NCERT Solutions for Class 4 Maths Mela Chapter 05 Sharing and Measuring

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Question 1. Which part of the paper would you have chosen - one half or two quarters? Why?
Answer: One half and two quarters are the same amount. I would pick either one since they both give you the same amount of paper (1/2 = 2/4).
In simple words: Half and two quarters are exactly equal. It does not matter which one you pick.

Exam Tip: Recognize that different fractions can have the same value - this shows understanding of equivalent fractions.

Question 2. Do you think Ikra shared the paper equally? Why? Try with a paper.
Answer: Yes, Ikra shared the paper equally. When you fold a paper into halves, you get two parts that match. When you fold it into quarters, you get four parts that match. Two quarters makes one half, so the sharing was fair.
In simple words: Yes, she shared it equally. Two quarters is the same as one half.

Exam Tip: Always verify equal sharing by folding or measuring - visual proof is stronger than just saying it is equal.

Question 3. How do you know that the paper has been divided equally?
Answer: We can tell the paper is divided equally by folding and checking if the parts line up perfectly. We can also measure each part to make sure they are the same size. Another way is to look at the areas and compare them by sight.
In simple words: Fold the parts and see if they fit on top of each other. Or measure them to check they are the same.

Exam Tip: Name at least one method of checking - folding, measuring, or visual comparison - to show you understand equal division.

Question 4. Why do you think Samina chose two quarters of the paper?
Answer: Samina picked two quarters because it sounded like she was getting more paper than one half. She did not know that two quarters (2/4) is equal to one half (1/2).
In simple words: She thought two quarters sounded like more. She did not realize they are the same.

Exam Tip: This shows a common misunderstanding - students often think more pieces means more amount, even when pieces are smaller.

Question 5. Colour the figures that are divided into halves correctly. How did you get the answer?
Answer: I check if a figure is divided equally by folding and seeing if the parts overlap perfectly.
In simple words: Fold it and see if both parts match up exactly.

Exam Tip: When checking if halves are equal, folding is the most reliable method to confirm matching parts.

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Question 6. Divide the shapes into halves by drawing a line.
Answer: A line drawn through the middle of each shape will divide it into two equal parts. The line should go through the centre so both sides match perfectly when folded.
In simple words: Draw a line down the middle so both halves look the same.

Exam Tip: The dividing line must pass through the centre of the shape to create truly equal halves.

Question 7. Divide these shapes into 4 equal parts/quarters.
Answer: To divide a shape into four equal parts, draw two lines that cross in the middle. One line can go up and down, and the other line can go left and right. This makes four pieces of the same size.
In simple words: Draw one line up and down, and one line left and right. This makes four equal pieces.

Exam Tip: The two lines must cross at the exact centre and be perpendicular to create four truly equal quarters.

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Question 8. In how many different ways can you fold/cut a rectangular paper in two equal parts? Try it with a rectangular paper.
Answer: A rectangular paper can be folded or cut into halves in several ways. You can fold it horizontally by bringing the top edge to the bottom edge. You can fold it vertically by bringing the left edge to the right edge. You can also fold it diagonally from one corner to the opposite corner. Each method creates two equal parts.
In simple words: Fold it across the middle, fold it up and down, or fold it corner to corner. All three ways make equal halves.

Exam Tip: Show all three methods (horizontal, vertical, and diagonal) to demonstrate complete understanding of dividing rectangles into halves.

Question 9. Now try to draw and show five different ways in which we can fold/cut a rectangle into four equal parts (1/4 or quarter).
Answer: A rectangle can be divided into four equal parts in many ways. One way is to draw a vertical line down the middle and a horizontal line across the middle, making a cross. Another way is to draw both diagonals from corner to corner, which also creates four pieces. You can also fold the rectangle in half one way and then fold that result in half again. Each method produces four equal quarters.
In simple words: Draw a cross through the middle, draw both diagonal lines, or fold twice. All make four equal parts.

Exam Tip: Provide at least three different methods with clear drawings to show you understand multiple ways to create quarters.

