Mini Minds Hub · Free printable
Dividing Decimals: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Dividing Decimals is a free printable maths worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Children divide decimals by whole numbers, then by other decimals, by shifting the decimal point so the divisor becomes a whole number. It takes about 15 minutes and needs only a pencil. Page 2 gives the grown up the answers, help and a stretch idea.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children divide decimals. The sheet includes decimals divided by whole numbers, such as 4.8 ÷ 2 and 0.84 ÷ 4. It also includes decimals divided by decimals, such as 3.6 ÷ 0.4 and 0.72 ÷ 0.09. The key idea is to shift the decimal point in both numbers so the divisor becomes a whole number, then divide. There is space for working and an answer on each question.
- 4.8 ÷ 2
- 6.3 ÷ 3
- 0.84 ÷ 4
- 7.5 ÷ 5
- 3.6 ÷ 0.4
- 2.4 ÷ 0.6
- 0.72 ÷ 0.09
- 1.5 ÷ 0.3
A worked example
5.6 ÷ 0.8
This question is not on the sheet. It shows two ways to think about the same idea.
Method 1: shift the decimal point- The divisor is 0.8. To make it a whole number, multiply it by 10 to get 8.
- Do the same to the other number, or the answer changes. 5.6 × 10 = 56.
- Now divide: 56 ÷ 8 = 7.
- 5.6 is 56 tenths. 0.8 is 8 tenths.
- The question asks how many groups of 8 tenths fit into 56 tenths.
- That is 56 ÷ 8 = 7.
Why shift the decimal point?
Dividing by a whole number is usually easier than dividing by a decimal. When you multiply both numbers in a division by the same amount, such as 10 or 100, the answer stays the same. That is why shifting the decimal point in both numbers works. The calculation looks friendlier, but it has the same answer as the one you started with.
Decimals appear in money, measuring and sport, so this skill is useful beyond school. Year 7 children often know the steps but forget why they work. Asking them to explain the shift, and to estimate first, helps them check their answers. It also builds a feel for how big or small an answer should be.
Skills and curriculum link
- Place value
- Division
- Estimating
- Shifting the decimal point
- Checking answers
Ideas that help with decimals
- Same change to bothMultiplying both numbers in a division by the same amount keeps the answer the same. This is the idea behind shifting the decimal point.
- Place valueEach place is ten times bigger than the place to its right. Tenths and hundredths follow the same pattern as tens and ones.
- Estimate firstRound each number to something simple and divide. This tells you roughly how big the answer should be.
- Check by multiplyingMultiply your answer by the divisor. If you get back to the number you started with, the division is correct.
Key words
- Decimal pointThe dot that separates whole numbers from parts of a whole.
- DividendThe number being divided.
- DivisorThe number you divide by.
- QuotientThe answer to a division.
- Place valueThe value of a digit, decided by where it sits in the number.
- EstimateA sensible guess found by rounding the numbers first.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Revise place value shifts first, for example what happens to the digits when you multiply by 10 or 100.
- Work through the first question together. Ask your child to say what they would do and why.
- Let them try the rest alone. The sheet takes about 15 minutes. Remind them to estimate first.
- Check with page 2. Ask, "How did you decide how far to shift the decimal point?" Come back another day to repeat the tricky ones.
Help, stretch and game ideas
If it feels too hard
Do the first four as short division. Write the decimal point above the line first, directly over the decimal point in the number being divided. Then divide digit by digit as usual. Move on to the harder questions once these feel secure.
To stretch confident children
Ask your child to make up two division questions with a decimal divisor and swap them with a friend. Each must explain, in words, why shifting the decimal point in both numbers keeps the answer the same.
Make it a game
Roll two dice. Use one for the ones and one for the tenths to make a decimal, such as 4.3. Divide it by 0.5 and write the answer. Take turns, and check each other's work by multiplying back.
Mistakes to watch for
Watch forA child shifts the decimal point in the divisor but not in the number being divided.
Try thisRemind them that both numbers must change by the same amount. Write the shift beside each number, such as × 10 and × 10.
Watch forThe answer has the right digits but the decimal point in the wrong place, such as 8 instead of 0.08 for 0.64 ÷ 8.
Try thisEstimate first. 0.64 is less than 1, so dividing it into 8 parts must give a very small answer.
Watch forA child thinks dividing always makes a number smaller, so they doubt an answer that is bigger than the start.
Try thisAsk how many halves fit into 3. Dividing by a number less than 1 can give a bigger answer.
Talk about it
- How do you know which way to move the decimal point?
- Why do we shift it in both numbers, not just one?
- What is a sensible estimate for this question before you work it out?
- How could you check your answer using multiplication?
- Where might you meet decimal division in real life?
- Which question did you find trickiest, and what helped?
Take it off the page
Shop prices
Look at prices on a till receipt or in a catalogue. Make up questions, such as sharing a cost equally between friends, and work them out on paper.
Measuring lengths
Use a ruler or tape measure. Choose a length in metres and ask how many pieces of 0.5 m or 0.2 m could be cut from it.
Place value cards
Make cards for digits and a decimal point. Build a decimal, then multiply it by 10 or 100 by moving the cards. Say what has happened to each digit.
Who it is for
Parents
Sit with your child for the first question, then let them lead. Ask them to explain each step in their own words. About 15 minutes is plenty. If they get stuck, go back to the short division help.
Teachers
Use it as a starter after teaching place value shifts, or as a plenary, homework or early finisher task. The questions move from whole number divisors to decimal divisors, so it suits mixed ability groups. Page 2 has support, stretch and answers.
Home educators
Pair it with real measuring or shopping tasks, so decimals feel useful. It prints again for brothers and sisters, and it works as revision a few weeks later. Ask your child to explain their method, not just give answers.
Where this fits
Before this, children work with place value, multiply and divide by 10, 100 and 1000, and divide whole numbers. Those skills make shifting the decimal point feel natural.
After this, children can use decimal division in work on fractions, percentages, ratio and problems with measures. Being secure here makes that later work much easier.
Questions parents and teachers ask
- What age is Dividing Decimals for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. Older or younger children who need to practise dividing decimals can also use it, with help from page 2 if needed.
- What will children practise?
They practise dividing decimals by whole numbers and by decimals. The main idea is shifting the decimal point so the divisor becomes a whole number, which builds place value, division and estimating skills.
- How long does it take?
It takes about 15 minutes. Work through the first question together, then let your child try the rest alone. Short, focused sessions usually work better than long ones.
- What if it feels too hard?
Start with the first four questions as short division. Write the decimal point above the line first. Come back to the decimal divisors once that feels comfortable. Page 2 has more help ideas.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers and sisters, or for revision a few weeks later.
- Can teachers use it in class?
Yes. It works as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 has support, stretch and answers.
- Is this a screen free activity?
Yes. It needs only paper and a pencil. It works well for quiet time, rainy days, homework or school holidays, and it prints well in black and white on plain A4 paper.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.