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📗 Class 7 maths · session 2 of 12 · 60 minutes · free

Fractions and decimals

Welcome to Captain Calc's math headquarters! Join our mission today to conquer fractions and decimals with superhero power.

🎯 Practice mode🖨 Print a worksheet

🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.

A complete lesson · 60 minutes

Teach it, see it, practise it, all on this page.

Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.

See the teacher's plan
  1. Warm-up3 min
  2. Warm-up games5 min
  3. Multiplying Fractions with Captain Calc8 min
  4. Dividing Fractions using Reciprocals7 min
  5. Multiplying Decimals7 min
  6. Dividing Decimals7 min
  7. Fraction Power-Up Training6 min
  8. Decimal Laser Precision5 min
  9. Captain Calc's City Missions6 min
  10. Quiz5 min
  11. Set the project1 min

By the end you can

  • Multiply fractions and mixed numbers correctly
  • Divide fractions using reciprocals
  • Multiply and divide decimal numbers with precision
  • Solve real-life word problems involving fractions and decimals

Before you start

  • Basic multiplication and division of whole numbers
  • Understanding proper, improper fractions and decimal place values

Have ready

  • Grid notebook and pencil
  • Ruler for visual division

Class 7 · CBSE, ICSE and state boards

Warm-up · think first

Captain Calc has 12 power crystals. He uses 1/3 of them to boost his suit. How many crystals did he use?

Show the answer

4 crystals, because 12 ÷ 3 = 4.

Teacher tip: Ask students to share how they split whole numbers into equal fractional parts.

More warm-ups for every class →

🎮 Warm-up games · 5 quick games

Play with Captain Calc

Six minutes with Captain Calc. Vote, say why, then show the answer.

  1. Which one does not belong: 1/2, 2/4, 0.5, 3/5? (1/2 · 2/4 · 0.5 · 3/5)
    Answer: 3/5 does not belong because 1/2, 2/4, and 0.5 are all equal to 0.5, while 3/5 equals 0.6.
  2. Would you rather get 3/4 of a ₹100 reward or 0.8 of a ₹100 reward? (3/4 of ₹100 · 0.8 of ₹100)
    Answer: 0.8 of ₹100 gives ₹80, while 3/4 of ₹100 gives ₹75. So 0.8 of ₹100 is greater!
  3. Multiplying two proper fractions gives a answer smaller than both fractions. (Always · Sometimes · Never)
    Answer: Always. Proper fractions are less than 1, so multiplying them scales the value down.
  4. I am a decimal number. Multiply me by 10 and I become 45. Divide me by 10 and I become 0.45. What number am I?
    Answer: 4.5
  5. Where do you see fractions and decimals used together in everyday life in India?
    Answer: Buying 2.5 kg of rice, petrol pumps measuring 1.5 litres, or cricket run rates like 6.5 runs per over!

Part 1 of 4 · learn, see, practise

Multiplying Fractions with Captain Calc

To multiply two fractions, multiply the top numbers (numerators) together and bottom numbers (denominators) together.

For mixed fractions, convert them to improper fractions before multiplying.

Always simplify your final fraction to its simplest form.

Example 1

Multiply 2/3 × 5/7.

  1. Step 1: Multiply numerators: 2 × 5 = 10.
  2. Step 2: Multiply denominators: 3 × 7 = 21.
  3. Step 3: Combine to get 10/21.

Answer: 10/21

Example 2

Multiply 1 1/2 × 4/5.

  1. Step 1: Convert 1 1/2 to 3/2.
  2. Step 2: Multiply numerators: 3 × 4 = 12.
  3. Step 3: Multiply denominators: 2 × 5 = 10.
  4. Step 4: Simplify 12/10 to get 6/5 or 1 1/5.

Answer: 6/5

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 10/21
  2. 9
  3. 2
  4. 15
  5. 1/6
  6. 3

Part 2 of 4 · learn, see, practise

Dividing Fractions using Reciprocals

To divide by a fraction, turn the division sign into multiplication and flip the second fraction.

Flipping a fraction gives its reciprocal (for example, reciprocal of 3/4 is 4/3).

Convert mixed numbers into improper fractions before finding their reciprocal.

Example 1

Divide 3/4 ÷ 1/2.

  1. Step 1: Reciprocal of 1/2 is 2/1.
  2. Step 2: Multiply 3/4 × 2/1 = 6/4.
  3. Step 3: Simplify 6/4 to get 3/2.

Answer: 3/2

Example 2

Divide 2 1/3 ÷ 7/9.

  1. Step 1: Convert 2 1/3 to 7/3.
  2. Step 2: Reciprocal of 7/9 is 9/7.
  3. Step 3: Multiply 7/3 × 9/7 = 63/21 = 3.

Answer: 3

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 3/2
  2. 15
  3. 1/16
  4. 3
  5. 7/18
  6. 3

Part 3 of 4 · learn, see, practise

Multiplying Decimals

Multiply decimal numbers ignoring the decimal points first as whole numbers.

