Students often refer to Kerala State Syllabus SCERT Class 6 Maths Solutions and Class 6 Maths Chapter 4 Arithmetic of Parts Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 6 Maths Chapter 4 Solutions Arithmetic of Parts
Class 6 Kerala Syllabus Maths Solutions Chapter 4 Arithmetic of Parts Questions and Answers
Arithmetic of Parts Class 6 Questions and Answers Kerala Syllabus
Intext Questions (Page No. 50)
In each of the pictures below, write the parts of each colour and the total coloured parts as fractions. Write the sum of the fractions obtained from each picture in the lowest terms.
Question 1.
Answer:
The fraction of circle coloured in blue = \(\frac {3}{8}\)
The fraction of circle coloured in green = \(\frac {1}{8}\)
The circle is divided into 8 equal parts.
Sum of fractions is \(\frac{1}{8}+\frac{3}{8}=\frac{4}{8}=\frac{1}{2}\)
Question 2.
Answer:
The fraction of circle coloured in orange = \(\frac {3}{8}\)
The fraction of circle coloured in brown = \(\frac {3}{8}\)
The circle is divided into 8 equal parts.
Sum of fractions is \(\frac{3}{8}+\frac{3}{8}=\frac{6}{8}=\frac{3}{4}\)
Question 3.
Answer:
The fraction coloured in yellow = \(\frac {1}{10}\)
The fraction coloured in red = \(\frac {3}{10}\)
The ribbon is divided into 10 equal parts.
Sum of fractions is \(\frac{1}{10}+\frac{3}{10}=\frac{4}{10}=\frac{2}{5}\)
Question 4.
Answer:
The fraction coloured in yellow = \(\frac {5}{16}\)
The fraction coloured in green = \(\frac {7}{16}\)
The ribbon is divided into 10 equal parts.
Sum of fractions is \(\frac{5}{16}+\frac{7}{16}=\frac{12}{16}=\frac{3}{4}\)
Addition of Fractions (Page No. 56)
Question 1.
In each pair of pictures below, find the fraction of the circle we get by cutting up the coloured pieces of both circles and putting them together:
Answer:
Question 2.
Calculate the sums given below:
(i) \(\frac{1}{4}+\frac{1}{8}\)
(ii) \(\frac{3}{4}+\frac{1}{6}\)
(iii) \(\frac{1}{3}+\frac{2}{5}\)
(iv) \(\frac{1}{2}+\frac{2}{5}\)
(v) \(\frac{2}{3}+\frac{1}{5}\)
Answer:
Question 3.
There are two taps to fill a tank with water. If the first tap alone is opened, the tank would fill up in 10 minutes. If the second tap alone is opened, it would take 15 minutes to fill up the tank.
(i) If the first tap alone is opened, what fraction of the tank would be filled in one minute?
(ii) If the second tap alone is opened, what fraction of the tank would be filled in one minute?
(iii) If both the taps are opened, what fraction of the tank would be filled in one minute?
(iv) If both the taps are opened, how much time would it take for the tank to be filled up?
Answer:
(i) The first tap fills the whole tank in 10 minutes.
Therefore, in 1 minute it fills upto \(\frac {1}{10}\) of the tank.
(ii) The second tap fills the whole tank in 15 minutes.
Therefore, in 1 minute it fills upto \(\frac {1}{15}\) of the tank.
(iii) If both taps are opened,
First tap fills \(\frac {1}{10}\)
Second tap fills \(\frac {1}{15}\)
So together they fill = \(\frac{1}{10}+\frac{1}{15}=\frac{1 \times 3}{10 \times 3}+\frac{1 \times 2}{15 \times 2}\) = \(\frac{3}{30}+\frac{2}{30}=\frac{5}{30}=\frac{1}{6}\)
That means both taps together fill \(\frac {1}{6}\) of the tank in 1 minute.
(iv) The time taken to fill the tank when both taps are opened.
\(1 \div \frac{1}{6}=\frac{1}{\frac{1}{6}}=1 \times \frac{6}{1}\) = 6 minutes
Some Other Sums (Page No. 57)
Question 1.