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Question 10. What is Sumedha observing about her share as each guest comes in?
Answer: Sumedha sees that her share of dhokla becomes smaller each time a new guest arrives. When there are 2 people, she gets 1/2. When there are 3 people, she gets 1/3. When there are 4 people, she gets 1/4. When there are 5 people, she gets 1/5. As more people join, her piece gets smaller.
In simple words: As more people come, Sumedha's piece gets smaller and smaller.

Exam Tip: Understand that as the denominator increases, the size of each person's share decreases.

Question 11. In which situation will Sumedha get to eat more dhokla: when shared among 9 people or 11 people?
Answer: Sumedha will get more dhokla when it is shared among 9 people. Her share would be 1/9 in that case, compared to 1/11 when shared among 11 people. Since 1/9 is a larger piece than 1/11, she eats more with fewer people sharing.
In simple words: When there are fewer people, each piece is bigger. So 9 people is better than 11 people for her.

Exam Tip: Compare fractions by recognizing that a smaller denominator means a larger share when the numerator is 1.

Question 12. How many pieces of 1/6 would make a complete dhokla?
Answer: Six pieces of 1/6 would make one whole dhokla. This is because 6 times 1/6 equals 6/6, which equals 1 complete whole (6 × 1/6 = 6/6 = 1).
In simple words: You need 6 pieces of 1/6 to make a whole. Each piece is 1/6, so 6 pieces = 1 whole.

Exam Tip: The numerator of the result tells you how many unit fractions you need - here, 6 one-sixths make a whole.

Question 13. What would be Sumedha's share, if Idha and Vinayak both give their share of dhokla to her?
Answer: When the dhokla is split among 5 people, each person gets 1/5. If Idha and Vinayak both give their portions to Sumedha, she would have her own share plus both of theirs. That means 1/5 + 1/5 + 1/5, which equals 3/5 of the dhokla.
In simple words: Sumedha gets 1/5, plus 1/5 from Idha, plus 1/5 from Vinayak. That is 3/5 total.

Exam Tip: When adding fractions with the same denominator, add only the numerators and keep the denominator the same.

Question 14. How much dhokla would each person get if it was shared equally among 6 people? Try also with 8 people. Who will get the bigger pieces of dhokla? Draw and explain.
Answer: If the dhokla is split among 6 people, each person gets 1/6. If it is split among 8 people, each person gets 1/8. When shared among 6 people, the pieces are bigger because 1/6 is greater than 1/8. The more people who share, the smaller each piece becomes.
In simple words: Six people get 1/6 each. Eight people get 1/8 each. Six people get bigger pieces.

Exam Tip: Show both shaded diagrams and compare the shaded areas visually to prove which fraction is larger.

Question 15. Shade a portion of the dhokla to represent the fraction Sumedha would get when the dhokla is shared equally among the given number of people. Discuss why the fractions get smaller.
Answer: As you shade the circles for 2, 3, 4, 5, 8, and 9 people, the shaded portion gets smaller each time. This happens because the same whole is being divided into more and more equal parts. When you split something into more pieces, each piece must be smaller than before. So 1/2 is bigger than 1/3, which is bigger than 1/4, and so on.
In simple words: When you divide into more parts, each part gets smaller. That is why 1/2 is bigger than 1/9.

Exam Tip: Shade each circle carefully and label it clearly to show how the size of the shaded region decreases as the denominator increases.

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Question 16. Share your observations about the different pieces and the whole using the fraction kit.
Answer: By using the fraction kit, we learn that a whole can be split into equal parts in many different ways. As the denominator gets larger, each piece becomes smaller in size. We can also combine different fractions together to make a whole again. For example, two 1/2 pieces make a whole, three 1/3 pieces make a whole, and so on.
In simple words: A whole can be split many ways. Bigger denominators mean smaller pieces. Pieces can be put back together to make a whole.

Exam Tip: Mention the relationship between denominator size and piece size - this shows deep understanding of fraction concepts.

Question 17. Take any two different pieces of the fraction kit and compare them. Discuss which one is smaller and why?
Answer: When comparing two fractions like 1/2 and 1/3, the 1/3 piece is smaller. This is because when a whole is split into fewer parts, each part is larger. When a whole is split into more parts, each part is smaller. So 1/2 is larger than 1/3, and 1/3 is larger than 1/4.
In simple words: The fraction with a bigger denominator is smaller. So 1/3 is smaller than 1/2.

