Primary Mathematics Chapter 4 Operations On Fractions
Page 112 Exercise 4.1 Problem 1
We are asked to find the missing numbers
Given: \(\frac{1}{3}+\frac{1}{12}\)
As we can see that the denominators are not equal let us do LCM and then solve to get the result
\(\frac{1}{3}+\frac{1}{12}\) = \(\frac{4+1}{12}\)
= \(\frac{5}{12}\)
So therefore, the missing fraction is \(\frac{5}{12}\)
Therefore, we can say that the missing fraction is \(\frac{5}{12}\)
Page 112 Exercise 4.1 Problem 2
We are asked to find the missing numbers
Given: \(\frac{3}{8}+\frac{1}{2}\)
As we can see that the denominators are not equal let us do LCM and then solve to get the result.
\(\frac{3}{8}+\frac{1}{2}\) = \(\frac{3+4}{8}\)
= \(\frac{7}{8}\)
So therefore, the missing fraction is \(\frac{7}{8}\).
Therefore, we can say that the missing fraction is \(\frac{7}{8}\).
Page 112 Exercise 4.1 Problem 3
We are asked to find the missing numbers
Given: \(\frac{2}{5}+\frac{3}{10}\)
As we can see that the denominators are not equal let us do LCM and then solve to get the result.
\(\frac{2}{5}+\frac{3}{10}\) = \(\frac{4+3}{8}\)
= \(\frac{7}{10}\)
So therefore, the missing fraction is \(\frac{7}{10}\)
Therefore, we can say that the missing fraction is \(\frac{7}{10}\)
Page 113 Exercise 4.1 Problem 4
We are asked to write the answers in simplest form.
So, by solving we get
\(\frac{1}{2}+\frac{1}{4}\) = \(\frac{3}{4}\)
\(\frac{1}{6}+\frac{2}{3}\) = \(\frac{1+4}{3}\)=\(\frac{5}{3}\)
\(\frac{2}{9}+\frac{2}{3}\) = \(\frac{2+6}{9}\)=\(\frac{9}{3}\)= 3
\(\frac{1}{9}+\frac{2}{3}\) = \(\frac{1+6}{3}\)=\(\frac{7}{3}\)
\(\frac{1}{5}+\frac{1}{10}\) = \(\frac{2+1}{10}\)=\(\frac{3}{10}\)
\(\frac{3}{10}+\frac{1}{5}\) = \(\frac{3+2}{10}\)=\(\frac{5}{10}\)= \(\frac{1}{2}\)
\(\frac{1}{8}+\frac{3}{4}\) = \(\frac{1+6}{8}\)=\(\frac{7}{8}\)
\(\frac{3}{8}+\frac{1}{4}\) = \(\frac{3+2}{4}\)=\(\frac{5}{4}\)
\(\frac{1}{8}+\frac{1}{4}\) = \(\frac{1+2}{8}\)=\(\frac{3}{8}\)
\(\frac{1}{4}+\frac{1}{12}\) = \(\frac{3+1}{12}\)=\(\frac{4}{12}\)= \(\frac{1}{3}\)
Therefore, we can say that the simplified fractions are \(\frac{3}{4}\),\(\frac{5}{3}\),3, \(\frac{7}{3}\),\(\frac{3}{10}\),\(\frac{1}{2}\),\(\frac{7}{8}\),\(\frac{5}{4}\) ,\(\frac{3}{8}\),\(\frac{1}{3}\)
Page 115 Exercise 4.2 Problem 1
We are asked to find the missing numbers.
Given: \(\frac{3}{4}- \frac{1}{2}\)
As we can see that the denominators are not the same.
Let us multiply the second fraction by 2 for the numerator and denominator, we get
⇒ \(\frac{3}{4}− \frac{1}{4}\)
= \(\frac{3−2}{4}\)
= \(\frac{1}{4}\)
Therefore, by solving the given fractions we get \(\frac{1}{4}\)
Therefore, we can say that by solving the given fractions we get \(\frac{1}{4}\)
Page 115 Exercise 4.2 Problem 2
We are asked to find the missing numbers
Given: \(\frac{5}{6}- \frac{2}{3}\)
As we can see the denominators are not the same.
Let us multiply the second fraction by 2 for the numerator and denominator, we get
⇒ \(\frac{5}{6}- \frac{4}{6}\)
= \(\frac{5-4}{6}\)
= \(\frac{1}{6}\)
Therefore, by solving the given fractions we get \(\frac{1}{6}\)
Therefore, we can say that by solving the given fractions we get \(\frac{1}{6}\)
Page 115 Exercise 4.2 Problem 3
We are asked to find the missing numbers.
