Figure it Out
Q1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____ kg.
Answer:
Each guava weighs 1/3 kg.
Q2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg.
Answer:
Each packet weighs 1/4 kg.
Q3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ____ glass of sugarcane juice.
Answer:
Each friend drank 3/4 glass.
Q4. The big fish weighs 1/2 kg. The small one weighs 1/4 kg. Together they weigh ____ kg.
Answer:
Together they weigh 1/2 + 1/4 = 3/4 kg.
Q5. Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half. Write your answer here.
Answer:
Quarter (1/4), half (1/2), three quarters (3/4), one and a quarter (1 1/4), one and a half (1 1/2), two and a half (2 1/2).
Qa. The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? a.
Answer:
1/3 of a whole chikki.
Qb. b.
Answer:
1/4 of a whole chikki.
Qc. c.
Answer:
1/6 of a whole chikki.
Qd. d.
Answer:
1/8 of a whole chikki.
Qe. e.
Answer:
1/2 of a whole chikki.
Qf. f.
Answer:
1/5 of a whole chikki.
Qg. g.
Answer:
1/12 of a whole chikki.
Qh. h.
Answer:
1/10 of a whole chikki.
Q1. Continue this table of 1/2 for 2 more steps.
Answer:
6 times 1/2 = 6/2 = 3; 7 times 1/2 = 7/2
Q2. Can you create a similar table for 1/4?
Answer:
For 1/4: 1 time 1/4 = 1/4, 2 times 1/4 = 2/4, 3 times 1/4 = 3/4, 4 times 1/4 = 4/4 = 1, 5 times 1/4 = 5/4, etc.
Q3. Make 1/3 using a paper strip. Can you use this to also make 1/6?
Answer:
Fold a paper strip into 3 equal parts to show 1/3. To make 1/6, fold each of the 3 parts in half to get 6 equal parts. Each small part is 1/6.
Q4a. Draw a picture and write an addition statement as above to show: a. 5 times 1/4 of a roti
Answer:
Draw 5 separate 1/4 roti pieces arranged. Addition statement: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4
Q4b. b. 9 times 1/4 of a roti
Answer:
Draw 9 separate 1/4 roti pieces. Addition statement: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 9/4
Q5. Match each fractional unit with the correct picture: 1/3, 1/5, 1/8, 1/6
Answer:
Match 1/3 with a shape divided into 3 equal parts, 1/5 with 5 equal parts, 1/8 with 8 equal parts, 1/6 with 6 equal parts.
Q1. On a number line, draw lines of lengths 1/10, 3/10, and 4/5.
Answer:
Draw a number line from 0 to 1. Divide the segment 0-1 into 10 equal parts. Mark 1/10 at the first division, 3/10 at the third division, and 4/5 = 8/10 at the eighth division.
Q2. Write five more fractions of your choice and mark them on the number line.
Answer:
Answers vary. Example: 1/2, 2/3, 3/4, 1/5, 7/10. Mark them on the number line by dividing into appropriate equal parts.
Q3. How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
Answer:
Infinite fractions lie between 0 and 1. For example, we can always find a fraction between any two fractions by taking their average.
Q4. What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is 1/2. So the blue line is 1/2 units long. Write the fraction that gives the length of the black line in the box.
Answer:
The black line extends from 0 to the second mark after 1/2, so its length is 1 unit. The fraction is 2/2 = 1.
Q5. Write the fraction that gives the lengths of the black lines in the respective boxes. (0, 1/2, 1, 1/5, 2/5, 3/5, 4/5)
Answer:
Black line from 0 to 1: 1 = 5/5. Black line from 0 to 1/5: 1/5. Black line from 0 to 2/5: 2/5. Black line from 0 to 3/5: 3/5. Black line from 0 to 4/5: 4/5.
Q1. How many whole units are there in 7/2?
Answer:
7/2 = 1/2 × 7 = 3.5 = 3 whole units and 1/2. So, 3 whole units.
Q2. How many whole units are there in 4/3 and in 7/3?
Answer:
4/3 = 1 + 1/3, so 1 whole unit. 7/3 = 2 + 1/3, so 2 whole units.
Q1a. Figure out the number of whole units in each of the following fractions: a. 8/3
Answer:
8/3 = 2 + 2/3, so 2 whole units.
Q1b. b. 11/5
Answer:
11/5 = 2 + 1/5, so 2 whole units.