Exam Tip: Always explain why one fraction is larger or smaller by referring to how many parts the whole is divided into.

Question 18. Sumedha noticed that when a whole is equally divided in a larger number of parts, each part gets smaller. Do you agree with Sumedha?
Answer: Yes, I agree with Sumedha completely. When you divide a whole into more equal pieces, each individual piece becomes smaller. For instance, 1/8 is smaller than 1/4 because 8 parts are smaller than 4 parts. This rule is always true for unit fractions.
In simple words: When you split into more parts, each part is smaller. Always.

Exam Tip: Use concrete examples with drawings to support this principle - visual proof is powerful.

Question 19. Sumedha says, "When I join 5 pieces of 1/5, it makes a whole dhokla." Try to do it yourself with your fraction kit.
Answer: This statement is correct. When you take five pieces of 1/5 and put them together, they form one complete whole. This works because 5 times 1/5 equals 5/5, and 5/5 equals 1 (5 × 1/5 = 5/5 = 1).
In simple words: Five pieces of 1/5 fit together to make a whole. 5 × 1/5 = 1 whole.

Exam Tip: Show that the numerator and denominator are equal in the result (5/5) to demonstrate that a whole is formed.

Question 20. Sumedha says that this part is one-third of the complete whole. Why is she saying so?
Answer: Sumedha says this because when a whole is split into three equal parts, each part represents 1/3 of the whole. A single part out of three equal parts is called one-third or 1/3.
In simple words: When you divide into three equal parts, one part is 1/3 of the whole.

Exam Tip: Connect the denominator directly to the number of equal parts the whole is divided into.

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Question 21. Fill in the blanks. Both fractions are parts of the same whole. Use your fraction kit if needed. (1) ___ is greater than ___ (1/5, 1/4). (2) ___ > ___ (1/9, 1/6). (3) 1/6 ___ 1/8. (4) ___ is smaller than ___ (___, ___).
Answer: (1) 1/4 is greater than 1/5. (2) 1/6 > 1/9. (3) 1/6 > 1/8. (4) 1/8 is smaller than 1/4.
In simple words: Fractions with smaller denominators are bigger. So 1/4 is bigger than 1/5.

Exam Tip: Remember - when numerators are the same, the fraction with the smaller denominator is always larger.

Question 22. Look at the garden and answer the questions about fractions of each flower type. (First garden: Mogra in 1/5 part, Marigold in ___ part, Jasmine in ___ part, Rose in 2/5 part.)
Answer: Marigold takes up 1/5 of the garden. Jasmine takes up 1/5 of the garden.
In simple words: Each flower type (except Rose) is 1/5. Rose takes 2/5, which is two parts.

Exam Tip: Count the flower sections carefully and match them to the fraction labels given.

Question 23. Look at the second garden and answer the questions. (Mogra in ___ part, Marigold in ___ part, Rose in 3/5 part.)
Answer: Mogra takes up 1/5 of the garden. Marigold takes up 1/5 of the garden.
In simple words: Each of the other flowers is 1/5. Rose takes 3/5 (three parts).

Exam Tip: Recognize that equal-sized sections have equal fractions, and count sections to find the remaining fractions.

Question 24. Look at the third garden and answer the questions. (Marigold in ___ part, Rose in 4/5 part.)
Answer: Marigold takes up 1/5 of the garden.
In simple words: Marigold is 1/5. Rose is 4/5 (four parts).

Exam Tip: Since the denominator is 5, all fractions must have 5 as the denominator - use this to find missing parts.

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Question 25. Make a flower garden with seven flowering seeds - Mogra, marigold, Jasmine, Rose, Lily, Hibiscus, and Periwinkle. (a) Marigold in one-seventh (1/7) and Rose and Hibiscus in three-sevenths (3/7) part each.
Answer: In this garden with 7 sections, Marigold takes 1 section (1/7). Rose takes 3 sections (3/7). Hibiscus takes 3 sections (3/7). The remaining flowers share the leftover space. Each section in a 7-part garden represents 1/7 of the whole.
In simple words: Divide the garden into 7 equal parts. Color 1 part for Marigold, 3 parts for Rose, and 3 parts for Hibiscus.