Given: \(\frac{2}{3}- \frac{1}{12}\)
As we can see the denominators are not the same
Let us multiply the first fraction by 4 for the numerator and denominator, we get
⇒ \(\frac{8}{12}- \frac{1}{12}\)
= \(\frac{8- 1}{12}\)
= \(\frac{7}{12}\)
Therefore, by solving the given fractions we get \(\frac{7}{12}\)
Therefore, we can say that by solving the given fractions we get \(\frac{7}{12}\)
Page 116 Exercise 4.2 Problem 4
Given: Some subtraction to compute.
To calculate the given subtractions and make an appropriate word with the answers connecting with the letters, where the word should represent a four-sided figure.
Recall that, subtraction is the process of removing a number from a larger number.
Compute each subtraction row-wise and match the letters with the numbers given in the box.
Follow the steps given below.
Perform the subtractions in the first row.
The LCM of the number 2,6 is 6.
Therefore
⇒ \(\frac{1}{2}- \frac{1}{6}\)
=\(\frac{(6÷2)×1−(6÷6)×1}{6}\)
=\(\frac{3−1}{6}\)
=\(\frac{2}{6}\)
=\(\frac{1}{3}\) [Reduce the fraction]
Similarly, the LCM of the number 4,8 is 8.
Therefore
⇒ \(\frac{3}{4}- \frac{5}{8}\)
=\(\frac{3×2−1×5}{8}\)
= \(\frac{6−5}{8}\)
=\(\frac{1}{8}\).
Also, the LCM of the numbers 3,9 is 9.
Therefore \(\frac{2}{3}- \frac{2}{9}\) = \(\frac{2×3−2×1}{9}\)
= \(\frac{6−2}{9}\)
= \(\frac{4}{9}\).
Perform the subtractions in the second row.
The LCM of the numbers 4,12 is 12.
Therefore \(\frac{3}{4}- \frac{1}{12}\) = \(\frac{3×3−1×1}{12}\)
=\(\frac{9−1}{12}\)
= \(\frac{8}{12}\).
= \(\frac{2}{3}\).
Similarly, the LCM of the numbers 5,10 is 10.
⇒ \(\frac{2}{5}- \frac{1}{10}\) = \(\frac{2×2−1×1}{10}\)
=\(\frac{4−1}{10}\)
= \(\frac{3}{10}\).
Also, the LCM of the numbers 6,12 is 12.
Then
⇒ \(\frac{5}{6}- \frac{5}{12}\) = \(\frac{5×2−5×1}{12}\)
= \(\frac{10−5}{12}\)
= \(\frac{5}{12}\).
Perform the subtractions in the Third row.
The LCM of the numbers 5,10 is 10.
Therefore
⇒ \(\frac{4}{5}- \frac{3}{10}\) = \(\frac{4×2−3×1}{10}\)= \(\frac{8−1}{10}\)
= \(\frac{5}{10}\)
= \(\frac{1}{2}\). [Reduction the fraction]
Similarly, the LCM of the numbers 2,12 is 12.
\(\frac{1}{2}- \frac{5}{12}\) = \(\frac{1×6−5×1}{12}\)
= \(\frac{6−5}{12}\)
= \(\frac{1}{12}\).
Also, the LCM of the number 12,3 is 12.
Then
⇒ \(\frac{7}{2}- \frac{1}{3}\) = \(\frac{7−4}{12}\)
= \(\frac{3}{12}\)
= \(\frac{1}{4}\).
Match the answers with the letters to form a word that represents a four-sided figure.
The answers to the subtractions are given by
Thus, the letters that match the answers are given by
The letters that match the answers and the word that represents a four-sided figure are given by
Page 117 Exercise 4.3 Problem 1
We are given that Meredith brought a piece of cloth.
She used \(\frac{3}{8}\) of it to make a dress.
We are asked to find the remaining clothes that she has.
Let us consider the remaining cloth as x.
So, from the question
1 = x + \(\frac{3}{8}\)
Transferring \(\frac{3}{8}\) from RHS to LHS.
x = 1 − \(\frac{3}{8}\)
x = \(\frac{5}{8}\)
Therefore, we can say that \(\frac{5}{8}\) the part of the cloth is left.
Therefore, we can say that Meredith has \(\frac{5}{8}\) the part of cloth left with her.
Page 117 Exercise 4.3 Problem 2
Given: John spent \(\frac{1}{2}\) of his money on a toy car. He spent 1
⇒ \(\frac{1}{6}\) of his money on a pen.
To find the fraction of the money he spends altogether.
Here, add the fraction of the money he spends on a toy car and pen.
⇒ \(\frac{1}{2}\)+\(\frac{1}{6}\)
Multiply and divide the first fraction by 3, to get a common denominator.