Q1c. c. 9/4
Answer:
9/4 = 2 + 1/4, so 2 whole units.
Q2. Can all fractions greater than 1 be written as such mixed numbers?
Answer:
Yes, all fractions greater than 1 can be written as mixed numbers because we can find the whole number part by dividing numerator by denominator.
Q3a. Write the following fractions as mixed fractions (e.g., 9/2 = 4 1/2): a. 9/2
Answer:
9/2 = 4 1/2
Q3b. b. 9/5
Answer:
9/5 = 1 4/5
Q3c. c. 21/19
Answer:
21/19 = 1 2/19
Q3d. d. 47/9
Answer:
47/9 = 5 2/9
Q3e. e. 12/11
Answer:
12/11 = 1 1/11
Q3f. f. 19/6
Answer:
19/6 = 3 1/6
Qa. Write the following mixed numbers as fractions: a. 3 1/4
Answer:
3 1/4 = 13/4
Qb. b. 7 2/3
Answer:
7 2/3 = 23/3
Qc. c. 9 4/9
Answer:
9 4/9 = 85/9
Qd. d. 3 1/6
Answer:
3 1/6 = 19/6
Qe. e. 2 3/11
Answer:
2 3/11 = 25/11
Qf. f. 3 9/10
Answer:
3 9/10 = 39/10
Q1. Are the lengths 1/2 and 3/6 equal?
Answer:
Yes, because 3/6 = 1/2.
Q2. Are 2/3 and 4/6 equivalent fractions? Why?
Answer:
Yes, because 4/6 = 2/3 (both represent the same part of the whole).
Q3. How many pieces of length 1/6 will make a length of 1/2?
Answer:
3 pieces, because 3 × 1/6 = 3/6 = 1/2.
Q4. How many pieces of length 1/6 will make a length of 1/3?
Answer:
2 pieces, because 2 × 1/6 = 2/6 = 1/3.
Q1. Are 3/6, 4/8, 5/10 equivalent fractions? Why?
Answer:
Yes, because 3/6 = 1/2, 4/8 = 1/2, 5/10 = 1/2. All equal 1/2.
Q2. Write two equivalent fractions for 2/6.
Answer:
1/3 and 4/12 (or other valid equivalent fractions).
Q3. 4/6 = = = = ............ (Write as many as you can)
Answer:
4/6 = 2/3 = 8/12 = 12/18 = 16/24 = 20/30 = ... (infinite equivalent fractions)
Q1. Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts. Fraction of roti each child gets is ______. Division fact: Addition fact: Multiplication fact:
Answer:
Each child gets 3/4 roti. Draw 3 rotis divided into 4 equal parts each. Division fact: 3 ÷ 4 = 3/4. Addition fact: 3/4 + 3/4 + 3/4 + 3/4 = 3. Multiplication fact: 4 × 3/4 = 3.
Q2. Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.
Answer:
Each child gets 2/4 = 1/2 roti. Draw 2 rotis each divided into 2 equal halves, giving 4 halves total. Division fact: 2 ÷ 4 = 1/2. Addition fact: 1/2 + 1/2 + 1/2 + 1/2 = 2. Multiplication fact: 4 × 1/2 = 2.
Q3. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get? What if we put two such groups together? one group where 2 cakes are divided equally between 5 children, and another group again with 4 cakes and 10 children. Now, if there are 10 children in my group, how many cakes will I need so that they get same amount of cake as Anil?
Answer:
Anil gets 2/5 cake. For 10 children to get same share (2/5 each), total cakes needed = 10 × 2/5 = 20/5 = 4 cakes.
Q1. Add the following fractions using Brahmagupta’s method: a. 2/7 + 5/7 + 6/7 b. 3/4 + 1/3 c. 2/3 + 5/6 d. 2/3 + 2/7 e. 3/4 + 1/3 + 1/5 f. 2/3 + 4/5 g. 4/5 + 2/3 h. 3/5 + 5/8 i. 9/2 + 5/4 j. 8/3 + 2/7 k. 3/4 + 1/3 + 1/5 l. 2/3 + 4/5 + 3/7 m. 9/2 + 5/4 + 7/6
Answer:
a. All have denominator 7. Add numerators: 2+5+6=13. Answer: 13/7.
b. LCM of 4 and 3 is 12. 3/4 = 9/12, 1/3 = 4/12. Sum = 13/12.
c. LCM of 3 and 6 is 6. 2/3 = 4/6, 5/6 stays. Sum = 9/6 = 3/2.
