Fractions Or Rational Number

<<–2/”>a >body>



FRACTIONS

Any unit can be divided into any numbers of equal parts, one or more of this parts is called fraction of that unit. e.g. one-forth (1/4), one-third (1/3), three-seventh (3/7) etc. 

The lower part indicates the number of equal parts into which the unit is divided, is called denominator. The upper part, which indicates the number of parts taken from the fraction is called the numerator. The numerator and the denominator of a fraction are called its terms.

• A fraction is unity, when its numerator and denominator are equal.
• A fraction is equal to zero if its numerator is zero.
• The denominator of a fraction can never be zero.
• The value of a fraction is not altered by multiplying or dividing the numerator and the denominator by the same number.e.g. 2/3 = 2/6 = 8/12 = (2/4)/(3/4)
• When there is no common factor between numerator and denominator it is called in its lowest terms.e.g. 15/25 = 3/5
• When a fraction is reduced to its lowest term, its numerator and denominator are prime to each other.
• When the numerator and denominator are divided by its HCF, fraction reduces to its lowest term.

Proper fraction: A fraction in which numerator is less than the denominator. e.g. 1/4, 3/4, 11/12 etc.

Improper Fraction:  A fraction in which numerator is equal to or more than the denominator. e.g. 5/4, 7/4, 13/12 etc.

Like fraction: Fractions in which denominators are same is called like fractions.

e.g. 1/12, 5/12, 7/12, 13/12 etc.

Unlike fraction: Fractions in which denominators are not same is called, unlike fractions.

e.g. 1/12, 5/7, 7/9 13/11 etc.

Compound Fraction: Fraction of a fraction is called a compound fraction.

e.g. 1/2 of 3/4 is a compound fraction.

Complex Fractions: Fractions in which numerator or denominator or both are fractions, are called complex fractions.

Continued fraction: Fraction that contain additional fraction is called continued fraction. 

e.g. 

Rule: To simplify a continued fraction, begin from the bottom and move upwards.

Decimal Fractions: Fractions in which denominators are 10 or multiples of 10 is called, decimal fractions. e.g. 1/10, 3/100, 2221/10000 etc.

Recurring Decimal: If in a decimal fraction a digit or a set of digits is repeated continuously, then such a number is called a recurring decimal. It is expressed by putting a dot or bar over the digits. e.g.

Pure recurring decimal: A decimal fraction in which all the figures after the decimal point is repeated is called a pure recurring decimal.

Mixed recurring decimal: A decimal fraction in which only some of the figures after the decimal point is repeated is called a mixed recurring decimal.

Conversion of recurring decimal into proper fraction: 

CASE I: Pure recurring decimal

Write the repeated digit only once in the numerator and put as many nines as in the denominator as the number of repeating figures. e.g. 

CASE II: Mixed recurring decimal

In the numerator, take the difference between the number formed by all the digits after the decimal point and that formed by the digits which are not repeated. In the denominator, take the number formed as many nines as there are repeating digits followed by as many zeros as is the number of non-repeating digits. e.g.

Questions

Level-I

Answers

Level-I

Answer:1 Option B

Explanation:

Answer:2 Option C

Explanation:

Answer:3 Option A

Explanation:

Answer:4 Option B

Explanation:

Answer:5 Option C

Explanation:

= 17.2

Answer:6 Option C

Explanation:

Answer:7 Option C

Explanation:

Answer:8 Option C

Explanation:

Given expression = (11.98)² + (0.02)² + 11.98 x x.

For the given expression to be a perfect square, we must have

11.98 x x = 2 x 11.98 x 0.02 or x   = 0.04

Answer:9 Option D

Explanation:

Answer:10 Option D

Explanation:

Let 3889 + 12.952 – x = 3854.002.

Then x = (3889 + 12.952) – 3854.002

   = 3901.952 – 3854.002

   = 47.95.

Level-II

Answer:11 Option B

Explanation:

4 x 162 = 648. Sum of decimal places = 6.
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10^-4

Answer:12 Option B

Explanation:

Answer:13 Option A

Explanation:

Answer:14 Option B

Explanation:

Suppose commodity X will cost 40 paise more than Y after z years.