⇒ \(\frac{3}{6}\)+\(\frac{1}{6}\)
Simplifying
⇒ \(\frac{3+1}{6}\)
⇒ \(\frac{4}{6}\)
⇒ \(\frac{2}{3}\)
Therefore, the fraction of money John spends altogether on his car is \(\frac{2}{3}\)
Page 118 Exercise 4.3 Problem 3
Given: Mary drank \(\frac{7}{10}\) L of orange juice.
Jim drank \(\frac{1}{5}\) L of orange juice less than Mary.
To find – The fraction of orange juice they drank altogether.
Here, add the fraction of orange juice drank by Mary and Jim.
Jim drank \(\frac{1}{5}\) L of orange juice less than Mary.
Therefore, orange juice drank by Jim;
⇒ \(\frac{7}{10}\) −\(\frac{1}{5}\)
⇒ \(\frac{7−2}{10}\)
⇒ \(\frac{5}{10}\)
⇒ \(\frac{1}{2}\)
Add the fraction of orange juice drank by Mary and Jim
⇒ \(\frac{7}{10}\)+\(\frac{1}{2}\)
⇒ \(\frac{7+5}{10}\)
⇒ \(\frac{12}{10}\)= \(\frac{6}{5}\)
Therefore, the fraction of orange juice Mary and Jim drank altogether is \(\frac{6}{5}\) L.
Page 118 Exercise 4.3 Problem 4
Given: Lily bought 1 yd of ribbon. She used \(\frac{1}{2}\) yd to tie a package and \(\frac{3}{10}\) to make a bow.
To find – How much ribbon she had left.
Here, add the fraction of ribbon used.
Then subtract it from the total ribbon brought.
She used \(\frac{1}{2}\)yd to tie a package and \(\frac{3}{10}\) to make a bow.
Therefore, the total ribbon used
⇒ \(\frac{1}{2}\)+\(\frac{3}{10}\)
⇒ \(\frac{5+3}{10}\)
⇒ \(\frac{8}{10}\)
⇒ \(\frac{4}{5}\)
Subtract the fraction of ribbon used from the total ribbon brought
⇒ 1 − \(\frac{4}{5}\)
⇒ \(\frac{1}{5}\)
Therefore, the length of ribbon Lily left with is \(\frac{1}{5}\) yd.
Page 119 Exercise 4.4 Problem 1
Given: 1\(\frac{1}{12}\)+ 3\(\frac{1}{3}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ \(\frac{1}{12}\) + 3\(\frac{1}{3}\)
Add the whole numbers together, and then the fractions
⇒ 4\(\frac{1}{12}\)+ \(\frac{1}{3}\)
Multiple and divide the second fraction by 4
⇒ 4\(\frac{1}{12}\)+ \(\frac{1×4}{3×4}\)
⇒ 4\(\frac{1}{12}\)+\(\frac{4}{12}\)
⇒ 4\(\frac{5}{12}\)
The simplest form of the given expression 1\(\frac{1}{12}\)+ 3\(\frac{1}{3}\)= 4\(\frac{5}{12}\)
Page 119 Exercise 4.4 Problem 2
Given: 1\(\frac{3}{4}\)+ 1\(\frac{1}{8}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
1\(\frac{3}{4}\)+ 1\(\frac{1}{8}\)
Add the whole numbers together, and then the fractions
⇒ 2 \(\frac{3×2}{4×2}\)+ \(\frac{1}{8}\)
⇒ 2 \(\frac{6}{8}\)+ \(\frac{1}{8}\)
⇒ 2 \(\frac{7}{8}\)
The simplest 1\(\frac{3}{4}\) + 1\(\frac{1}{8}\) = 2 \(\frac{7}{8}\)
Page 119 Exercise 4.4 Problem 3
Given: 2\(\frac{3}{10}\)+ 2\(\frac{2}{5}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 2\(\frac{3}{10}\)+ 2\(\frac{2}{5}\)
Add the whole numbers together, and then the fractions
⇒ 4\(\frac{3}{10}\) + \(\frac{2}{5}\)
Multiple and divide the second fraction by 2
⇒ 4\(\frac{3}{10}\)+\(\frac{2×2}{5×2}\)
⇒ 4\(\frac{3}{10}\)+\(\frac{4}{10}\)
⇒ 4\(\frac{7}{10}\)
The simplest form of the given expression 2\(\frac{3}{10}\)+ 2\(\frac{2}{5}\) = 4\(\frac{7}{10}\)
Page 119 Exercise 4.4 Problem 4
