Day 6: Master of Parts (Fractions & Decimals) | Middle Stage (Grades 6, 7 & 8) | Apex Institute of Maths and Sciences

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Day 6: Master of Parts (Fractions & Decimals) | Middle Stage (Grades 6, 7 & 8) | Apex Institute of Maths and Sciences

Day 6: Master of Parts (Fractions & Decimals) 🍰💰

Middle Stage (Grades 6, 7 & 8) | Apex Institute of Maths and Sciences

🎯 1. Concept: Two Languages, One Meaning

Welcome to Day 6! Today we look at the two ways mathematicians talk about “pieces” of a whole: Fractions and Decimals.

They are exactly the same thing, just written in different languages. Half of a pizza is 1/2 in fraction language, and it is 0.5 in decimal language. You need to be fluent in both!

💡 2. The Golden Rules of Operations

Multiplying Fractions: Just multiply straight across! Top × Top, Bottom × Bottom. No need for a common denominator! (Example: 1/2 × 3/4 = 3/8).

Dividing Fractions (Keep-Change-Flip): You actually never divide fractions. Instead, you Keep the first fraction, Change the ÷ sign to ×, and Flip the second fraction upside down. Then just multiply! (Example: 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2).

Multiplying Decimals: Pretend the decimals aren’t there, multiply like normal numbers, then count how many total numbers were behind the decimal points and put the point back in your answer!

🌍 3. Math in Our Daily Life

Fractions and decimals run our kitchens and our wallets!

Scenario 1 (Money & Decimals): Indian Rupees use decimals. If you have ₹50 and 50 paise, you write it as ₹50.50. If you buy a candy for ₹10.25, you are using decimal subtraction to find your change!

Scenario 2 (Baking & Fractions): A recipe for cookies needs 3/4 cup of sugar. But you only want to make HALF the recipe because you don’t have many guests. You have to multiply 3/4 by 1/2 to know exactly how much sugar to use (3/8 cup).

📝 4. Analytical Tasks

Grab your math journal and try these real-world tasks:

  • Task A: The Money Convert: Write down the decimal value of these fractions of a Rupee: 1/2, 1/4, and 3/4. (Hint: Think about 50 paise, 25 paise, and 75 paise).
  • Task B: The Keep-Change-Flip: Write out the steps to solve 2/3 ÷ 1/5 using the Keep-Change-Flip rule.

✅ 5. Day 6 Application Test

Let’s test your fraction and decimal logic! This quiz gets progressively harder. Grab some rough paper, select your answers, and click submit.

Easy
1. How do you write the fraction 1/2 as a decimal?
Solution: Half of 1 whole is 0.5 (Think of it as 50%).
Easy
2. What is the golden memory rule for DIVIDING fractions?
Solution: You KEEP the first fraction, CHANGE division to multiplication, and FLIP the second fraction!
Easy
3. If 0.25 is 1/4 (one quarter), what fraction is 0.75?
Solution: 0.75 is three quarters. So as a fraction, it is 3/4.
Easy
4. What is 1/2 × 1/2?
Solution: Multiply straight across. Top: 1 × 1 = 1. Bottom: 2 × 2 = 4. The answer is 1/4.
Medium
5. You have ₹50.50 in your pocket. You find a ₹20 note and a 75 paise coin on the road. How much money do you have in total now?
Solution: Line up the decimals! 50.50 + 20.75. 50 + 75 paise is 125 paise (which is ₹1.25). 50 + 20 + 1.25 = ₹71.25.
Medium
6. A cake recipe asks for 3/4 cup of sugar. You only want to make HALF of the cake. What is 1/2 of 3/4?
Solution: The word “of” means multiply! 1/2 × 3/4 = (1×3)/(2×4) = 3/8.
Medium
7. What is 0.5 × 0.5?
Solution: Multiply 5 × 5 = 25. There are 2 total digits behind the decimals in the problem, so put the decimal 2 spots back: 0.25. (Also, 1/2 of 1/2 is a quarter!)
Medium
8. You have 2 whole pizzas. You want to cut them into small 1/4 slices. How many slices will you get? (Math: 2 ÷ 1/4)
Solution: Keep-Change-Flip! Keep 2/1, Change ÷ to ×, Flip 1/4 to 4/1. Math is 2 × 4 = 8. (Each pizza gives 4 slices, so 2 pizzas give 8).
Hard
9. 🧠 Puzzle: You have a plank of wood that is 2.5 meters long. You need to cut it into smaller pieces that are exactly 0.5 meters long. How many pieces will you get?
Solution: 2.5 ÷ 0.5. To make it easy, move the decimal one spot to the right for both: 25 ÷ 5. The answer is 5 pieces!
Hard
10. 🧠 Puzzle: You go shopping. You buy a shirt for ₹250.75 and a cap for ₹120.50. You hand the shopkeeper a ₹500 note. What is your exact change?
Solution: First, add your items: 250.75 + 120.50 = 371.25. Next, subtract from 500: 500.00 – 371.25. Borrowing correctly gives you ₹128.75.
⚠️ Please answer all 10 questions before submitting!
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36 thoughts on “Day 6: Master of Parts (Fractions & Decimals) | Middle Stage (Grades 6, 7 & 8) | Apex Institute of Maths and Sciences”

  4. I have a brellint work that to from apex education .Im grat full to have this educational work .
    Thank you so much apex education.

    Reply

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