Then, (4.20 + 0.40z) – (6.30 + 0.15z) = 0.40

 0.25z = 0.40 + 2.10

 X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.

Answer:15 Option D

Answer:16 Option C

Explanation:

Clearly, 0.8 lies between 0.75 and 0.833.

Answer:17 Option C

Explanation:

Answer:18 Option C

Explanation:

  617.00

    6.017

    0.617

 +  6.0017

  ——–

  629.6357

  ———

Answer:19 Option B

Explanation:

= 0.058  0.06.

Answer:20 Option B

Explanation:

2 x 5 = 10.

Sum of decimal places = 4

 0.002 x 0.5 = 0.001

,

Fractions are a way of representing parts of a whole. They are written with two numbers, the numerator and the denominator. The numerator is the number of parts you are considering, and the denominator is the total number of parts. For example, if you have a pizza that has been cut into 8 slices, and you eat 3 slices, you have eaten $\frac{3}{8}$ of the pizza.

Fractions can be added, subtracted, multiplied, and divided. To add or subtract fractions, you need to make sure that the denominators are the same. Then, you just add or subtract the numerators. To multiply fractions, you multiply the numerators and the denominators. To divide fractions, you flip the second fraction upside down and multiply.

You can simplify fractions by finding a common denominator. The common denominator is the least common multiple of the two denominators. For example, to simplify $\frac{1}{2}$ and $\frac{1}{3}$, you would find the least common multiple of 2 and 3, which is 6. Then, you would multiply $\frac{1}{2}$ by $\frac{3}{3}$ to get $\frac{3}{6}$, and you would multiply $\frac{1}{3}$ by $\frac{2}{2}$ to get $\frac{2}{6}$. Finally, you would add the two fractions: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

You can compare fractions by looking at their numerators and denominators. A fraction with a larger numerator is greater than a fraction with a smaller numerator, if the denominators are the same. For example, $\frac{3}{4}$ is greater than $\frac{2}{4}$, because 3 is greater than 2. If the numerators are the same, then the fraction with the smaller denominator is greater. For example, $\frac{1}{2}$ is greater than $\frac{1}{3}$, because 2 is smaller than 3.

Equivalent fractions are fractions that represent the same amount. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions, because they both represent 1 half of a whole. You can find equivalent fractions by multiplying the numerator and denominator by the same number. For example, $\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}$.

Proper fractions are fractions where the numerator is less than the denominator. For example, $\frac{1}{2}$ and $\frac{3}{4}$ are proper fractions. Improper fractions are fractions where the numerator is greater than or equal to the denominator. For example, $\frac{3}{2}$ and $\frac{4}{4}$ are improper fractions. Mixed numbers are a combination of a whole number and a proper fraction. For example, $\frac{1}{2} + 1 = \frac{3}{2}$ is a mixed number.

Fractions can be represented on a number line. To do this, you need to find the equivalent fraction with a denominator of 100. For example, $\frac{1}{2}$ is equivalent to $\frac{50}{100}$. Then, you can mark off 50 equal parts on the number line, and place the fraction at the appropriate point.

Percents are a way of representing parts of a whole out of 100. To convert a fraction to a percent, you multiply the fraction by 100 and add a percent sign. For example, to convert $\frac{1}{2}$ to a percent, you would multiply $\frac{1}{2} \times 100 = 50$. Then, you would add a percent sign to get 50%.

Decimals are a way of representing parts of a whole using tenths. To convert a fraction to a decimal, you divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, you would divide 1 by 2 to get 0.5.

Rational numbers are numbers that can be expressed as a fraction $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$. Real numbers are all the numbers that can be represented on a number line, including rational numbers and irrational numbers.

I hope this ARTICLE has been helpful in explaining fractions and rational numbers. If you have any further questions, please do not hesitate to ask.

Here are some frequently asked questions and short answers about fractions:

• What is a fraction?
  A fraction is a part of a whole. It is written as two numbers, one on top of the other, with a line between them. The number on top is called the numerator, and the number on the bottom is called the denominator.

• What are the different types of fractions?
  There are three main types of fractions: proper fractions, improper fractions, and mixed numbers.