Given: 1\(\frac{2}{3}\)+ 5\(\frac{2}{15}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 1\(\frac{2}{3}\)+ 5\(\frac{2}{15}\)
Add the whole numbers together, and then the fractions
⇒ \(\frac{2}{3}\)+ 6\(\frac{2}{15}\)
Multiple and divide the first fraction by 5
⇒ \(\frac{2×5}{3×5}\) + 6\(\frac{2}{15}\)
⇒\(\frac{10}{15}\) +6\(\frac{2}{15}\)
⇒ 6\(\frac{12}{15}\)
⇒ 6\(\frac{4}{5}\)
The simplest form of the given expression 1\(\frac{2}{3}\)+ 5\(\frac{2}{15}\) = 6\(\frac{4}{5}\)
Page 120 Exercise 4.4 Problem 5
Given: 2\(\frac{1}{6}\) + 1\(\frac{2}{3}\)
To find – The simplest form
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 2\(\frac{1}{6}\)+ 1\(\frac{2}{3}\)
Add the whole numbers together, and then the fractions
⇒ 3 \(\frac{1}{6}\)+ \(\frac{2}{3}\)
Multiple and divide the second fraction by 2
⇒ 3 \(\frac{1}{6}\)+ \(\frac{2(2)}{3(2)}\)
⇒ 3 \(\frac{1}{6}\) + \(\frac{4}{6}\)
⇒ 3 \(\frac{5}{6}\)
⇒ 3 \(\frac{5}{6}\)
The simplest form of the given expression 2\(\frac{1}{6}\)+ 1\(\frac{2}{3}\)= 3 \(\frac{5}{6}\)\
Page 120 Exercise 4.4 Problem 6
Given: 2\(\frac{3}{8}\)+ 2\(\frac{3}{4}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 2\(\frac{3}{8}\)+ 2\(\frac{3}{4}\)
Add the whole numbers together, and then the fractions
⇒ 4\(\frac{3}{8}\)+ \(\frac{3}{4}\)
Multiple and divide the second fraction by 2
⇒ 4\(\frac{3}{8}\)+\(\frac{3(2)}{4(2)}\)
⇒ 4\(\frac{3}{8}\)+ \(\frac{6}{8}\)
⇒ 4\(\frac{9}{8}\)
The simplest form of the given expression 2\(\frac{3}{8}\)+ 2\(\frac{3}{4}\)= 4\(\frac{9}{8}\)
Page 120 Exercise 4.4 Problem 7
Given:
3\(\frac{1}{3}\)+ 2\(\frac{7}{9}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 3\(\frac{1}{3}\)+ 2\(\frac{7}{9}\)
Add the whole numbers together, and then the fractions
⇒ 5\(\frac{1}{3}\)+\(\frac{7}{9}\)
Multiple and divide the first fraction by 3
⇒ 5 \(\frac{1(3)}{3(3)}\)+ \(\frac{7}{9}\)
⇒ 5 \(\frac{3}{9}\)+\(\frac{7}{9}\)
⇒ 5\(\frac{10}{9}\)
The simplest form of the given expression 3\(\frac{1}{3}\)+ 2\(\frac{7}{9}\)= 5\(\frac{10}{9}\)
Page 120 Exercise 4.4 Problem 8
Given:
2\(\frac{3}{12}\)+ 2 \(\frac{1}{6}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 2\(\frac{3}{12}\)+ 2 \(\frac{1}{6}\)
Add the whole numbers together, and then the fractions
⇒ 4\(\frac{3}{12}\)+ \(\frac{1}{6}\)
Multiple and divide the second fraction by 2
⇒ 4\(\frac{3}{12}\)+ \(\frac{1(2)}{6(2)}\)
⇒ 4\(\frac{3}{12}\)+ \(\frac{2}{12}\)
⇒ 4\(\frac{5}{12}\)
The simplest form of the given expression 2\(\frac{3}{12}\)+ 2 \(\frac{1}{6}\)= 4\(\frac{5}{12}\)
Page 121 Exercise 4.5 Problem 1
Given: 4\(\frac{7}{8}\)−1\(\frac{1}{2}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions
Adding the given mixed fraction:
⇒ 4\(\frac{7}{8}\)−1\(\frac{1}{2}\)
Add the whole numbers together, and then the fractions
⇒ 3\(\frac{7}{8}\)−\(\frac{1}{2}\)
Multiple and divide the second fraction by 4
⇒ 3\(\frac{7}{8}\)− \(\frac{1(4)}{2(4)}\)
⇒ 3\(\frac{7}{8}\)− \(\frac{4}{8}\)
⇒ 3\(\frac{3}{8}\)
The simplest form of the given equation 4\(\frac{7}{8}\)−1\(\frac{1}{2}\) = 3\(\frac{3}{8}\)
Page 121 Exercise 4.5 Problem 2