For each fraction given below, can you mentally calculate the fraction to be added to make it 1?
(i) \(\frac {2}{7}\)
(ii) \(\frac {4}{7}\)
(iii) \(\frac {3}{8}\)
(iv) \(\frac {3}{10}\)
Answer:
(i) \(\frac {5}{7}\) is added with \(\frac {2}{7}\) to get 1.
That is, \(\frac{2}{7}+\frac{5}{7}=\frac{7}{7}\) = 1
(ii) \(\frac {3}{7}\) is added with \(\frac {4}{7}\) to get 1.
That is, \(\frac{3}{7}+\frac{4}{7}=\frac{7}{7}\) = 1
(iii) \(\frac {5}{8}\) is added with \(\frac {3}{8}\) to get 1.
That is, \(\frac{3}{8}+\frac{5}{8}=\frac{8}{8}\) = 1
(iv) \(\frac {7}{10}\) is added with \(\frac {3}{10}\) to get 1.
That is, \(\frac{7}{10}+\frac{3}{10}=\frac{10}{10}\) = 1
Textbook Page No. 60
Question 1.
Calculate the sums below:
(i) \(\frac{5}{6}+\frac{1}{3}\)
(ii) \(\frac{7}{8}+\frac{1}{4}\)
(iii) \(\frac{5}{6}+\frac{1}{4}\)
(iv) \(\frac{5}{8}+\frac{3}{4}\)
(v) \(2 \frac{1}{3}+3 \frac{1}{2}\)
Answer:
Question 2.
One jar contains one and a half litres of milk, and another contains two and three-quarters litres of milk. How much milk is in both jars together?
Answer:
Milk contained in first jar = 1\(\frac {1}{2}\) litres
Second jar contained in second jar = 2\(\frac {3}{4}\) litres
Milk contained in both jars is,
Question 3.
Two strings of lengths one and a half metres are joined end to end. What is the total length?
Answer:
Lengths of strings = 1\(\frac {1}{2}\)
Two strings are joined together,
\(1 \frac{1}{2}+1 \frac{1}{2}=(1+1)+\left(\frac{1}{2}+\frac{1}{2}\right)\)
= 2 + \(\frac {2}{2}\)
= 2 + 1
= 3 metres
Question 4.
Ahirath bought one and a half kilograms of beans and three-quarters kilograms of yams. What is the total weight?
Answer:
Quantity of beans Ahirath bought = 1\(\frac {1}{2}\) kg
Quantity of yam Ahirath bought = \(\frac {3}{4}\) kg
Removing Parts (Page No. 61)
Question 1.
(i) \(\frac{1}{2}-\frac{1}{8}\)
Answer:
(ii) \(\frac{3}{4}-\frac{1}{8}\)
Answer:
(iii) \(\frac{1}{3}-\frac{1}{5}\)
Answer:
(iv) \(\frac{2}{5}-\frac{1}{3}\)
Answer:
(v) \(\frac{2}{3}-\frac{1}{5}\)
Answer:
Textbook Page No. 64
Question 1.
Natasha drew a circle and coloured \(\frac {5}{12}\) of it. What fraction of the circle remains to be coloured?
Answer:
Coloured portion of the circle = \(\frac {5}{12}\)
Portion of the circle to be coloured is,
\(1-\frac{5}{12}=\frac{12}{12}-\frac{5}{12}\)
= \(\frac{12-5}{12}\)
= \(\frac {7}{12}\)
Question 2.
A bucket can hold 10 litres of water, and it contains 3\(\frac {3}{4}\) litres. How much more is needed to fill it?