Exam Tip: Ensure sections are equal in size and that labels match the fraction amounts specified in the question.

Question 26. (b) Lily in three-sevenths (3/7), Marigold in two-sevenths (2/7), and Periwinkle in another two-sevenths (2/7).
Answer: In this garden, Lily takes 3 sections (3/7). Marigold takes 2 sections (2/7). Periwinkle takes 2 sections (2/7). The remaining 2 sections (2/7) are for other flowers like Jasmine, Rose, or Hibiscus. Each section represents 1/7 of the whole garden.
In simple words: Divide into 7 equal parts. Color 3 for Lily, 2 for Marigold, and 2 for Periwinkle.

Exam Tip: Add the fractions to check: 3/7 + 2/7 + 2/7 = 7/7 = 1 (a complete garden).

Question 27. (c) Mogra in five-sevenths (5/7) part and Hibiscus in two-sevenths (2/7).
Answer: In this garden, Mogra takes 5 sections (5/7). Hibiscus takes 2 sections (2/7). Together, these two flowers fill the entire garden (5/7 + 2/7 = 7/7 = 1). Each section represents 1/7 of the whole.
In simple words: Divide into 7 equal parts. Color 5 parts for Mogra and 2 parts for Hibiscus.

Exam Tip: Verify the answer by adding: 5/7 + 2/7 = 7/7 = 1, confirming the entire garden is accounted for.

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Question 28. Write the fractions for each of the toppings in the following dosas.
Answer: Look at each dosa and count how many sections have each topping. Write the fraction with the number of sections having that topping as the numerator and the total number of sections as the denominator. For example, if 3 out of 12 sections have chilli paneer, write 3/12 (or simplify to 1/4).
In simple words: Count the sections with each topping. Write that number as the top of the fraction. The total sections go on the bottom.

Exam Tip: Count carefully and match each topping to its correct fraction by looking at the dosa sections.

Question 29. Now you can make different dosas based on demand. Make a dosa with 2/3 topping of Spicy onion and 1/3 of Classic potato. Also, make a dosa with 3/8 of Classic potato, 2/8 of Chilly paneer, and 4/8 of Tangy tomato mix.
Answer: For the first dosa, divide it into 3 equal sections. Shade 2 sections for Spicy onion and 1 section for Classic potato. For the second dosa, divide it into 8 equal sections. Shade 3 sections for Classic potato, 2 sections for Chilly paneer, and 4 sections for Tangy tomato mix. Check that all sections are filled: 2/3 + 1/3 = 1 and 3/8 + 2/8 + 4/8 = 1.
In simple words: Draw circles divided into equal parts. Color each part according to the fraction given.

Exam Tip: Verify that the fractions add up to 1 whole, and use different colors clearly to show each topping.

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Let Us Do

Question 1. There are 12 cookies. What fraction of cookies will each get if the number of children are as follows:
(a) 3 children
(b) 6 children
(c) 2 children
(d) 4 children
Answer: When we divide cookies equally among children, each child gets a certain number of cookies and also a fraction of all the cookies.

(a) 3 children: Each child gets 12 ÷ 3 = 4 cookies. Each child receives 4/12, which simplifies to 1/3 of all the cookies.

(b) 6 children: Each child gets 12 ÷ 6 = 2 cookies. Each child receives 2/12, which simplifies to 1/6 of all the cookies.

(c) 2 children: Each child gets 12 ÷ 2 = 6 cookies. Each child receives 6/12, which simplifies to 1/2 of all the cookies.

(d) 4 children: Each child gets 12 ÷ 4 = 3 cookies. Each child receives 3/12, which simplifies to 1/4 of all the cookies.
In simple words: When you share cookies with more children, each child gets a smaller share. When you share with fewer children, each child gets a bigger share.

Exam Tip: Always divide the total number of items by the number of children, and then express the individual share as a fraction of the whole.

