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Fraction on the number line is a concept of plotting numbers as well as different types of fractions on the number line. Subsequently, the fractions have to be solved first, and after that, the fraction value has to be fitted in the range for mentioning it in the number line.
- Fractions on the number line represent part of a whole number.
- These number lines help in denoting a decimal number with higher precision.
- A fraction is divided into two parts, namely numerator and denominator.
- Fraction on the number line is represented by making equal parts from zero to one.
- For example, to represent 1/7 on a number line.
- Divide 0 to 1 into 7 equal parts and label them as 1/7.
Read More: Properties of Real Numbers
Key Terms: Fractions, Number Line, Whole Number, Multiply, Denominator, Numerator, Subtract, Absolute Values, Formula, Negative, Positive
Representation of Fractions on the Number Line
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To represent fractions on the number line, follow the below steps:
- First, draw a number line of equal length.
- In case the given fraction is a proper fraction.
- In such cases, mark points 0 and 1 on the number line.
- In case the given fraction is an improper fraction, then first convert it into a mixed fraction.
- Now, make an equal number of points on the number line marked in the third point.
- Start from the left side and count the number of parts shown by the numerator.
- Mark the required point on the line.
Absolute Value Number Line
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The absolute value of the number line is those numbers that lie on the right side of the number line, and that of the numbers on the left side of the number line is known as the absolute value of the number line.
- Moreover, the illustration for that is that we have given the numbers -1, -2, -3, -4, 1, 2, 3, 4, and 0 to be installed on the number line.
- The illustration for the absolute values on the number lines is mentioned in the image below.
Read More: Revision of Arithmetic Properties
Types of Fractions
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The different types of fractions are as follows:
Proper Fractions
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The proper fractions are those in which the numerator is less than that of its denominator in the fraction. Hence, it can be said that the resultant of the fraction is always less than one.
- The method of representing proper fractions on the number line is always the same as that of representing the other fractions.
- In the illustration, we have some fractions to be represented in the number line, and they’re 3/5, 8/9; we have to solve them first.
- Similarly, 8/9 = 0.88 and 3/5 = 0.6.
- Hence, the fractions are between the range of 0 and 1, and the fractions are proper fractions.
Proper FractionsRead More: Root 2 is irrational
Mixed Fractions
Mixed fractions are the fractions that have the form of 3 7/8 . Similarly, the method of representing the fraction on the number line is the same as that of the other fractions.
Solved Example for Mixed Fraction
Given below are some example of calculating the fraction by the mixed fraction method. However, there exists a particular formula for solving the mixed fraction.
Suppose 5 2/3 = ?
Multiply the number by the denominator.
The whole number is 5.
The denominator is 3.
5 x 3 = 15.
Add the result to the numerator:
The numerator is 2.
15 + 2 = 17
The numerator is 17.
The denominator remains 3.
5 2/3 = 1 7/3
Mixed FractionsIn the formula, the denominator of the mixed fraction gets multiplied by the number with the fraction and gets added with the numerator of the number, and hence we get the number.
Read More: Complex Numbers and Quadratic Equations
Equivalent Fractions
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The fractions that have different numerators and denominators but are equal to the values that are known are called equivalent fractions. For instance, 2/4 and 3/6 are equivalent fractions as both fractions are equal to ½.
- The number line is divided into two parts where one side is negative, and the other side is positive.
- The number 0 is placed at the centre, which divides the number line into two parts.
- Hence, it can be said that the zero is neither negative nor positive.
- Equivalent fractions can be mentioned on the number line with the same method like for the other types of fractions.
Like Fractions
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The fractions that have the same denominators are called Like fractions. In other words, the group of two or more fractions that have the same numbers in the denominators is known as fractions. For instance, 1/7, 2/7, 5/7, and so on. The denominators of these fractions are equal to 7.
Unlike Fractions
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The fractions that have different denominators are generally known as unlike fractions. For instance, fractions like 2/3, 4/9, 6/67, 9/89 are unlike fractions.