Answer:
Total quantity of water that can be held in the bucket = 10 litres
Quantity of water contained in the bucket = 3\(\frac {3}{4}\) litres
The quantity of water needed to fill the bucket is,
10 – 3\(\frac {3}{4}\) = \(\left(9 \frac{1}{4}+\frac{3}{4}\right)-\left(3 \frac{3}{4}\right)\)
= \(\left(9+\frac{1}{4}+\frac{3}{4}\right)-\left(3+\frac{3}{4}\right)\)
= (9 – 3) + \(\left(\frac{1}{4}+\frac{3}{4}-\frac{3}{4}\right)\)
= 6 + \(\frac {1}{4}\)
= 6\(\frac {1}{4}\) litres
OR
If \(\frac {1}{4}\) added to 3\(\frac {3}{4}\), we get 4
And if 6 is added to 4 will results 10
That means, 6 + \(\frac {1}{4}\) = 6\(\frac {1}{4}\) litres
Question 3.
From a string, one and three-quarters of a metre long, a piece half a metre long is cut off. What is the length of the remaining piece?
Answer:
Length of the original string = 1\(\frac {3}{4}\) metre
Piece cut off = \(\frac {1}{2}\) metre
Length of the remaining piece is
Question 4.
A panchayat constructed a new road, 14\(\frac {3}{4}\) kilometres long last year. This year, a road 16\(\frac {1}{4}\) kilometres long was constructed. How much more was constructed this year?
Answer:
Road constructed last year = 14\(\frac {3}{4}\) km
Road constructed this year = 16\(\frac {1}{4}\) km
The more roads constructed this year are,
Question 5.
Ashadev bought 20 metres of string. He cut off a piece 5\(\frac {3}{4}\) metres long first, and then a piece 6\(\frac {1}{2}\) metres long later. What is the length of the string left?
Answer:
Total length of the string = 20 metres
First cut piece = 5\(\frac {3}{4}\) metre
Second cut piece = 6\(\frac {1}{2}\) metres
Total length of the string cut is,
Length of the remaining string is,
Question 6.
The milk society got 75\(\frac {1}{4}\) litres in the morning and 55\(\frac {1}{2}\) litres in the evening. Of this 85\(\frac {3}{4}\) litres of milk is sold. How much milk is left?
Answer:
Milk received in the morning = 75\(\frac {1}{4}\) litres
Milk received in the evening = 55\(\frac {1}{2}\) litres
Milk sold is = 85\(\frac {3}{4}\) litres
Remaining milk is,
Large and Small (Page No. 66)
Question 1.
Find the larger and smaller of each pair of fractions below and write this using the < or > symbol:
(i) \(\frac{2}{5}, \frac{3}{5}\)
(ii) \(\frac{2}{5}, \frac{2}{3}\)
(iii) \(\frac{2}{5}, \frac{3}{4}\)
(iv) \(\frac{3}{7}, \frac{2}{9}\)
(v) \(\frac{2}{7}, \frac{3}{8}\)
(vi) \(\frac{4}{9}, \frac{3}{8}\)
Answer:
(i) Here, the denominators are the same.
So compare the numerators.
That is 2 < 3,
Therefore \(\frac{2}{5}<\frac{3}{5}\)
(ii) Here, the numerators are the same.
So the smaller denominator is larger.
Therefore \(\frac{2}{3}>\frac{2}{5}\)
(iii) Convert the fractions into forms with the same denominators
\(\frac{2}{5}=\frac{2 \times 4}{5 \times 4}=\frac{8}{20}\) and \(\frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}\)
Therefore \(\frac{2}{5}<\frac{3}{4}\)
(iv) Convert the fractions into forms with the same denominators
\(\frac{3}{7}=\frac{3 \times 9}{7 \times 9}=\frac{27}{63}\) and \(\frac{2}{9}=\frac{2 \times 7}{9 \times 7}=\frac{14}{63}\)
Therefore \(\frac{3}{7}>\frac{2}{9}\)
(v) Convert the fractions into forms with the same denominators
\(\frac{2}{7}=\frac{2 \times 8}{7 \times 8}=\frac{16}{56}\) and \(\frac{3}{8}=\frac{3 \times 7}{8 \times 7}=\frac{21}{56}\)
Therefore \(\frac{2}{7}<\frac{3}{8}\)
(vi) Convert the fractions into forms with the same denominators
\(\frac{4}{9}=\frac{4 \times 8}{9 \times 8}=\frac{32}{72}\) and \(\frac{3}{8}=\frac{3 \times 9}{8 \times 9}=\frac{27}{72}\)
Therefore \(\frac{4}{9}>\frac{3}{8}\)
Question 2.