• Proper fractions are less than 1. They are written with the numerator smaller than the denominator. For example, 1/2 is a proper fraction.

• Improper fractions are greater than or equal to 1. They are written with the numerator greater than or equal to the denominator. For example, 3/2 is an improper fraction.

• Mixed numbers are a combination of a whole number and a proper fraction. They are written with the whole number part before the fraction part, and a space between them. For example, 2 1/2 is a mixed number.

• How do you add fractions?
  To add fractions, you need to make sure that the denominators are the same. Then, you add the numerators and keep the denominator the same. For example, to add 1/2 and 1/4, you would first need to make the denominators the same. You can do this by multiplying 1/2 by 2/2, which gives you 2/4. Then, you can add the numerators, 2 + 1 = 3. So, 1/2 + 1/4 = 3/4.

• How do you subtract fractions?
  To subtract fractions, you need to make sure that the denominators are the same. Then, you subtract the numerators and keep the denominator the same. For example, to subtract 1/2 from 1/4, you would first need to make the denominators the same. You can do this by multiplying 1/2 by 2/2, which gives you 2/4. Then, you can subtract the numerators, 2 – 1 = 1. So, 1/2 – 1/4 = 1/4.

• How do you multiply fractions?
  To multiply fractions, you multiply the numerators and the denominators. For example, to multiply 1/2 and 1/4, you would multiply 1 x 1 = 1 and 2 x 4 = 8. So, 1/2 x 1/4 = 1/8.

• How do you divide fractions?
  To divide fractions, you flip the second fraction upside down and multiply. For example, to divide 1/2 by 1/4, you would flip 1/4 upside down to get 4/1. Then, you would multiply 1/2 x 4/1 = 4/2. So, 1/2 ÷ 1/4 = 4/2.

• What are the properties of fractions?
  There are several properties of fractions that you should know. These properties include:

• The commutative property of addition: a + b = b + a

• The associative property of addition: (a + b) + c = a + (b + c)
• The commutative property of multiplication: a x b = b x a
• The associative property of multiplication: (a x b) x c = a x (b x c)
• The distributive property of multiplication over addition: a x (b + c) = a x b + a x c
• The identity property of addition: a + 0 = a
• The identity property of multiplication: a x 1 = a
• The inverse property of addition: a + (-a) = 0

• The inverse property of multiplication: a x (1/a) = 1

• What are some real-world applications of fractions?
  Fractions can be used to represent many different things in the real world. For example, they can be used to represent parts of a whole, such as a pizza that is cut into 8 slices. They can also be used to represent ratios, such as the ratio of boys to girls in a class. Fractions can also be used to represent decimals, such as 0.5, which is equal to 1/2.

I hope this helps!

Sure, here are some MCQs without mentioning the topic Fractions Or Rational Number:

1. Which of the following is not a fraction?
   (A) 1/2
   (B) 1/3
   (C) 1/4
   (D) 1/5

2. Which of the following is equivalent to 1/2?
   (A) 2/4
   (B) 3/6
   (C) 4/8
   (D) 5/10

3. Which of the following is equivalent to 1/3?
   (A) 2/6
   (B) 3/9
   (C) 4/12
   (D) 5/15

4. Which of the following is equivalent to 1/4?
   (A) 2/8
   (B) 3/12
   (C) 4/16
   (D) 5/20

5. Which of the following is equivalent to 1/5?
   (A) 2/10
   (B) 3/15
   (C) 4/20
   (D) 5/25

6. Which of the following is greater than 1/2?
   (A) 1/3
   (B) 1/4
   (C) 1/5
   (D) 1/6

7. Which of the following is less than 1/2?
   (A) 2/3
   (B) 3/4
   (C) 4/5
   (D) 5/6

8. Which of the following is equal to 1/2 + 1/4?
   (A) 3/4
   (B) 1/2
   (C) 2/3
   (D) 5/8

9. Which of the following is equal to 1/2 – 1/4?
   (A) 1/4
   (B) 1/8
   (C) 3/8
   (D) 5/8

10. Which of the following is equal to 1/2 x 1/4?
    (A) 1/8
    (B) 1/16
    (C) 1/32
    (D) 1/64

I hope these MCQs are helpful!