Given: 7\(\frac{4}{5}\)−3\(\frac{1}{10}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 7\(\frac{4}{5}\)−3\(\frac{1}{10}\)
Add the whole numbers together, and then the fractions
⇒ 4\(\frac{4}{5}\)−\(\frac{1}{10}\)
Multiple and divide the first fraction by 2
⇒ 4\(\frac{4(2)}{5(2)}\)−\(\frac{1}{10}\)
⇒ 4\(\frac{8}{10}\)−\(\frac{1}{10}\)
⇒ 4\(\frac{7}{10}\)
The simplest form of the given equation 7\(\frac{4}{5}\)−3\(\frac{1}{10}\) = 4\(\frac{8}{10}\)
Page 121 Exercise 4.5 Problem 3
Given: 2\(\frac{5}{12}\)−1\(\frac{1}{4}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 2\(\frac{5}{12}\)−1\(\frac{1}{4}\)
Add the whole numbers together, and then the fractions
⇒ 1\(\frac{5}{12}\)−\(\frac{1}{4}\)
Multiple and divide the second fraction by 3
⇒ 1\(\frac{5}{12}\)−\(\frac{1(3)}{4(3)}\)
⇒ 1\(\frac{5}{12}\)−\(\frac{3}{12}\)
⇒ 1\(\frac{2}{12}\)= 1\(\frac{1}{6}\)
The simplest form of the given equation 2\(\frac{5}{12}\)−1\(\frac{1}{4}\)= 1\(\frac{1}{6}\)
Page 121 Exercise 4.5 Problem 4
Given:
3\(\frac{2}{3}\)−2\(\frac{1}{9}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒3\(\frac{2}{3}\)−2\(\frac{1}{9}\)
Add the whole numbers together, and then the fractions
⇒ 1\(\frac{2}{3}\)−\(\frac{1}{9}\)
Multiple and divide the first fraction by 3
⇒ 1\(\frac{2(3)}{3(3)}\)−\(\frac{1}{9}\)
⇒ 1\(\frac{6}{9}\)−\(\frac{1}{9}\)
⇒ 1\(\frac{5}{9}\)
The simplest form of the given equation 3\(\frac{2}{3}\)−2\(\frac{1}{9}\)= 1\(\frac{5}{9}\)
Page 122 Exercise 4.5 Problem 5
Given:
4\(\frac{1}{3}\)−1\(\frac{2}{9}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 4\(\frac{1}{3}\)−1\(\frac{2}{9}\)
Add the whole numbers together, and then the fractions
⇒ 3\(\frac{1}{3}\)−\(\frac{2}{9}\)
Multiple and divide the first fraction by 3
⇒ 3\(\frac{1(3)}{3(3)}\)−\(\frac{2}{9}\)
⇒ 3\(\frac{3}{9}\)−\(\frac{2}{9}\)
⇒ 3\(\frac{3}{9}\)
The simplest form of the given equation 4\(\frac{1}{3}\)−1\(\frac{2}{9}\)= 3\(\frac{3}{9}\)
Page 121 Exercise 4.5 Problem 6
Given:
3\(\frac{3}{4}\)−\(\frac{1}{12}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 3\(\frac{3}{4}\)−\(\frac{1}{12}\)
Add the whole numbers together, and then the fractions
⇒ 3\(\frac{3}{4}\)−\(\frac{1}{12}\)
Multiple and divide the first fraction by 3
⇒ 3\(\frac{3(3)}{4(3)}\)−\(\frac{1}{12}\)
⇒ 3\(\frac{9}{12}\)−\(\frac{1}{12}\)
⇒ 3\(\frac{8}{12}\)= 3\(\frac{2}{3}\)
The simplest form of the given equation 3\(\frac{3}{4}\)−\(\frac{1}{12}\)= 3\(\frac{2}{3}\)
Page 121 Exercise 4.5 Problem 7
Given:
3\(\frac{5}{9}\)−1\(\frac{1}{3}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒3\(\frac{5}{9}\)−1\(\frac{1}{3}\)
Add the whole numbers together, and then the fractions
⇒ 2\(\frac{5}{9}\)−\(\frac{1}{3}\)
Multiple and divide the second fraction by 3
⇒ 2\(\frac{5}{9}\)−\(\frac{1(3)}{3(3)}\)
⇒ 2\(\frac{5}{9}\)−\(\frac{3}{9}\)
⇒ 2\(\frac{2}{9}\)
The simplest form of the given equation 3\(\frac{5}{9}\)−1\(\frac{1}{3}\)= 2\(\frac{2}{9}\)
Page 121 Exercise 4.5 Problem 8
Given:
4\(\frac{7}{8}\)−2\(\frac{5}{16}\)
To find – The simplest form.