Arrange each triple of fractions below from the smallest to the largest and write it using the < symbol:
(i) \(\frac{2}{5}, \frac{3}{4}, \frac{3}{5}\)
(ii) \(\frac{3}{7}, \frac{2}{9}, \frac{2}{7}\)
(iii) \(\frac{1}{2}, \frac{1}{3}, \frac{2}{3}\)
Answer:
(i) Convert the fractions into forms with the same denominators
\(\frac{2}{5}=\frac{2 \times 4}{5 \times 4}=\frac{8}{20}, \quad \frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}, \quad \frac{3}{5}=\frac{3 \times 4}{5 \times 4}=\frac{12}{20}\)
\(\frac{8}{20}<\frac{12}{20}<\frac{15}{20}\)
Therefore \(\frac{2}{5}<\frac{3}{5}<\frac{3}{4}\)
(ii) Convert the fractions into forms with the same denominators
\(\frac{3}{7}=\frac{3 \times 9}{7 \times 9}=\frac{27}{63}, \quad \frac{2}{9}=\frac{2 \times 7}{9 \times 7}=\frac{14}{63}, \frac{2}{7}=\frac{2 \times 9}{7 \times 9}=\frac{18}{63}\)
\(\frac{14}{63}<\frac{18}{63}<\frac{27}{63}\)
Therefore \(\frac{2}{9}<\frac{2}{7}<\frac{3}{7}\)
(iii) Convert the fractions into forms with the same denominators
\(\frac{1}{2}=\frac{1 \times 3}{2 \times 3}=\frac{3}{6}, \quad \frac{1}{3}=\frac{1 \times 2}{3 \times 2}=\frac{2}{6} \quad, \frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6}\)
\(\frac{2}{6}<\frac{3}{6}<\frac{4}{6}\)
Therefore \(\frac{1}{3}<\frac{1}{2}<\frac{2}{3}\)
Class 6 Maths Chapter 4 Kerala Syllabus Arithmetic of Parts Questions and Answers
Class 6 Maths Arithmetic of Parts Questions and Answers
Question 1.
Compare \(\frac {5}{8}\) and \(\frac {3}{4}\)?
Answer:
Convert the fractions into forms with the same denominators
\(\frac{5}{8}<\frac{6}{8}\)
Therefore \(\frac{5}{8}<\frac{3}{4}\)
Question 2.
Arrange from smallest to largest: \(\frac{1}{6}, \frac{1}{2}, \frac{5}{12}\)
Answer:
Convert the fractions into forms with the same denominators
\(\frac{1}{6}=\frac{1 \times 2}{6 \times 2}=\frac{2}{12}, \quad \frac{1}{2}=\frac{1 \times 6}{2 \times 6}=\frac{6}{12} \quad, \frac{5}{12}\)
\(\frac{2}{12}<\frac{5}{12}<\frac{6}{12}\)
Therefore \(\frac{1}{6}<\frac{5}{12}<\frac{1}{2}\)
Question 3.
Calculate: \(\frac{3}{5}+\frac{1}{2}\)
Answer:
Question 4.
A bottle contains 2\(\frac {1}{4}\) litres of juice, and another bottle contains 1\(\frac {2}{3}\) litres. What is the total amount of juice?
Answer:
Juice in first bottle = 2\(\frac {1}{4}\) litres
Juice in second bottle = 1\(\frac {2}{3}\) litres
Total amount of the juice is;
Question 5.
A ribbon is 2\(\frac {1}{2}\) metres long. Another ribbon is 3\(\frac {1}{3}\) metres long. What is their total length?
Answer:
First ribbon = 2\(\frac {1}{2}\) metres
Second ribbon = 3\(\frac {1}{3}\) metres
Total length is:
Question 6.