Count the total number of decimal places in both factors combined.

Place the decimal point in your product counting that many places from the right.

Example 1

Multiply 0.3 × 0.4.

  1. Step 1: Multiply whole numbers: 3 × 4 = 12.
  2. Step 2: Count decimal places: 1 place in 0.3 plus 1 place in 0.4 equals 2 total places.
  3. Step 3: Place decimal point 2 places from the right to get 0.12.

Answer: 0.12

Example 2

Multiply 3.12 × 1.5.

  1. Step 1: Multiply 312 × 15 = 4680.
  2. Step 2: Total decimal places = 2 + 1 = 3 places.
  3. Step 3: Count 3 places from right: 4.680, which equals 4.68.

Answer: 4.68

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 1.2
  2. 15
  3. 0.1
  4. 4.68
  5. 0.004
  6. 10

Part 4 of 4 · learn, see, practise

Dividing Decimals

To divide by a decimal, make the divisor a whole number by multiplying both dividend and divisor by 10, 100, or 1000.

Divide the new numbers using standard division.

Keep track of decimal alignment carefully when dividing.

Example 1

Divide 4.5 ÷ 9.

  1. Step 1: Divide 45 by 9 to get 5.
  2. Step 2: Since 4.5 has 1 decimal place, quotient has 1 decimal place.
  3. Step 3: Answer is 0.5.

Answer: 0.5

Example 2

Divide 7.5 ÷ 0.25.

  1. Step 1: Multiply both numbers by 100 to get 750 ÷ 25.
  2. Step 2: Divide 750 by 25.
  3. Step 3: 750 ÷ 25 = 30.

Answer: 30

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 0.5
  2. 3.68
  3. 1.2
  4. 30
  5. 4
  6. 15

Watch out

Common mistakes

Adding numerators directly while multiplying fractions instead of multiplying them

Remember to multiply numerator by numerator and denominator by denominator.

Forgetting to flip the second fraction when dividing

Always keep the first fraction, change division to multiplication, and flip the second fraction.

Misplacing the decimal point after multiplying decimals

Count the total decimal places in both numbers combined, then count that many places from right in your answer.

Dividing decimals without making the divisor a whole number

Multiply both dividend and divisor by 10, 100, or 1000 so the divisor becomes a whole number first.

Class activity 1 of 3

Fraction Power-Up Training

Captain Calc needs quick calculations to charge his hero suit using fraction operations!

  1. Solve each fraction calculation step by step.
  2. Simplify your answer to lowest terms.
  3. Type the numerical answer in the box.

Answers (for the teacher)
  1. 2/5
  2. 6
  3. 3/2
  4. 10
  5. 2

Class activity 2 of 3

Decimal Laser Precision

Calibrate Captain Calc's math beam by solving these decimal challenge items!

  1. Perform decimal multiplication or division.
  2. Check decimal point position carefully.
  3. Type the exact final decimal value.

Answers (for the teacher)
  1. 4.2
  2. 1
  3. 0.8
  4. 40
  5. 0.045

Class activity 3 of 3

Captain Calc's City Missions

Help Captain Calc solve real-life urban problems in Mumbai using math skills!

  1. Read the word problem carefully.
  2. Decide whether to multiply or divide.
  3. Solve and enter the correct numerical value.

Answers (for the teacher)
  1. 300
  2. 0.5
  3. 6
  4. 66
  5. 8

After class · project

Super Hero Budget & Recipe Planner

Design a hero party menu calculating fractional servings and decimal costs for Captain Calc's team.

What to make: A completed one-page Hero Party Planner Sheet with accurate fraction and decimal math.

Stretch: Calculate a 0.1 discount on total costs and find the final discounted total!

How it is marked

Look forDone well when
Math AccuracyAll decimal multiplications and fraction divisions are 100% correct.
Clarity & LayoutSteps are clearly labelled with proper units and easy to follow.
Real-world ContextQuantities and prices reflect realistic Indian market values.

Project template

Copy it onto paper or print the practice sheet.

Item Name: _____ | Unit Price: ₹_____ per kg/litre
Quantity needed for team: _____ kg/litre
Total Cost Calculation: _____ × _____ = ₹_____
Portion per hero: Total quantity ÷ 8 = _____ kg/litre

Homework

Practise at home

Try each on paper, then tap to see the answer and working. Or print the practice sheet.

  1. Multiply 5/6 × 9/10.

    3/4. Working: (5 × 9) / (6 × 10) = 45/60 = 3/4.

  2. Divide 4/5 by 8/15.

    3/2. Working: 4/5 × 15/8 = 60/40 = 3/2.

