What does it mean?
Division by a decimal often asks how many portions of that size fit. For 3.6 kg divided into 0.6 kg portions, the answer counts portions, so the result is 6 rather than a decimal mass. Division by a number below one can therefore make the numerical result larger.
Division can share a quantity equally or count how many equal groups fit. 4.8 ÷ 4 shares 48 tenths into four groups of 12 tenths. For a decimal divisor, multiply both dividend and divisor by the same power of ten: 3.6 ÷ 0.6 = 36 ÷ 6 = 6. The quotient stays the same.
Learning goal: Divide decimals with meaning. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Decimal place value: tenths and hundredths if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Multiply both dividend and divisor by the same power of ten to make the divisor a whole number. For 3.6 ÷ 0.6, multiply both by 10 to get 36 ÷ 6. For 4.5 ÷ 0.15, multiply both by 100 to get 450 ÷ 15. The ratio is unchanged because both quantities were rescaled equally.
Notation: division as grouping
Key rule and when to use it
For a non-zero divisor, multiplying both dividend and divisor by the same non-zero number preserves the quotient. Check quotient × original divisor = original dividend.
Worked examples, step by step
Example 1: Calculate 4.8 ÷ 4.
- Share 48 tenths into 4 equal groups.
- Each group has 12 tenths.
- Rename 12 tenths as 1.2.
Answer: 1.2
Example 2: Calculate 3.6 ÷ 0.6.
- Ask how many 0.6 groups fit in 3.6.
- Use 36 ÷ 6 as the matching fact.
Answer: 6
Example 3: How many 0.25 L servings are in 2 L?
- Write the division 2 ÷ 0.25.
- Rescale both numbers by 100: 200 ÷ 25 = 8.
- There are 8 servings. Check 8 × 0.25 L = 2 L.
Common mistakes and important boundaries
Changing only the divisor changes the answer. 3.6 ÷ 6 is not equivalent to 3.6 ÷ 0.6. Division by zero is not defined; never use a zero divisor. Check a proposed quotient by multiplying it by the original divisor to rebuild the original dividend.
A point to explain
Dividing by a number below 1 asks how many small groups fit.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Dividing Decimals: Equal Measures and Rescaling — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
3.6 ÷ 0.3 = ?
Answer and a way to check
12
Ask how many groups of the divisor fit in the dividend.
2.4 ÷ 0.6 = ?
Answer and a way to check
4
Ask how many groups of the divisor fit in the dividend.
1.5 ÷ 0.5 = ?
Answer and a way to check
3
Ask how many groups of the divisor fit in the dividend.
9.6 ÷ 0.8 = ?
Answer and a way to check
12
Ask how many groups of the divisor fit in the dividend.
3.6 kg of apples is packed into bags of 0.3 kg. How many bags?
Answer and a way to check
12
Ask how many groups of the divisor fit in the dividend.
Calculate 7.5 ÷ 0.25.
Answer and a way to check
30
Rescale both numbers by 100: 750 ÷ 25 = 30. Check 30 × 0.25 = 7.5.
Calculate 0.48 ÷ 4.
Answer and a way to check
0.12
48 hundredths shared in four groups gives 12 hundredths per group.
A learner changes 4.2 ÷ 0.7 into 4.2 ÷ 7. What is missing?
Answer and a way to check
Multiply the dividend by 10 too: 42 ÷ 7 = 6.
Rescaling only one number changes the quotient. Check the corrected answer with 6 × 0.7 = 4.2.
Dividing Decimals: Equal Measures and Rescaling — answer key
12 Ask how many groups of the divisor fit in the dividend.
4 Ask how many groups of the divisor fit in the dividend.
3 Ask how many groups of the divisor fit in the dividend.
12 Ask how many groups of the divisor fit in the dividend.
12 Ask how many groups of the divisor fit in the dividend.
30 Rescale both numbers by 100: 750 ÷ 25 = 30. Check 30 × 0.25 = 7.5.
0.12 48 hundredths shared in four groups gives 12 hundredths per group.
Multiply the dividend by 10 too: 42 ÷ 7 = 6. Rescaling only one number changes the quotient. Check the corrected answer with 6 × 0.7 = 4.2.
Questions students and parents ask
How do I divide a decimal by 100?
Each digit takes a place worth one hundredth as much: 34.5 ÷ 100 = 0.345. The leading zero before the decimal point helps make the value readable.
Does dividing always make a number smaller?
No. For positive numbers, dividing by a number between 0 and 1 counts smaller portions and gives a result larger than the starting number.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Decimal place value: tenths and hundredths. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Use a familiar portion size such as a half-litre or quarter-litre. Connect the count of portions to the numerical division before using a written rule.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Divide decimals with meaning”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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