Reshma had 12\(\frac {1}{2}\) metres of ribbon. She used 4\(\frac {3}{4}\) metres for a project. How much ribbon is left?
Answer:
Total ribbon = 12\(\frac {1}{2}\) metres
Ribbon used = 4\(\frac {3}{4}\) metres
The remaining ribbon is,
Question 7.
A container holds 18 litres of oil. 6\(\frac {2}{3}\) litres are used in the morning and 5\(\frac {1}{6}\) litres in the evening. How much oil is left?
Answer:
Total quantity of oil held in the container = 18 litres
Oil used is,
The quantity of oil remaining is,
Question 8.
A pipe is 9\(\frac {1}{2}\) metres long. A piece 3\(\frac {3}{4}\) metres is cut from it. How much pipe remains?
Answer:
Length of the original pipe = 9\(\frac {1}{2}\) metres
Length of the cut piece = 3\(\frac {3}{4}\) metres
Length of the remaining pipe is,
Question 9.
A recipe needs 1\(\frac {1}{4}\) cups of sugar. Aliya only has \(\frac {3}{4}\) cup. How much more does she need?
Answer:
Required sugar = 1\(\frac {1}{4}\) cups
Available sugar = \(\frac {3}{4}\) cups
Sugar needed is,
Question 10.
Meera walked 2\(\frac {2}{5}\) kilometre in the morning and 3\(\frac {3}{5}\) kilometre in the evening. How much did she walk in total?
Answer:
Meera walked in the morning = 2\(\frac {2}{5}\) km
Walked in the evening = 3\(\frac {3}{5}\) km
Total she walked:
Class 6 Maths Chapter 4 Notes Kerala Syllabus Arithmetic of Parts
→ To find the sum of two fractional measures put together, we must see them as a set of the same equal pieces.
→ Convert both fractional measures to forms with the same denominator.
→ Increasing the numerator alone makes a fraction larger.
→ Of two fractions with the same denominator, the one with the larger numerator is the larger and the one with the smaller numerator is the smaller.
→ If the denominator alone of a fraction is increased, the fraction becomes smaller.
→ Of two fractions with the same numerator, the one with the larger denominator is smaller and the one with the smaller denominator is larger.
→ To compare two fractions with the same denominator, we need only compare the numerator; to compare two fractions with the same numerator, we need only compare the denominators.
In our everyday life, we often come across situations where we need to work with parts of a whole, like dividing a chocolate bar between friends, measuring ingredients for a recipe, or cutting ribbon into equal pieces. This idea of working with parts is what we study in this chapter, Arithmetic of Parts. This chapter mainly deals with understanding fractions – numbers that represent parts of a whole, dividing object quantities into equal parts, performing operations such as addition, subtraction, multiplication, and division with fractions, comparing and converting fractions, especially simplifying them to their lowest terms. This chapter helps build a strong foundation in dealing with fractions and their applications in real-life situations.
Joining Parts
A circle is divided into 4 equal parts, and two of them are joined together to get half of the circle.
The quarter circle joined to a quarter circle makes half a circle.
That means, two quarters make a half.
We can write like this: \(\frac{1}{4}+\frac{1}{4}=\frac{1}{2}\)
Suppose a circle is divided into eight equal parts ,and two of them are joined together.
2 of 8 equal parts is \(\frac {2}{8}\); also, \(\frac{2}{8}=\frac{1 \times 2}{4 \times 2}=\frac{1}{4}\)
So we have \(\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}\)
Question 1.
Join \(\frac {1}{8}\) of a circle and \(\frac {3}{8}\) of the circle, what fraction of the circle would we get?
Answer:
We took 1 + 3 = 4 parts of 8 equal parts, that is \(\frac {4}{8}\)
Reducing the numerator and denominator,
\(\frac{1}{8}+\frac{3}{8}=\frac{4}{8}=\frac{1}{2}\)
Question 2.
Look at the picture given below;
What sum of fractions of the ribbon do we get from this?
