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When the whole number parts are equal, we first convert mixed fractions to improper fractions and then compare the two by using cross multiplication method. The fraction with greater whole number part is greater. For example 3\(\frac{1}{2}\) > 2\(\frac{1}{2}\)

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In comparing unlike fractions, we first convert them into like fractions by using the following steps and then compare them. Step I: Obtain the denominators of the fractions and find their LCM (least common multiple). Step II: Each fractions are converted to its equivalent

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Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2}{13}\) because 7 > 2. In comparison of like fractions here are some

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In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators. 3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10 In the fractions having the same numerator, that fraction is

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There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1(one), then the fraction is said to be in its simple form or in lowest

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In changing fractions we will discuss how to change fractions from improper fraction to a whole or mixed number, from mixed number to an improper fraction, from whole number into an improper fraction. Changing an improper fraction to a whole number or mixed number:

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The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerator < denominator). Two parts are shaded in the above diagram.

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Fraction as division is also known as fraction as quotient. Examples on Fraction as division If 8 biscuits are distributed between 2 children equally, then each of them will get 8 ÷ 2 = 4 biscuits. If 4 biscuits are distributed between 2 children equally, then each of

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We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First we find the L.C.M. of the denominators of the fractions to make the

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We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we find the L.C.M. of the denominators of the fractions to make the denominators

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The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with respect to the whole shape in the figures from (i) to (viii) In; (i) Shaded

Continue reading "Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples"

In 5th Grade Numbers Worksheets we will solve how to read and write large numbers, use of place value chart to write a number in expanded form, compare with another number and arrange numbers in ascending and descending order. The greatest possible number formed using each

Continue reading "5th Grade Numbers Worksheets | Place Value | Standard Form | Rounding"

In 5th Grade Numbers Worksheets we will solve how to read and write large numbers, use of place value chart to write a number in expanded form, represent the large number on the abacus, write the number in standard form, compare with another number and arrange numbers

Continue reading "4th Grade Numbers Worksheets | Place Value Chart | Expended Form"

While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the tens place is replaced by ‘0’ and the hundreds place is increased by 1.

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While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the digit in the hundreds place is = to or > 5, then the hundreds place is replaced by ‘0’ and the thousands place is

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Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number may be rounded off to the nearest 10. Rules for Rounding off to Nearest 10

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The Trigonometrical ratios table will help us to find the values of trigonometric standard angles. The standard angles of trigonometrical ratios are 0°, 30°, 45°, 60° and 90°. The values of trigonometrical ratios of standard angles are very important to solve the

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The solved examples on the basic properties of tangents will help us to understand how to solve different type problems on properties of triangle. 1. Two concentric circles have their centres at O. OM = 4 cm and ON = 5 cm. XY is a chord of the outer circle and a tangent to

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In International place-value system, there are three periods namely Ones, thousands and millions for the nine places from right to left. Ones period is made up of three place-values. Ones, tens, and hundreds. The next period thousands is made up of one, ten and hundred-thous

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We will discuss circumcentre and incentre of a triangle. In general, the incentre and the circumcentre of a triangle are two distinct points. Here in the triangle XYZ, the incentre is at P and the circumcentre is at O. A special case: an equilateral triangle, the bisector

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In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:

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Worked-out problems related to place value of digits in a numeral. Find the difference between the place value and face value of digit 6 in the numeral 2960543. Find the product of the place values of two 4s in the numeral 30426451. Write the smallest 5-digit number

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We will discuss here the Incircle of a triangle and the incentre of the triangle. The circle that lies inside a triangle and touches all the three sides of the triangle is known as the incircle of the triangle. If all the three sides of a triangle touch a circle then the

Continue reading "Incircle of a Triangle |Incentre of the Triangle|Point of Intersection"

In place value chart, the digits are grouped in the threes in a big number. The number is read from left to right as … billion …million …. thousands …ones. The place value chart of the International System is given below: Place Value Chart 100,000 = 100 thousand 1,000,000

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We will learn how to write the numeral in standard form. Here the standard form means the process of writing very large expanded form of a number into small form or small number. How to write the number in standard form? Here we will convert expanded form into standard

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The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number. For example, 9,99,99,999 is predecessor of 10,00,00,000 or we can also

Continue reading "Successor and Predecessor | Successor of a Whole Number | Predecessor "

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the

Continue reading "Formation of Greatest and Smallest Numbers | Arranging the Numbers"

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the smallest number then the numbers are arranged in descending order.