To add mixed numbers, we first add the whole numbers together, and then the fractions.
Adding the given mixed fraction:
⇒ 4\(\frac{7}{8}\)−2\(\frac{5}{16}\)
Add the whole numbers together, and then the fractions
⇒ 2\(\frac{7}{8}\)−\(\frac{5}{16}\)
Multiple and divide the first fraction by 2
⇒ 2\(\frac{7(2)}{8(2)}\)−\(\frac{5}{16}\)
⇒ 2\(\frac{14}{16}\)−\(\frac{5}{16}\)
⇒ 2\(\frac{9}{16}\)
The simplest form of the given equation 4\(\frac{7}{8}\)−2\(\frac{5}{16}\)= 2\(\frac{9}{16}\)
Page 123 Exercise 4.6 Problem 1
Given: John used 3\(\frac{5}{6}\)m of wire to create flower pot hangers, leaving him with 1\(\frac{7}{12}\) m. J
To find – The length of wire he had at first.
Here, add the length of wire used to make the flower pot and the length of the wire
Adding the length of wire used to make the flower pot and the length of the wire left.
⇒ 3\(\frac{5}{6}\)+1\(\frac{7}{12}\) m. J
Add the whole numbers together, and then the fractions
⇒ 4\(\frac{5}{6}\)+\(\frac{7}{12}\)
Multiple and divide the first fraction by 2
⇒ 4\(\frac{5(2)}{6(2)}\)+\(\frac{7}{12}\)
⇒ 4\(\frac{10}{12}\)+\(\frac{7}{12}\)
⇒ 4\(\frac{3}{12}\)= 4\(\frac{1}{4}\)
The length of wire he had first is 4\(\frac{1}{4}\).
Page 123 Exercise 4.6 Problem 2
Given: The capacity of a container is 4\(\frac{4}{5}\) gal.
It contains 1\(\frac{3}{10}\) gal of water.
To find the water needed to fill the container
Here, subtract the amount of water in the container from the capacity of the container.
Subtract the amount of water in the container from the capacity of the container.
⇒ 4\(\frac{4}{5}\) − 1\(\frac{3}{10}\)
Add the whole numbers together, and then the fractions
⇒ 3\(\frac{4}{5}\) – \(\frac{3}{10}\)
Multiple and divide the first fraction by 2
⇒ 3\(\frac{4(2)}{5(2)}\) – \(\frac{3}{10}\)
⇒ 3\(\frac{8}{10}\) – \(\frac{3}{10}\)
⇒ 3\(\frac{5}{10}\) = 3\(\frac{1}{2}\)
Water required to fill the container is 3\(\frac{1}{2}\).
Page 124 Exercise 4.6 Problem 3
Given: Mrs. Lopez bought 3\(\frac{3}{4}\) kg of beans, 1\(\frac{1}{2}\) kg of lettuce, and 1\(\frac{3}{4}\)kg of carrots.
To find – The total kilograms of vegetables she brought all together.
Here, add all the amount of vegetables brought.
Add all the amount of vegetables brought.
⇒ 3\(\frac{3}{4}\) + 1\(\frac{1}{2}\) + 1\(\frac{3}{4}\)
Add the whole numbers together, and then the fractions;
⇒ 5\(\frac{3}{4}\) + \(\frac{1}{2}\) + \(\frac{3}{4}\)
Multiple and divide the second fraction by 2
⇒ 5\(\frac{3}{4}\) + \(\frac{1(2)}{2(2)}\) + \(\frac{3}{4}\)
⇒ 5\(\frac{3}{4}\) + \(\frac{2}{4}\) + \(\frac{3}{4}\)
⇒ 5\(\frac{8}{4}\) = 5(2) = 10
The total amount of vegetables she brought is 10kg
Page 124 Exercise 4.6 Problem 4
Given: Lauren purchased 7\(\frac{1}{2}\) lb of flour.
She baked several banana cakes using 2\(\frac{2}{5}\) Ib of flour.
She baked several chocolate cakes with another 3\(\frac{3}{10}\) lb of flour.
To find – The total amount of flour used.
Here, add the amount of flour used for banana cakes and chocolate cakes.
Add the amount of flour used for banana cakes and chocolate cakes.
⇒ 2\(\frac{2}{5}\) + 3\(\frac{3}{10}\)
Add the whole numbers together, and then the fractions
⇒ 5\(\frac{2}{5}\) + \(\frac{3}{10}\)
Multiple and divide the first fraction by 2
⇒ 5\(\frac{2(2)}{5(2)}\) + \(\frac{3}{10}\)
⇒ 5\(\frac{4}{10}\) + \(\frac{3}{10}\)
⇒ 5\(\frac{7}{10}\)
The total amount of flour used is 5\(\frac{7}{10}\)
Page 124 Exercise 4.6 Problem 5
Given: Lauren purchased \(\frac{1}{2}\) lb of flour.