Question 2. Simran calls her school friends for her birthday party. 1/3 of her friends receive a hairband as their return gift. Place hairbands on 1/3 of her friends.
Answer: To solve this problem, we need to know the total number of friends. From the pictures shown, there are 9 friends in total. To find 1/3 of 9 friends, we divide: 9 ÷ 3 = 3. This means 3 friends would get hairbands as their return gift.
In simple words: To find 1/3 of a group, divide the total number by 3. So 1/3 of 9 friends is 3 friends.

Exam Tip: Always identify the total number first, then divide by the denominator to find the fraction.

Question 3. Draw flowers in 1/5 of the given number of pots.
Answer: Looking at the pots shown in the image, we can count a total of 15 pots. To find 1/5 of 15 pots, we calculate: 1/5 × 15 = 3 pots. So we should draw flowers in 3 of the 15 pots to represent 1/5 of the total number.
In simple words: To find 1/5 of any number, divide that number by 5. So 1/5 of 15 pots means 3 pots.

Exam Tip: Remember that fractions are parts of a whole - always count the total first, then find the required fraction by dividing.

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Let Us Find Fractions in Our Surroundings

Question 1. Yesterday Mummy asked to divide a box of barfis into four equal parts. There are 16 barfis in the box. Draw a picture of 16 barfis and find 1/4 of the whole. How many barfis are in each part?
Answer: To find 1/4 of 16 barfis, we need to divide the 16 barfis into 4 equal groups. We calculate: 16 ÷ 4 = 4. Therefore, 1/4 of 16 barfis equals 4 barfis, and each part would contain 4 barfis. In the figure shown, the part circled in a box represents this 1/4 fraction of the whole.
In simple words: When you divide something into 4 equal parts, each part is 1/4 of the whole. So 1/4 of 16 barfis is 4 barfis.

Exam Tip: To find a fraction of a whole number, always divide the total by the denominator of the fraction.

Question 2. Rohan has a piece of ribbon to decorate his notebook. Mohan's ribbon is one-fourth as long as Rohan's ribbon. How long will Rohan's ribbon be? Draw it.
Answer: If Mohan's ribbon measures 1/4 of Rohan's ribbon, then we can work backwards to find Rohan's length. Rohan's ribbon must be 4 times as long as Mohan's ribbon. For example, if Mohan's ribbon is 2 cm long, then Rohan's ribbon would be 4 × 2 = 8 cm long. The diagram shows Mohan's shorter ribbon underneath, and Rohan's ribbon divided into 4 equal parts, with Mohan's ribbon being equal to one of those parts.
In simple words: If one ribbon is 1/4 the length of another, the longer ribbon is 4 times bigger.

Exam Tip: Understanding the relationship between fractions helps - if something is 1/4 of the whole, then the whole is 4 times that amount.

Try Yourself

Question. Observe your surroundings and think of situations where we use fractions and write any two of them in the space provided below.
Answer: Fractions appear in many everyday situations all around us. One common use of fractions happens when we slice pizzas or cakes into equal pieces - each piece becomes a fraction of the whole. For instance, if a pizza gets cut into 8 slices, then each slice is 1/8 of the complete pizza. Another everyday application occurs when someone is cooking and measuring ingredients - recipes often call for amounts like 1/2 cup of milk or 1/4 teaspoon of salt, which are fractional measurements of the standard cup or spoon.
In simple words: We use fractions when we share food and when we measure things in cooking.

Exam Tip: Look for real-world examples in your daily life - sharing food, measuring, dividing tasks or money are all good examples of fractions being used.

Let Us Do

Question. Write down what fraction you observe after each fold. 1/3 = 2/6 = ____ = ____ = ____
Answer: When we keep folding a paper and marking equal parts, the fractions keep changing but their value stays the same. Starting with 1/3 and 2/6, if we continue folding and doubling the number of parts each time, the next equivalent fractions would be 4/12, then 8/24, and finally 16/48. All these fractions are equal to each other and to 1/3.
In simple words: When you fold paper into more and more parts, the fractions look different but mean the same amount.

Exam Tip: Equivalent fractions have the same value even though the numerator and denominator are different - you can check by dividing or by multiplying both top and bottom by the same number.