Continue reading "Arranging Numbers | Ascending Order | Descending Order |Compare Digits"

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits. To learn

Continue reading "Comparison of Numbers | Compare Numbers Rules | Examples of Comparison"

We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its digits. This is shown here: In 2385, the place values of the digits are

Continue reading "Expanded form of a Number | Writing Numbers in Expanded Form | Values"

The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know that the position of a digit in a number determines its corresponding value

Continue reading "Place Value | Place, Place Value and Face Value | Grouping the Digits "

We have already learned to count up to 6-digit numbers. We know six digit numbers are expressed in terms of hundreds of thousands but now we will learn numbers beyond six digits. We know that the greatest 6-digit number is 999,999. If we add 1 to 999,999, we get the smallest

Continue reading "Counting Beyond 999,999 | Learn Numbers Beyond Six Digits|6-digit Numb"

In worksheet on Operations on Roman Numerals we will solve various types of practice questions on Addition on Roman Numerals; subtraction of Roman Numerals; multiplication of Roman Numerals; division of Roman Numerals and some word problems on Roman Numerals. Here you will

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Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) VII (b) IX (c) XI (d) XIV (e) XIX (f) XXVII (g) XXIX (h) XII

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The four basic operations on Roman numerals are addition; subtraction; multiplication and division. The Roman numerals satisfy the commutative, associative and distributive laws for addition, subtraction, multiplication and division.If we add, subtract, multiply or div

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We will learn about Roman Numeration and its rules. We know that there are seven basic Roman Numerals. They are I, V, X, L, C, D and M. These numerals stand for the number 1, 5, 10, 50, 100, 500

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Practice the worksheet on comparison of roman numerals. In worksheet on comparison of roman numerals we will solve various types of practice questions on roman numerals. Here you will get 20 different types of questions on comparison of roman numerals. Compare the given

Continue reading "Worksheet on Comparison of Roman Numerals | Hindu - Arabic Numerals"

In worksheet on estimating median and the quartiles using ogive we will solve various types of practice questions on measures of central tendency. Here you will get 4 different types of questions on estimating median and the quartiles using ogive.1.Using the data given below

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How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol of Roman Numerals and their values are: Romans used different

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In worksheet on finding the quartiles and the interquartile range of raw and arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the quartiles and the interquartile

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In worksheet on finding the median of arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the median of arrayed data. 1. Find the median of the following frequency

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For a frequency distribution, the median and quartiles can be obtained by drawing the ogive of the distribution. Follow these steps. Step I: Change the frequency distribution into a continuous distribution by taking overlapping intervals. Let N be the total frequency.

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In worksheet on finding the median of raw data we will solve various types of practice questions on measures of central tendency. Here you will get 9 different types of questions on finding the median of raw data. 1. Find the median. (i) 23, 6, 10, 4, 17, 1, 3 (ii) 1, 2, 3

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If in a continuous distribution the total frequency be N then the class interval whose cumulative frequency is just greater than \(\frac{N}{2}\) (or equal to \(\frac{N}{2}\)) is called the median class. In other words, median class is the class interval in which the median

Continue reading "Median Class | continuous distribution | Cumulative Frequency"

The variates of a data are real numbers (usually integers). So, thay are scattered over a part of the number line. An investigator will always like to know the nature of the scattering of the variates. The arithmetic numbers associated with distributions to show the nature

Continue reading "Range & Interquartile Range |Measures of Dispersion|Semi-interquartile"

Here we will learn how to find the quartiles for arrayed data. Step I: Arrange the grouped data in ascending order and from a frequency table. Step II: Prepare a cumulative-frequency table of the data. Step III:(i) For Q1: Select the cumulative frequency that is just greater

Continue reading "Find the Quartiles for Arrayed Data | Lower Quartiles |Upper Quartiles"

If the data are arranged in ascending or descending order then the variate lying at the middle between the largest and the median is called the upper quartile (or the third quartile), and it denoted by Q3. In order to calculate the upper quartile of raw data, follow these

Continue reading "Upper Quartile and the Method of Finding it for Raw Data |3rd Quartile"

The three variates which divide the data of a distribution in four equal parts (quarters) are called quartiles. As such, the median is the second quartile. Lower quartile and the method of finding it for raw data: If the data are arranged in ascending or descending order

Continue reading "Lower Quartile and the Method of Finding it for Raw Data | Definition"

To find the median of arrayed (grouped) data we need to follow the following steps: Step I: Arrange the grouped data in ascending or descending order, and form a frequency table. Step II: Prepare a cumulative-frequency table of the data. Step III: Select the cumulative

Continue reading "Finding the Median of Grouped Data | Median of Arrayed Data | Examples"

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