She baked several banana cakes using 2\(\frac{2}{5}\) Ib of flour.
She baked several chocolate cakes with another 3\(\frac{3}{10}\) lb of flour.
To find – The total amount of flour used.
Here, subtract the amount of flour used for banana cakes and chocolate cakes from the total amount of flour brought
Subtract the amount of flour used for banana cakes and chocolate cakes from the total amount of flour brought.
⇒ 7\(\frac{1}{2}\) – 5\(\frac{7}{10}\)
Add the whole numbers together, and then the fractions
⇒ 2\(\frac{1}{2}\) – \(\frac{7}{10}\)
Multiple and divide the first fraction by 5
⇒ 2 \(\frac{1(5)}{2(5)}\). 10
⇒ 2\(\frac{5}{10}\). 10
⇒ 2\(\frac{-2}{10}\) = − 2\(\frac{1}{5}\)
⇒ 1\(\frac{4}{5}\)
The total amount of flour left is 1\(\frac{4}{5}\)
Page 126 Exercise 4.7 Problem 1
Given: \(\frac{1}{3}\) × 9
The answer should be in the simplest form
Therefore
⇒ \(\frac{1}{3}\)× 9 = \(\frac{9}{3}\)
= 3
Simplest form of \(\frac{1}{3}\) × 9 = 3
Page 126 Exercise 4.7 Problem 2
Given: \(\frac{1}{2}\)× 12 =
The answer should be in the simplest form
Therefore
⇒ \(\frac{1}{2}\)× 12 = \(\frac{12}{2}\)
= 6
Simplest form of \(\frac{1}{2}\)×12 = 6
Page 126 Exercise 4.7 Problem 3
Given: \(\frac{1}{4}\)× 14 =
The answer should be in the simplest form
Therefore
⇒ \(\frac{1}{4}\)× 14 = \(\frac{14}{4}\)
= \(\frac{7}{2}\)
= 3\(\frac{1}{2}\)
Simplest form of \(\frac{1}{4}\) × 14= 3\(\frac{1}{2}\)
Page 126 Exercise 4.7 Problem 4
Given: \(\frac{1}{6}\) × 5 =
Multiply write in simplest forms.
The expression is \(\frac{1}{6}\)×5= \(\frac{5}{6}\)
The simplest form is \(\frac{5}{6}\)
Page 127 Exercise 4.8 Problem 1
Given: 4 by \(\frac{1}{3}\)
Multiply
The expression is
4× \(\frac{1}{3}\)
The solution of expression is \(\frac{4}{3}\)
Page 127 Exercise 4.8 Problem 2
Given : 5 by \(\frac{3}{4}\)
Multiply
The expression is
5× \(\frac{3}{4}\)= \(\frac{15}{4}\)
The solution of expression is \(\frac{15}{4}\)
Page 128 Exercise 4.8 Problem 3
Given: 8 × \(\frac{1}{3}\) =
Multiply and write in the simplest form
The expression is 8×\(\frac{8}{3}\)
The simplest form is \(\frac{8}{3}\)
Page 128 Exercise 4.8 Problem 4
Given: 12×\(\frac{1}{2}\)=
Multiply and write in simplest form.
The expression
12×\(\frac{1}{2}\)=\(\frac{6}{1}\)
The simplest form = \(\frac{6}{1}\)
Page 128 Exercise 4.8 Problem 5
Given: 14×\(\frac{1}{4}\)=
Multiply and write in simplest form.
The expression is
14× \(\frac{1}{4}\)=\(\frac{7}{2}\)
The simplest form is \(\frac{7}{2}\)
Page 128 Exercise 4.8 Problem 6
Given: 5× \(\frac{1}{6}\)
Multiply and write in simplest form.
The Expression is
5× \(\frac{1}{6}\)
= \(\frac{5}{6}\)
The simplest form is \(\frac{5}{6}\)
Page 129 Exercise 4.9 Problem 1
We are given a set of fruits.
We are asked to divide the whole set into two equal parts.
From the given set, by counting the number of fruits we get the total count as 16.
Now, we have to divide the whole set into two parts with an equal number of fruits.
So, the number of fruits in each set is given as
Now, dividing the given set into two sets with 8 fruits in each we get
Therefore, the given set is divided into two equal parts which are given as
There are 8 fruits in each set.
Page 129 Exercise 4.9 Problem 2
We are given a set of ice – creams.
We are asked to divide the whole set into three equal parts.