Answer:
The ribbon is divided into 8 equal parts
The fraction of the ribbon coloured in red = \(\frac {1}{8}\)
The fraction of the ribbon coloured in green = \(\frac {5}{8}\)
Sum of the fraction is, \(\frac{1}{8}+\frac{5}{8}=\frac{6}{8}=\frac{3}{4}\)
Addition of Fractions
If a circle is cut into four equal pieces and two of them joined together, we get half a circle:
If one more piece is joined to this, we get three-quarters of a circle.
That is half and a quarter make three quarters, \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\)
Question 1.
What sum do we get from this picture below?
Answer:
Here, the circle is divided into 8 equal pieces
The pieces coloured in red = 1
The pieces coloured in yellow = 4
Fraction of the coloured portion = \(\frac{1}{8}+\frac{4}{8}=\frac{5}{8}\)
The lowest form of \(\frac{4}{8}=\frac{1}{2}\)
Therefore the sum is \(\frac{1}{8}+\frac{1}{2}=\frac{5}{8}\)
Question 2.
Look at the picture below.
\(\frac {1}{4}\) of a circle and \(\frac {3}{8}\) of another circle of the same size are cut out, and these pieces are put together. What fraction of the full circle is this?
Answer:
In the first figure, the circle is divided into 4 equal parts, and 1 is coloured.
Here one one-fourth of the circle can be considered as two one-eighths joined together.
That is \(\frac{1}{4}=\frac{2}{8}\)
In the second figure, the circle is divided into 8 equal parts, and 3 is coloured.
That is \(\frac {3}{8}\)
Therefore, the fraction of the full circle is \(\frac{1}{4}+\frac{3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{5}{8}\)
Question 3.
Two ribbons of length \(\frac {3}{10}\) metre and \(\frac {2}{5}\) metre are joined end to end. What is the total length?
Answer:
The first ribbon is 3 of 10 equal parts of a 1 metre long ribbon:
The second ribbon is 2 of 5 equal parts of a 1 metre long ribbon:
Considering \(\frac {2}{5}\) metre as 4 of 10 equal parts of a metre:
The sum of fraction is \(\frac{3}{10}+\frac{2}{5}=\frac{3}{10}+\frac{4}{10}=\frac{7}{10}\)
Therefore, the total length is \(\frac {7}{10}\) metre.
To find the sum of two fractional measures put together, we must see them as a set of the same equal pieces.
Convert both fractional measures to forms with the same denominator.
Question 4.
Two ribbons of length \(\frac {1}{2}\) metre and \(\frac {2}{5}\) metre are joined end to end. What is the total length?
Answer:
For the same denominators we want for both must be a multiple of 2 and 5.
That is \(\frac{1}{2}=\frac{1 \times 5}{2 \times 5}=\frac{5}{10}\) and \(\frac{2}{5}=\frac{2 \times 2}{5 \times 2}=\frac{4}{10}\)
Total length of the ribbon is \(\frac{1}{2}+\frac{2}{5}=\frac{5}{10}+\frac{4}{10}=\frac{9}{10}\)
Some Other Sums
Of the two fractions added, one is some parts of one divided into equal parts taken together, and the other is the remaining parts taken together. When both these are taken together, we get all the parts or the whole.
\(\frac{1}{2}+\frac{1}{2}\) = 1
\(\frac{1}{3}+\frac{2}{3}\) = 1
\(\frac{1}{4}+\frac{3}{4}\) = 1
\(\frac{1}{5}+\frac{4}{5}\) = 1
\(\frac{2}{5}+\frac{3}{5}\) = 1
Question 1.
What fraction to be added to get 1?
(i) \(\frac {3}{7}\)
(ii) \(\frac {5}{6}\)
(iii) \(\frac {5}{9}\)
Answer:
(i) \(\frac{3}{7}+\frac{4}{7}=\frac{7}{7}\) = 1
(ii) \(\frac{5}{6}+\frac{1}{6}=\frac{6}{6}\) = 1
(iii) \(\frac{5}{9}+\frac{4}{9}=\frac{9}{9}\) = 1
Question 2.
Draw two circles of the same size and colour half of one and two-thirds of the other. If we cut out these pieces, can we put them together?
