FRACTIONS

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 part of everyday life. We use them to divide things up, to compare quantities, and to measure things. In this ARTICLE, we will learn about fractions, how to add and subtract them, how to multiply and divide them, and how to compare them. We will also learn about equivalent fractions, decimals, mixed numbers, rational numbers, percents, Probability, word problems, and fractions on a number line.

Introduction to Fractions

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. The denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we are talking about. For example, if we have a cake that is cut into 8 pieces, and we eat 3 pieces, we can say that we ate $\frac{3}{8}$ of the cake.

Adding and Subtracting Fractions

To add or subtract fractions, we need to make sure that the denominators are the same. If they are not, we can find a common denominator. The common denominator is the least common multiple of the two denominators. To find the least common multiple, we can list out the multiples of each denominator until we find a number that is on both lists. For example, if we want to add $\frac{1}{2}$ and $\frac{1}{3}$, the least common multiple of 2 and 3 is 6. So, we can rewrite $\frac{1}{2}$ as $\frac{3}{6}$ and $\frac{1}{3}$ as $\frac{2}{6}$. Now, we can add the fractions:

$$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$

Multiplying and Dividing Fractions

To multiply fractions, we multiply the numerators and the denominators. For example, to multiply $\frac{1}{2}$ and $\frac{3}{4}$, we would multiply 1 and 3, and then 2 and 4. The answer is $\frac{3}{8}$.

To divide fractions, we flip the second fraction upside down and multiply. For example, to divide $\frac{1}{2}$ by $\frac{3}{4}$, we would flip $\frac{3}{4}$ upside down to get $\frac{4}{3}$. Then, we would multiply $\frac{1}{2}$ and $\frac{4}{3}$. The answer is $\frac{4}{6}$.

Equivalent Fractions

Equivalent fractions are fractions that have the same value. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions. We can find equivalent fractions by multiplying or dividing the numerator and denominator by the same number. For example, $\frac{1}{2} \times 2 = \frac{2}{4}$.

Comparing Fractions

To compare fractions, we need to find a common denominator. Once we have a common denominator, we can compare the numerators. The fraction with the larger numerator is the larger fraction. For example, to compare $\frac{1}{2}$ and $\frac{1}{3}$, we can find a common denominator of 6. Then, we can rewrite $\frac{1}{2}$ as $\frac{3}{6}$ and $\frac{1}{3}$ as $\frac{2}{6}$. Now, we can compare the numerators: 3 is greater than 2, so $\frac{1}{2}$ is greater than $\frac{1}{3}$.

Ordering Fractions

To order fractions, we need to find a common denominator. Once we have a common denominator, we can order the fractions by their numerators. The fraction with the larger numerator is the larger fraction. For example, to order $\frac{1}{2}$, $\frac{1}{3}$, and $\frac{1}{4}$, we can find a common denominator of 12. Then, we can rewrite $\frac{1}{2}$ as $\frac{6}{12}$, $\frac{1}{3}$ as $\frac{4}{12}$, and $\frac{1}{4}$ as $\frac{3}{12}$. Now, we can order the fractions: $\frac{6}{12} > \frac{4}{12} > \frac{3}{12}$. So, the order of the fractions is $\frac{1}{2} > \frac{1}{3} > \frac{1}{4}$.

Here are some frequently asked questions and short answers about the following topics:

• Decimals:
  • What is a decimal?
    A decimal is a number that is written with a decimal point. The decimal point separates the whole number part of the number from the fractional part of the number.
  • How do you read a decimal?
    To read a decimal, you read the whole number part of the number first, followed by the decimal point, and then the fractional part of the number. For example, the decimal 0.5 is read as “zero point five.”
  • How do you add decimals?
    To add decimals, you line up the decimal points and then add the numbers as you would any other numbers. When you reach the decimal point, carry the one over to the next column.
  • How do you subtract decimals?
    To subtract decimals, you line up the decimal points and then subtract the numbers as you would any other numbers. When you reach the decimal point, borrow a one from the next column if necessary.
  • How do you multiply decimals?
    To multiply decimals, you multiply the numbers as you would any other numbers, and then you place the decimal point in the product so that there are the same number of digits to the right of the decimal point in the product as there are in the two numbers being multiplied.
  • How do you divide decimals?
    To divide decimals, you can either flip the divisor (the number you are dividing by) and multiply, or you can use long division. When you flip the divisor, you multiply the two numbers as you would any other numbers, and then you place the decimal point in the quotient so that there are the same number of digits to the right of the decimal point in the quotient as there are in the dividend (the number you are dividing).
• Percents:
  • What is a percent?
    A percent is a number or part of a whole that is expressed as a fraction of 100. The word “percent” comes from the Latin word “per centum,” which means “out of one hundred.”
  • How do you write a percent as a decimal?
    To write a percent as a decimal, you divide the percent by 100. For example, 25% is equal to 25/100, which is equal to 0.25.
  • How do you write a decimal as a percent?
    To write a decimal as a percent, you multiply the decimal by 100 and add a percent sign. For example, 0.25 is equal to 0.25 x 100 = 25%.
  • How do you add percents?
    To add percents, you add the numbers as you would any other numbers, and then you add the percent signs. For example, 25% + 15% = 40%.
  • How do you subtract percents?
    To subtract percents, you subtract the numbers as you would any other numbers, and then you subtract the percent signs. For example, 25% – 15% = 10%.
  • How do you multiply percents?
    To multiply percents, you multiply the numbers as you would any other numbers, and then you add the percent signs. For example, 25% x 15% = 3.75%.
  • How do you divide percents?
    To divide percents, you divide the numbers as you would any other numbers, and then you divide the percent signs. For example, 25% / 15% = 1.67%.
• 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.
  • How do you add fractions?
    To add fractions, you 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 + 1/4, you would first make sure that the denominators are the same. You can do this by multiplying the first fraction by 2/2, or the second fraction by 1/1. So, 1/2 + 1/4 = (1/2 x 2/2) + (1/4 x 1/1) = 2/4 + 1/4 = 3/4.
  • How do you subtract fractions?
    To subtract fractions

Sure, here are some MCQs without mentioning the topic fractions:

1. What is the number that is 10 more than 50?
   (A) 60
   (B) 70
   (C) 80
   (D) 90

2. What is the number that is 10 less than 50?
   (A) 40
   (B) 30
   (C) 20
   (D) 10

3. What is the number that is 5 times 10?
   (A) 50
   (B) 100
   (C) 150
   (D) 200

4. What is the number that is 5 times 20?
   (A) 100
   (B) 150
   (C) 200
   (D) 250

5. What is the number that is 100 divided by 2?
   (A) 50
   (B) 25
   (C) 12.5
   (D) 6.25

6. What is the number that is 100 divided by 4?
   (A) 25
   (B) 12.5
   (C) 6.25
   (D) 3.125

7. What is the number that is 100 divided by 8?
   (A) 12.5
   (B) 6.25
   (C) 3.125
   (D) 1.875

8. What is the number that is 100 divided by 16?
   (A) 6.25
   (B) 3.125
   (C) 1.875
   (D) 0.9375

9. What is the number that is 100 divided by 32?
   (A) 3.125
   (B) 1.875
   (C) 0.9375
   (D) 0.625

10. What is the number that is 100 divided by 64?
    (A) 1.6666666666666666
    (B) 0.8333333333333333
    (C) 0.5
    (D) 0.3333333333333333