From the given set, by counting the number of ice creams we get the total count as 18.
Now, we have to divide the whole set into three parts with an equal number of ice creams.
So, the number of ice creams in each set is given as
\(\frac{18}{3}\) = 6
Now, dividing the given set into three sets with 6 ice creams in each we get
Therefore, the given set is divided into three equal parts which is given as
There are 6 ice creams in each set.
Page 129 Exercise 4.9 Problem 3
Given: A picture with flowers shown.
We are asked to represent what fraction of flowers are shaded in their simplest form.
In the figure, it is clear that the total number of flowers is 7 and the shaded flowers are.
So, the fraction of each set is shaded =\(\frac{2}{7}\)
As we cannot divide either numerator or denominator with a common number we can say that it is in its simplest form.
Therefore, the fraction of flowers that are shaded, expressed in simplest form is \(\frac{2}{7}\).
Page 129 Exercise 4.9 Problem 4
Given: Apple pictures are shown.
What fraction of each set is shaded
Write the simplest form.The total apples = 12 and
Shaded apples = 8
Then fraction of set is shaded =\(\frac{8}{12}\)
= \(\frac{1}{2}\)
The fraction of shaded = \(\frac{1}{2}\)
Page 129 Exercise 4.9 Problem 5
Given: Octopus pictures are shown.
What fraction of each set is shaded.
Each answer is in simplest form.The total octopus =12
The total octopus =12
Shaded Octopus = 9
And fraction of set is shaded = \(\frac{9}{12}\)
= \({3}{4}\)
The fraction of set shaded = \(\frac{3}{4}\)
Page 129 Exercise 4.9 Problem 6
Given: Some key pictures are shown.
Write fraction of each set is shaded and written in simplest form.
The total keys =21
And
Shaded keys = 9 and
Fraction of each set is shaded= \(\frac{9}{21}\)
= \(\frac{3}{7}\)
The fraction of each set is shaded = \(\frac{3}{7}\)
Page 130 Exercise 4.9 Problem 7
Given: A circle shape is shown.
Write the fraction of each set that is shaded and write the simplest form.
The total circle shape =8 and shaded shape of circle = 4
Then, the fraction of set is shaded = \(\frac{4}{8}\)
= \(\frac{1}{2}\)
The fraction of set is shaded = \(\frac{1}{2}\)
Page 129 Exercise 4.9 Problem 8
Given: A circle shape is shown.
Write the fraction of each set that is shaded and write the simplest form.
The total circle shape = 12 and
The shaded shape of the circle =10 then
The fraction of the set is shaded = \(\frac{5}{6}\)
The fraction of the set is shaded=\(\frac{5}{6}\)
Page 129 Exercise 4.9 Problem 9
Given: A triangle shape is shown.
Write the fraction of each set that is shaded and write the simplest form.
The total triangle shape=16 and
The shaded shape of the triangle = 4, then
The fraction of the set is shaded = \(\frac{1}{4}\)
Page 129 Exercise 4.9 Problem 10
Given: A triangle shape is shown.
Write the fraction of each set that is shaded and write the simplest form.
The total triangle shape =16 and
The shaded shape of the triangle = 6
The fraction of the set is shaded = \(\frac{6}{16}\)
The fraction of the set is shaded = \(\frac{3}{8}\)
The fraction of the set is shaded =\(\frac{3}{8}\)
Page 131 Exercise 4.9 Problem 11
Given: Some Apple’s pictures are shown.
Write the fraction of each set that is shaded and write the simplest form.
The total Apple’s are =15 , then
The fraction of green Apple’s=\(\frac{6}{15}\)
The fraction of green Apple’s=\(\frac{2}{5}\)
The fraction of green apples is \(\frac{2}{5}\)
Page 131 Exercise 4.9 Problem 12
Given: Some triangle, circle & square pictures are shown.
Write the fraction of each set is shaded & write the simplest form.
The total shapes are = 24 , then
The fraction of shapes in a circle = \(\frac{12}{24}\)
The fraction of shapes in a circle = \(\frac{1}{2}\), then
The fraction of shapes in a triangle = \(\frac{4}{24}\) or \(\frac{1}{6}\)
The fraction of shapes in squares = \(\frac{8}{24}\) or \(\frac{1}{3}\)
The fraction of the circle is \(\frac{1}{2}\) & triangles is \(\frac{1}{6}\) & square is \(\frac{1}{3}\)
Page 131 Exercise 4.9 Problem 13
Given: Some bead pictures are shown.
Write fractions and write each answer in the simplest form.
The total beads are20 and the fraction of black beads = \(\frac{10}{20}\) or \(\frac{1}{2}\)
The fraction of black beads is \(\frac{1}{2}\).