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Let Us Try

Question. Take another piece of paper and try the same starting with two equal parts, and halving every time. Share the findings with your friends. 1/2 = 2/4 = ____ = ____ = ____
Answer: Beginning with 1/2 and continuing the folding pattern where we split each part in half again, we get the next equal fractions: 4/8, then 8/16, and then 16/32. Each time we fold, we double the denominator and also double the numerator, keeping the overall value the same at 1/2.
In simple words: Keep doubling both the top and bottom numbers - the fraction still stays equal to 1/2.

Exam Tip: To find equivalent fractions, multiply or divide both the numerator and denominator by the same number.

Let Us Discuss

Observe the fraction chart and discuss the following questions. You may use your fraction kit also to explore the answers.

Question 1. How many 1/4s are equal to 1/2?
Answer: Two pieces of 1/4 are equal to 1/2. We can verify this: 1/4 + 1/4 = 2/4, and 2/4 simplifies to 1/2.
In simple words: Two fourths make one half.

Exam Tip: Use the fraction chart or draw it yourself to count how many small pieces fit into a larger piece.

Question 2. Is 2/3 less than or greater than 1/2?
Answer: The fraction 2/3 is greater than 1/2. Looking at the fraction chart, we can see that 2/3 takes up more space than 1/2 does.
In simple words: Two thirds is bigger than one half.

Exam Tip: Compare fractions by looking at the fraction chart or by finding a common denominator to see which is larger.

Question 3. Ten pieces of 1/10 make a complete whole. Is this statement true?
Answer: Yes, this statement is true. When we add ten pieces of 1/10 together, we get 10 × 1/10 = 10/10, which equals 1, a complete whole.
In simple words: Ten tenths make one whole.

Exam Tip: Remember that n pieces of 1/n always equals 1 - this is true for any denominator.

Question 4. Three pieces of 1/6 are equal to two pieces of 1/8. Is this true?
Answer: No, this statement is not true. Three pieces of 1/6 give us 3/6, which equals 1/2. Two pieces of 1/8 give us 2/8, which equals 1/4. Since 1/2 is not equal to 1/4, we can say that 1/2 ≠ 1/4.
In simple words: Three sixths equals one half, but two eighths equals one quarter, so they are not equal.

Exam Tip: Always simplify fractions before comparing them to check if they are truly equal.

Question 5. How many pieces of 1/8 make 1/4?
Answer: Two pieces of 1/8 make 1/4. We can verify: 2 × 1/8 = 2/8, which simplifies to 1/4.
In simple words: Two eighths make one fourth.

Exam Tip: Use multiplication to check - if 2 × 1/8 gives 1/4, then 2 pieces of 1/8 equal 1/4.

Question 6. Find the pieces that you can put together to make another bigger piece.
Answer: Looking at the fraction chart, we can find several combinations that make larger pieces. Two 1/4 pieces join together to make 1/2. Three 1/9 pieces join to make 1/3. Two 1/10 pieces join together to make 1/5. These are examples of combining smaller fractional pieces to form bigger fractional pieces.
In simple words: Smaller pieces can be put together to make bigger pieces.

Exam Tip: Practice combining fractions by adding them - this helps you understand how smaller pieces relate to larger ones.

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Let Us Do

Question 1. Bablu is playing with square shapes. He wants to cut them in such a way that each piece is equal in size. Circle the squares which have been cut into equal parts. Write the fraction for the shaded part, whenever possible.
Answer: Looking at each square, we need to check if all pieces are the same size.

(a) First square with vertical strips: The parts all appear to be equal in width and size. We should circle this one.

(b) Second square with a plus-shaped cutout: The pieces are not similar or equal in size. Do not circle this one.

(c) Third square with horizontal strips: The parts are equal. Circle this one. The shaded (coloured) part takes up 1 out of 3 equal strips, so the fraction is 1/3.

(d) Fourth square with diagonal cuts: The parts are equal - it is divided into 4 equal triangles. Circle this one.
In simple words: Only circle shapes that are cut into equal-sized pieces. For equal pieces, you can write a fraction.

Exam Tip: For a fraction to be correct, all parts must be equal in size - even if a shape looks divided, unequal pieces cannot be expressed as a simple fraction.

Question 2. Check if the children's claim below about the shaded parts of each of the pictures is correct. Circle the ones which you think are correct, cross out the ones which are not correct. You can draw additional lines to make the parts equal. Discuss your thinking.
Answer: Let us check each child's claim by looking at how the shapes are divided.