What if we cut them like this?
Answer:
Figure 1
The first circle is divided into 2 equal parts, and 1 is considered. In the second circle, it is divided into 3 equal parts, and 2 is considered from it.
If we join these two circles together, we get,
Figure 2
If we join these two circles together, we get,
Removing Parts
Here we can do this subtraction just as we did the addition of fractions:
If a half metre piece is cut off from a three-quarter metre long ribbon, then the length of the remaining portion is;
Answer:
Length of the ribbon is 1 metre.
Here, a half metre piece is cut off from a three-quarter metre long ribbon,
If one-third of a metre is removed from half a metre;
Answer:
Therefore, the remaining portion is \(\frac {1}{6}\) metres.
We have seen some pairs of fractions that add up to 1.
We can rewrite them as subtractions:
Question 3.
From one liter of milk, a quarter liter was used up. How much milk is left?
Answer:
The remaining portion of milk is,
\(1-\frac{1}{4}=\frac{4}{4}-\frac{1}{4}\)
= \(\frac{4-1}{4}\)
= \(\frac {3}{4}\) litres
Question 4.
From two and a half kilograms of yams, one and a quarter kilograms are cut off. What is the weight of the remaining piece?
Answer:
Weight of yam = 2\(\frac {1}{2}\)
The weight cut off from the yam = 1\(\frac {1}{4}\)
Weight of the remaining piece
Large and Small
Case 1: To find the largest fraction with the same denominator,
Increasing the numerator alone makes a fraction larger.
For example:
\(\frac{1}{7}<\frac{2}{7}<\frac{3}{7}<\frac{4}{7}<\frac{5}{7}<\frac{6}{7}\)
Which is larger, \(\frac {2}{5}\) or \(\frac {3}{5}\)?
Answer:
\(\frac {2}{5}\) is 2 parts of 5 equal parts taken together, and \(\frac {3}{5}\) is 3 parts of 5 equal parts taken together.
Therefore \(\frac {2}{5}\) is less than the number \(\frac {3}{5}\).
We can write like this:
\(\frac {2}{5}\) < \(\frac {3}{5}\) Or \(\frac {3}{5}\) is greater than \(\frac {2}{5}\).
That is, \(\frac {3}{5}\) > \(\frac {2}{5}\)
In general, we can say “Of two fractions with the same denominator, the one with a larger numerator is the larger and the one with a smaller numerator is the smaller.”
Case 2
If the denominator of a fraction is increased, the fraction becomes smaller.
For example:
\(\frac{7}{2}>\frac{7}{3}>\frac{7}{4}>\frac{7}{5}>\frac{7}{6}\)
Which is larger \(\frac {3}{4}\) and \(\frac {3}{5}\)?
Answer:
4 equal parts are larger than each of 5 equal parts.
3 of the first kind of pieces taken together is larger than 3 of the second kind of pieces.
This means \(\frac {3}{4}\) > \(\frac {3}{5}\)
In general, of two fractions with the same numerator, the one with the larger denominator is smaller and the one with the smaller denominator is larger.
In conclusion,
To compare two fractions with the same denominator, we need only compare the numerators
To compare two fractions with the same numerator, we need only compare the denominators.
If both the numerator and denominator are different, convert the fractions into forms with the same denominators.
Which of \(\frac {1}{2}\) and \(\frac {3}{5}\) are larger?
Answer:
\(\frac{1 \times 5}{2 \times 5}=\frac{5}{10}\) and \(\frac{3 \times 2}{5 \times 2}=\frac{6}{10}\)
That is, \(\frac{5}{10}<\frac{6}{10}\)
Therefore \(\frac{1}{2}<\frac{3}{5}\)
Which is larger, \(\frac {3}{5}\) or \(\frac {7}{5}\)?
Answer:
\(\frac {3}{5}\) < \(\frac {7}{5}\)
Which is larger, \(\frac {4}{5}\) or \(\frac {4}{6}\)?
Answer:
\(\frac {4}{5}\) > \(\frac {4}{6}\)