- Moreover, the addition and subtraction of these fractions is not easy as they have different denominators.
- To add or subtract the unlike fractions, it is important to first convert these fractions into like fractions.
Read More: Minors and Cofactors
Addition and Subtraction of Fractions
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There is a rule and parameters for adding and subtracting fractions, which means the addition and the subtraction are different in the case of the like or unlike fractions.
- If the two fractions have the same denominator, then the operation can be performed directly.
- In case the denominators are not the same, we have to take the HCF of the denominators.
- Get it divided with the HCF.
- Lastly, get it multiplied with the numerator of the fraction.
Solved Example for Addition and Subtration of Fractions
Given below are some example of calculating the fraction by the addition and subtraction of fraction method.
The illustration for the addition is given below –
- 2 / 5 + 7 / 5 = 9 / 5
Consider another example for addition and subtractionn of fractions. Now, in this case, we have to take the HCF, as the denominators are not the same –
- 3 / 2 + 5 / 4
- 6 + 5 / 4
- 11 / 4
Read More: Formulas for Logarithm
Things to Remember
- Fractions on the number line is the precise way to represent the fractions.
- The number line is the representation of the line in two parts, in which one side is negative, and the other is positive.
- The lines are divided with the 0 in the centre.
- Hence, it can be said that the zero is neither negative nor positive.
- The fractions that have the same denominators are called fractions.
- The fractions that have different denominators are generally known as unlike fractions.
Sample Questions
Ques. With numerator 6, find the equivalent fraction of 2/5. [2 marks]
Ans. As we know, 2 x 3 = 6. So, to get the equivalent fraction, we need to multiply both numerator and denominator by 3.
Thus, = >2/5 = 2x3/5x3 = 6/15
So, the required equivalent fraction is 6/15 this is because we have to maintain the equivalent fraction on both sides and it can be available through the multiplication with the same number in the denominator.
Ques. With denominator 7, find the equivalent fraction of 15/35. [2 marks]
Ans. As we know, 35/5 = 7. So, we divide both the numerator and the denominator of 15/35 by 5.
So, the required equivalent fraction is 3/7. Therefore, we have to find the equivalent with the denominator of 7. Hence, we have to divide the fraction of 15/35 with the 5 with the denominator and numerator, and hence we will get the below equivalent fraction -
Hence, 15/35 = 15/5 / 35/5 = 3/7.
Ques. If the denominator is 63, what will be the equivalent fraction of 2/9? [2 marks]
Ans. We should take, x/63 = 2/9
We are given the denominator of 63 and we have to find the fraction of 2/9. So, to find the equivalent fraction we have to assume the numerator X with the 9 and keep it equal to 2/9. With the cross multiplication, we will get the answer as below -
However,
- 9 * x = 2 * 63
- x = (2 * 63)/9
- x = 2 * 7
- x = 14
Hence, the equivalent fraction with the denominator will be 14/63.
Ques. Subtract the following expression: 12/7 – 6/5? [2 marks]
Ans. As the denominators are not the same, hence we have to take the HCF of the denominators of the fractions –
The formula to evaluate the Highest common factor is that we have to separately calculate the factorization of the denominators which will be 35 and after that we have to divide the HCF with the denominator and the result will have to be calculated with the numerator and the following values will arrive –
HCF of the expressions is – 35
- 60 - 42/35
- 18/35
Hence, the given expression is 18/35.
Ques. Evaluate the following expression to find the denominator of the expression – 12/x = 7/12 [2 marks]
Ans. Since we have given with the fractions in which one is a complete fraction and the second fraction consists of the numerator only. So, to find the denominator we have to cross multiply and then have to find the HCF after that we have to divide the HCF with the denominator and the result will have to be calculated with the numerator and the following values will arrive –
- 12/x = 7/12
- 12 * 12 = 7 * x
- 144 = 7 * x
- x = 144/7
The denominator of the expression is 7 and the fraction will be 12/7.