d. LCM of 3 and 7 is 21. 2/3 = 14/21, 2/7 = 6/21. Sum = 20/21.
e. LCM of 4,3,5 is 60. 3/4=45/60, 1/3=20/60, 1/5=12/60. Sum = 77/60.
f. LCM of 3 and 5 is 15. 2/3=10/15, 4/5=12/15. Sum = 22/15.
g. LCM of 5 and 3 is 15. 4/5=12/15, 2/3=10/15. Sum = 22/15.
h. LCM of 5 and 8 is 40. 3/5=24/40, 5/8=25/40. Sum = 49/40.
i. LCM of 2 and 4 is 4. 9/2=18/4, 5/4 stays. Sum = 23/4.
j. LCM of 3 and 7 is 21. 8/3=56/21, 2/7=6/21. Sum = 62/21.
k. Same as e. Answer: 77/60.
l. LCM of 3,5,7 is 105. 2/3=70/105, 4/5=84/105, 3/7=45/105. Sum = 199/105.
m. LCM of 2,4,6 is 12. 9/2=54/12, 5/4=15/12, 7/6=14/12. Sum = 83/12.
Q2. Rahim mixes 2/3 litres of yellow paint with 3/4 litres of blue paint to make green paint. What is the volume of green paint he has made?
Answer:
Add the volumes: 2/3 + 3/4. LCM of 3 and 4 is 12. 2/3 = 8/12, 3/4 = 9/12. Sum = 17/12 litres = 1 5/12 litres.
Q3. Geeta bought 2/5 meter of lace and Shamim bought 3/4 meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?
Answer:
Total lace = 2/5 + 3/4. LCM of 5 and 4 is 20. 2/5 = 8/20, 3/4 = 15/20. Sum = 23/20 meters = 1 3/20 meters. Since 1 3/20 > 1, the lace is sufficient to cover the whole border.
Q1. Carry out the following subtractions using Brahmagupta’s method: a. 5/8 – 3/8 b. 7/9 – 5/9 c. 10/27 – 1/27
Answer:
a. Same denominator 8. Subtract numerators: 5-3=2. Answer: 2/8 = 1/4.
b. Same denominator 9. Subtract numerators: 7-5=2. Answer: 2/9.
c. Same denominator 27. Subtract numerators: 10-1=9. Answer: 9/27 = 1/3.
Q1. Carry out the following subtractions using Brahmagupta’s method: a. 8/15 – 3/15 b. 2/5 – 4/15 c. 5/6 – 4/9 d. 2/3 – 1/2
Answer:
a. Same denominator 15. Subtract numerators: 8-3=5. Answer: 5/15 = 1/3.
b. LCM of 5 and 15 is 15. 2/5 = 6/15. Subtract: 6/15 - 4/15 = 2/15.
c. LCM of 6 and 9 is 18. 5/6 = 15/18, 4/9 = 8/18. Subtract: 15/18 - 8/18 = 7/18.
d. LCM of 3 and 2 is 6. 2/3 = 4/6, 1/2 = 3/6. Subtract: 4/6 - 3/6 = 1/6.
Q2. Subtract as indicated: a. 13/4 from 10/3 b. 18/5 from 23/3 c. 29/7 from 45/7
Answer:
a. 10/3 - 13/4. LCM of 3 and 4 is 12. 10/3 = 40/12, 13/4 = 39/12. Subtract: 40/12 - 39/12 = 1/12.
b. 23/3 - 18/5. LCM of 3 and 5 is 15. 23/3 = 115/15, 18/5 = 54/15. Subtract: 115/15 - 54/15 = 61/15.
c. Same denominator 7. Subtract numerators: 45-29=16. Answer: 16/7.
Q3. Solve the following problems: a. Jaya's school is 7/10 km from her home. She takes an auto for 1/2 km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school? b. Jeevika takes 10/3 minutes to take a complete round of the park and her friend Namit takes 13/4 minutes to do the same. Who takes less time and by how much?
Answer:
a. Total distance = 7/10 km. Auto distance = 1/2 km = 5/10 km. Walking distance = 7/10 - 5/10 = 2/10 = 1/5 km.
b. Compare 10/3 and 13/4. LCM of 3 and 4 is 12. 10/3 = 40/12, 13/4 = 39/12. Since 39/12 < 40/12, Namit takes less time. Difference = 40/12 - 39/12 = 1/12 minute.