(a) Diamond shape: The square is split into 4 equal triangles by its diagonals, with 1 triangle shaded. Kishore's claim of 1/4 is correct. Circle this one.

(b) Circle with horizontal lines: The circle is divided by horizontal lines into 6 equal sections, with 1 section shaded. Perry's claim of 1/6 is correct. Circle this one.

(c) Triangle: The triangle does not appear to be divided into completely equal parts. The shaded area looks closer to 1/5 of the triangle than 1/4, so Balu appears more likely to be correct. Circle Balu's answer.
In simple words: Check if pieces are equal before you believe the fraction claim.

Exam Tip: Always verify that all parts are equal before you accept a fraction answer - you may need to draw extra lines to make parts truly equal.

Question 3. Identify the fractions represented by the coloured parts in the given pictures.
Answer: This question asks you to look at the shapes and identify what fraction the coloured part makes. Since specific pictures would need to be analyzed individually, the general approach is: count how many equal parts the shape is divided into (this is your denominator), then count how many parts are coloured (this is your numerator). The fraction is then numerator/denominator.
In simple words: Count total parts for the bottom number, count coloured parts for the top number.

Exam Tip: Always make sure all parts are equal before writing your fraction.

Question 4. Identify the fraction of the whole that the blue parts make in each of the pictures given below.
Answer: Looking at the three grid patterns with blue shaded areas:

(a) First grid pattern: Counting all the small triangles in the grid, we see 18 total parts. The blue triangles number 9. Therefore the blue parts make 9/18, which simplifies to 1/2 of the whole.

(b) Second grid pattern: The total is 18 small triangles. The blue triangles number 6. So the blue parts make 6/18, which simplifies to 1/3 of the whole.

(c) Third grid pattern: The total is 18 small triangles. The blue triangles number 3. So the blue parts make 3/18, which simplifies to 1/6 of the whole.
In simple words: Count blue pieces and total pieces. The fraction is blue pieces over total pieces.

Exam Tip: After finding your fraction, try to simplify it by dividing both numerator and denominator by their greatest common factor.

Question 4 (continued). Identify the fraction of the whole that the blue parts make in each of the pictures given below. (Hexagon and pattern figures)
Answer: Looking at the three composite shapes:

(a) First hexagon pattern: There are 6 hexagons arranged together, with 4 hexagons shaded blue. The fraction is 4/6, which reduces to 2/3.

(b) Second diamond in square: The square is divided into 4 equal triangular sections by its diagonals. The blue diamond (made of 2 triangles) represents 2/4 of the square, which equals 1/2.

(c) Third parallelogram pattern: This shape is made up of 9 equal parallelogram units, with 6 of them shaded blue. The fraction is 6/9, which simplifies to 2/3.
In simple words: Count the blue pieces and the total pieces to make your fraction.

Exam Tip: Remember to reduce fractions to their simplest form by finding the greatest common divisor of the numerator and denominator.

Question 5. Divide the following into equal parts and shade the appropriate parts in each.
Answer: For each shape given with a target fraction:

(a) Rectangle - Shade 2/3: Divide the rectangle into 3 equal horizontal strips. Shade 2 of these 3 strips in the colour shown.

(b) Circle - Shade 4/6: Divide the circle into 6 equal parts (like pizza slices). Shade 4 of the 6 parts. This equals 2/3 when simplified.

(c) Cross/Plus shape - Shade 1/4: Divide the cross shape into 4 equal sections. Shade only 1 of these 4 parts.

(d) Cross/Plus shape - Shade 1/8: Divide the shape into 8 equal parts and shade 1 of them. You can also show 1/8 by first dividing into 4 parts, then dividing each of those into 2 smaller parts, then shading 1.

(e) Cross/Plus shape - Shade 3/4: Divide the shape into 4 equal parts. Shade 3 of the 4 parts, leaving only 1 part unshaded.
In simple words: Divide into equal parts based on the bottom number, then shade as many as the top number says.

Exam Tip: Always divide the whole into equal parts first - the denominator tells you how many equal parts to make. The numerator tells you how many to shade.