Ques. Add the following expression 15/21 and 8/21 and subtract the resultant expression with the 23/21. [2 marks]
Ans. Firstly, we have to calculate the sum of the expression that is 15/21 and 8/21. We know that, when the denominator is the same, then we have to add the numerator simply, as shown below-
- 15/21 + 8/21
- 23/21
Furthermore, we have to subtract the resultant with the fraction of 23/21. The operation for the subtraction is mentioned below –
- 23/21 – 23/21
- 0
Hence, the answer after the subtraction is 0.
Ques. State true or false with a reason for the following statement. When we multiply the fractions 2/3 with 3/2 the answer will be 0. [2 marks]
Ans. The above mentioned is false because when we multiply anything with the 0, the answer will be 0 but there exists no 0.
Hence, when we multiply the fractions 2/3 with 3/2, the 3 will cancel with 3, and simultaneously, the 2 will cancel with 2. Hence, we get 1x1, which is equal to 1.
Therefore, the result will be 1 and the statement is false.
Ques. What is the difference between the unlike fractions and like fractions with an illustration of both? [2 marks]
Ans. The fractions which the same denominator no matter how small or how big are known as the like fractions for illustration – 6/7, 212/7, and so on. Whereas, the fractions which have different denominators regardless the size are known as the unlike fractions for illustration – 7/87, 2/21, and so on.
Ques. How long does the number line exceed if the points that are to be marked is 503 on the number line? [2 marks]
Ans. The number line can be infinitely long from both ends whether it is the negative end or the positive end. If we want to mark the number 503 on the number, then it will be nearly about impossible to make such a long number line on the paper. Hence, the optimized solution to this is that just make the number line start from 0 and make dashes and mark the number 503.
Ques. What will be a condition when the answer of the operations on the fractions seems to be no answer? Show with an illustration. [2 marks]
Ans. The condition in which the answer of the operations on the fractions will be not answerable is when the number gets divided by 0. The illustration for that is mentioned below –
We have given with the fractions to multiply -
- 21/0 * 12/3
- 252/0
We know that the when the number get divided by 0, the answer will not be defined. Therefore, the answer to this is not available.
Ques. How many 1/3 kg pieces can be cut from a cake of weight 4 kg. [2 marks]
Ans. Let p be the number 1/3 kg pieces that are cut from a 4 kg cake.
- So, p × (1/3) = 4
- p = 4 × (3/1)
- p = 12
Ques. What is the product of 5/129 and its reciprocal. [2 marks]
Ans. Given fraction: 5/12
- Here, numerator = 5
- Denominator = 12
- Reciprocal of 5/12 = 12 / 5
- The product of 5/12 and its reciprocal = (5/12) × (12/5) = 1.
Ques. 1/4 of a number equals 2/5 ÷ 1/25. What is the number. [2 marks]
Ans. Let p be the number.
- According to the given,
- (1/4) × p = 2/5 ÷ 1/25
- p/4 = (2/5) × (25/1)
- p/4 = 2 × 5
- p = 4 × 10
- p = 40
Ques. Simran travels 240 km on two-fifths of his petrol tank. How far would he travel at the same rate with a full tank of petrol. [3 marks]
Ans. Distance travelled by Simran with two-fifths of petrol tank = 240 km
- Distance travelled by her with a full petrol tank = (240 ÷ 2/5) km
- (240 x 5)/2 km
- 200 x 5 km
- 1000 km.
Ques. Amit can do a piece of work in 12 hours. What part of the work can she do in 1 hour, in 5 hours, in 6 hours. [3 marks]
Ans. Let m be the whole work to be done.
- The part of work done by Amit in 12 hours = m
- Thus, the part of work done by her in 1 hour = m/12
- The part of work done by her in 5 hours = (m/12) x 5 = 5m/12
- The part of work done by her in 6 hours = (m/12) x 6 = m/2
- Therefore, Amit can do 1/12 part of work in 1 hour, 5/12 part of work in 5 hours and 1/2 part of work in 6 hours
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