such as multiplying both the dividend and divisor by a power of 10 to create a whole-number divisor. They apply these skills to measurement and real-world contexts.
Which place values matter most, and how does the decimal point guide the work?
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
- Name the place of each important digit before comparing or computing.
- Use place value patterns to explain what happens when values shift.
- Estimate first so the final answer can be checked for reasonableness.
- Use the topic language from class discussions: Students divide decimals by decimals using strategies such as multiplying both the dividend and divisor by a power of 10 to create a whole-number divisor. They apply these skills to measurement and real-world contexts.
See the Math
Follow a Worked Example
Example 1
Question: A number line shows division. If you divide 4.5 by 5, where does the quotient fall?
- A. Between 0 and 1
- B. Between 1 and 2
- C. Between 2 and 3
- D. Between 4 and 5
- \(4.5 \div 5 = 0.9\), which is between 0 and 1.
Answer: Between 0 and 1
Example 2
Question: Which model correctly shows \(0.6 \times 4\)?
- A. Option A
- B. Option B
- C. Neither model
- D. Both models
- \(0.6 \times 4\) means four groups of \(0.6\).
- Option A shows \(0.6\) four times, which is \(2.4\) in all.
Answer: Option A
Connect It to a Real Situation
Problem 1
Question: Maria buys 5 erasers at $0.75 each. How much does she spend?
- $3.25
- $3.50
- $3.75
- $4.00
Answer: $3.75
Why it works: Multiply \(5 \times 0.75 = 3.75\). Since \(0.75\) has 2 decimal places and 5 has 0, the product has 2 decimal places: $3.75.
Avoid Mistakes and Choose a Strategy
- Starting the computation before identifying what the numbers, units, or parts represent.
- Ignoring place value by lining up digits incorrectly instead of aligning decimal points or decimal places.
- Forgetting to estimate, which makes it easier to miss an unreasonable answer.
- Stopping at a number without explaining what the answer means in context.
- Read the situation slowly and name what each number or label represents.
- Use place value charts or aligned digits to keep the decimal meaning clear.
- Estimate first so you already know the answer's approximate size.
- Check the answer with an inverse operation, another representation, or a sentence explanation.
- Say the math idea out loud in simple words before writing the final answer.
Remember the Key Idea
Dividing Decimals by Decimals gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
GOLDEN RULE
Name the place value first, then compute or compare with aligned digits.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsWhat is \(3.6 \times 2.4\)?
- A \(8.64\)
- B \(8.84\)
- C \(9.44\)
- D \(9.64\)
Check answer and explanation
Answer A: \(8.64\)
Multiply as if the numbers were whole numbers: \(36 \times 24 = 864\). The factors \(3.6\) and \(2.4\) have a total of \(1 + 1 = 2\) decimal places, so place the decimal point two places from the right: \(864 arrow 8.64\). Therefore, \(3.6 \times 2.4 = 8.64\).
Maria buys 5 erasers at $0.75 each. How much does she spend?
- A $3.25
- B $3.50
- C $3.75
- D $4.00
Check answer and explanation
Answer C: $3.75
Multiply \(5 \times 0.75 = 3.75\). Since \(0.75\) has 2 decimal places and 5 has 0, the product has 2 decimal places: $3.75.
guided
1 questionEstimate: \(6.8 \times 4.9\). Which is the best estimate?
- A \(20\)
- B \(25\)
- C \(30\)
- D \(35\)
Check answer and explanation
Answer D: \(35\)
Round \(6.8 \approx 7\) and \(4.9 \approx 5\). Then \(7 \times 5 = 35\).
practice
5 questionsWhat is \(2.4 \div 3\)?
- A \(0.8\)
- B \(0.9\)
- C \(7.2\)
- D \(8.0\)
Check answer and explanation
Answer A: \(0.8\)
Divide: \(2.4 \div 3 = 0.8\). You can think of this as \(24 \div 3 = 8\), then place the decimal one place from the right: \(0.8\).
A number line shows where a product lands. What point represents \(0.5 \times 8\)?
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Check answer and explanation
Answer C: \(4\)
\(0.5 \times 8 = 4\), so the point belongs exactly at \(4\) on the number line.
When you multiply 7.2 by a number less than 1, what will be true about the product?
- A The product is larger than 7.2
- B The product is smaller than 7.2
- C The product equals 7.2
- D The product is negative
Check answer and explanation
Answer B: The product is smaller than 7.2
When a number is multiplied by a factor less than 1, the product is smaller than the original number.
Which multiplication problem is set up correctly to solve \(5.4 \times 3\)?
- A Option A
- B Option D
- C Option C
- D Option B
Check answer and explanation
Answer D: Option B
\(5.4\) has 1 decimal place. \(54 \times 3 = 162\), so we move the decimal 1 place left: \(16.2\).
A baker uses \(0.25\) kg of sugar in each batch of cookies. How much sugar for 4 batches?
- A \(0.4\) kg
- B \(0.8\) kg
- C \(1.0\) kg
- D \(1.2\) kg
Check answer and explanation
Answer C: \(1.0\) kg
\(0.25 \times 4 = 1.0\) kg. Multiply: \(25 \times 4 = 100\), then place decimal two places from right.
exit
3 questionsWhat is \(6.3 \div 3\)?
- A \(1.8\)
- B \(2.0\)
- C \(2.1\)
- D \(9.0\)
Check answer and explanation
Answer C: \(2.1\)
\(6.3 \div 3 = 2.1\). Think of \(63 \div 3 = 21\), then place decimal one place from right: \(2.1\).
A number line shows division. If you divide 4.5 by 5, where does the quotient fall?
- A Between 0 and 1
- B Between 1 and 2
- C Between 2 and 3
- D Between 4 and 5
Check answer and explanation
Answer A: Between 0 and 1
\(4.5 \div 5 = 0.9\), which is between 0 and 1.
Estimate: \(7.9 \div 2.1\). Which is the best estimate?
- A \(2\)
- B \(4\)
- C \(6\)
- D \(8\)
Check answer and explanation
Answer B: \(4\)
Round \(7.9 \approx 8\) and \(2.1 \approx 2\). Then \(8 \div 2 = 4\).