  3. Multiply 1.25 × 0.8.

    1. Working: 1.25 × 0.8 = 1.000 = 1.

  4. Divide 14.4 by 1.2.

    12. Working: 14.4 ÷ 1.2 = 144 ÷ 12 = 12.

  5. Rohan walks 2.4 km in 1 hour. How far does he walk in 3.5 hours?

    8.4 km. Working: 2.4 × 3.5 = 8.4.

  6. A container holds 0.4 litres of juice. How many containers can be filled from 6 litres?

    15. Working: 6 ÷ 0.4 = 60 ÷ 4 = 15.

🔥 Challenge round · finished early?

The hardest questions of the lesson, no notes

Cover the notes and try these from memory. They are meant to make you think hard: draw, try small cases, and check your answer.

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 1/6
  2. 3
  3. 7/18
  4. 3
  5. 0.004
  6. 10
  7. 4
  8. 15

🧠 Think-hard question

A tank is 3/5 full of water. When 15 litres of water are drained, it remains 1/4 full. Find the total capacity of the tank in litres.

Talk it through or use the drawing board. There is more than one way to get there.

🎯 Practice mode: one question at a time🧩 Brain warm-ups🎮 Maths and logic games

Quiz · 10 questions

Final quiz: check what you learned

Pick an answer to see if it is right and why. Your best score is saved on this device.

1What is 3/5 × 10/9 in simplest form?
Show the answer

2/3. Multiply numerators and denominators to get 30/45, which simplifies to 2/3.

2What is 4/7 ÷ 2/21?
Show the answer

6. Multiply 4/7 by reciprocal 21/2 to get 84/14 = 6.

3What is 0.4 × 0.03?
Show the answer

0.012. Multiply 4 × 3 = 12 and count 3 total decimal places to get 0.012.

4What is 5.4 ÷ 0.9?
Show the answer

6. Multiply both by 10 to get 54 ÷ 9 = 6.

5What is 3/4 expressed as a decimal?
Show the answer

0.75. Divide 3 by 4 to get 0.75.

6What is the reciprocal of 2 1/3?
Show the answer

3/7. Convert 2 1/3 to improper fraction 7/3, whose reciprocal is 3/7.

7Priya spends 2/5 of ₹500. How much money does she spend?
Show the answer

₹200. Multiply 500 × 2/5 = 1000/5 = 200.

8What is 12.35 × 100?
Show the answer

1235. Multiplying by 100 moves the decimal point 2 places to the right.

9What is 0.72 ÷ 8?
Show the answer

0.09. 72 ÷ 8 = 9, and placing 2 decimal places gives 0.09.

10A rope of length 15 m is cut into pieces of length 3/4 m each. How many pieces are made?
Show the answer

20. Divide 15 ÷ (3/4) = 15 × (4/3) = 60/3 = 20.

🖨 Print what we learned

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For parents and teachers

The 60-minute lesson plan

Use it as it is, or stretch any part over two sessions. Each row links to the part of the page you need.

TimePartThe teacherThe learner
0–3 minWarm-upAsk the question and wait for a guess before any hint.Guess, then explain.
3–8 minWarm-up gamesPlay three or four games. Ask for a reason each time.Vote and say why.
8–16 minMultiplying Fractions with Captain CalcExplain, then reveal the examples one step at a time.Practise up to the stretch question.
16–23 minDividing Fractions using ReciprocalsExplain, then show the examples.Practise.
23–30 minMultiplying DecimalsExplain, then show the examples.Practise.
30–37 minDividing DecimalsExplain, then show the examples.Practise; the stretch can be homework.
37–43 minFraction Power-Up TrainingLet learners work alone; hint only after a wrong check.Solve and check.
43–48 minDecimal Laser PrecisionDo the first item together.Finish the activity.
48–54 minCaptain Calc's City MissionsSet as homework if time is short.Solve the mission.
54–59 minQuizRead each question aloud; vote, then check.Answer and read why.
59–60 minSet the projectShow the template and agree a due date.Start the project.

Questions to ask

  • How does changing a division problem into a reciprocal multiplication make it easier?
  • What strategy helps you place the decimal point correctly when multiplying decimals?
  • How can you check if your answer to a fraction division problem is reasonable?

If it feels hard

Draw visual fraction bars or grids to help learners see why dividing by a fraction flips the numbers and why multiplying proper fractions yields a smaller value.

If it feels easy

A tank is 3/5 full of water. When 15 litres of water are drained, it remains 1/4 full. Find the total capacity of the tank in litres.

FAQ

Fractions and decimals: questions

Why do we flip the second fraction when dividing?

Dividing by a number is the same as finding how many parts of that size fit into the whole. Multiplying by the reciprocal computes this directly!

How do I know where to put the decimal point in division?

Convert the divisor into a whole number by multiplying both numbers by 10, 100, or 1000 first, then divide normally.

Is this lesson aligned with Class 7 CBSE and ICSE syllabus?

Yes, multiplication and division of fractions and decimals form a core unit in Class 7 mathematics boards across India.

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