Math Quiz: HCF and LCM Concepts
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Questions and Answers

What is the highest common factor (HCF) of the numbers 24, 36, and 60?

The HCF is 12.

How do you find the least common multiple (LCM) of 4, 5, and 6?

The LCM is 60.

Explain the relationship between factors and multiples.

Factors are numbers that divide another number without a remainder, while multiples are the products obtained when a number is multiplied by integers.

What real-life situation can be modeled using the concept of LCM?

<p>LCM can be used to determine when two events, like the recycling truck and garbage truck, will arrive on the same day again.</p> Signup and view all the answers

Calculate the HCF of 30, 45, and 75 using prime factorization.

<p>The HCF is 15.</p> Signup and view all the answers

What role does the concept of multiples play in determining the LCM?

<p>The LCM is derived from the multiples of the given numbers, specifically the smallest one that appears in all sets.</p> Signup and view all the answers

In what way do HCF and LCM help in simplifying fractions?

<p>They help in finding the simplest form by dividing both the numerator and denominator by their HCF.</p> Signup and view all the answers

Provide a practical example where factors can be useful in real life.

<p>Determining how to evenly distribute 28 apples among 4 friends can be done using factors.</p> Signup and view all the answers

What is the relationship between factors and multiples?

<p>Factors are the numbers that divide another number evenly, whereas multiples are obtained by multiplying a number by integers.</p> Signup and view all the answers

In the context of the multiplication table, how would you define the multiples of 2?

<p>The multiples of 2 are obtained by multiplying 2 with all integers, resulting in numbers like 2, 4, 6, 8, ..., up to 30.</p> Signup and view all the answers

How do you determine the HCF of two numbers using their factors?

<p>The HCF is found by identifying the highest common factor shared between the factors of the two numbers.</p> Signup and view all the answers

Using the numbers 12 and 18, what is their LCM?

<p>The LCM of 12 and 18 is 36.</p> Signup and view all the answers

If Rajdeep's father sold 125 guavas for Rs 2 each, how much money did he make?

<p>He made Rs 250 by selling 125 guavas at Rs 2 each.</p> Signup and view all the answers

Explain why the multiples of 3 are considered infinite.

<p>The multiples of 3 are infinite because you can keep multiplying 3 by larger integers without limit.</p> Signup and view all the answers

Define how HCF can be useful in simplifying fractions.

<p>HCF helps in simplifying fractions by dividing both the numerator and the denominator by their highest common factor.</p> Signup and view all the answers

In the context of real-life situations, how can knowing LCM be beneficial?

<p>Knowing the LCM allows individuals to find a common period for events that repeat, such as scheduling activities or coordinating timings.</p> Signup and view all the answers

What is the highest common factor (HCF) of 36 and 24?

<p>The HCF of 36 and 24 is 12.</p> Signup and view all the answers

Calculate the least common multiple (LCM) of 4 and 5.

<p>The LCM of 4 and 5 is 20.</p> Signup and view all the answers

If you have 12 apples and want to distribute them among 4 friends equally, how many apples will each friend receive?

<p>Each friend will receive 3 apples.</p> Signup and view all the answers

What are the factors of 30?

<p>The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.</p> Signup and view all the answers

If a rectangle has a length of 10 meters and width of 5 meters, what is the area?

<p>The area of the rectangle is 50 square meters.</p> Signup and view all the answers

Find the GCF of 18 and 27 using prime factorization.

<p>The GCF of 18 and 27 is 9.</p> Signup and view all the answers

What is the significance of finding the LCM in scheduling events?

<p>The LCM helps to determine when events will coincide or repeat.</p> Signup and view all the answers

How can you find the multiples of 7 up to 70?

<p>The multiples of 7 up to 70 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.</p> Signup and view all the answers

Flashcards

Order of Operations

A set of rules for evaluating mathematical expressions in a specific sequence (usually PEMDAS/BODMAS).

Factors

A factor is a number that divides another number evenly (no remainder).

Multiples

A multiple of a number is the product of that number and any whole number.

Highest Common Factor (HCF)

The largest factor that two or more numbers share.

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Least Common Multiple (LCM)

The smallest multiple that two or more numbers share.

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Simplification

The process of calculating the value of a mathematical expression by applying mathematical rules and order of operations.

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Mathematical Expression

A combination of numbers, variables, and operations.

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Evaluate an Expression

To find the numerical value of a mathematical expression.

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Line

A straight path that extends infinitely in both directions. It has no thickness and is represented by arrows.

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Line Segment

A part of a line that has two endpoints. It has a fixed length and is represented by a line with two points.

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Ray

A part of a line that has one endpoint and extends infinitely in one direction. It is represented by a line with an arrow at one end.

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Point

A location in space with no size or dimension. It is represented by a dot.

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Perimeter

The total distance around the outside of a closed shape. It is calculated by adding up the lengths of all the sides.

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Area

The amount of space a two-dimensional shape covers. It is measured in square units.

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Directed Numbers

Numbers that have a positive or negative sign indicating their direction on a number line.

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Number Line

A straight line used to represent numbers. It has zero at the center, positive numbers to the right, and negative numbers to the left.

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BODMAS rule

A rule that helps us solve math problems by doing operations in a specific order: Brackets, Orders (powers and roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

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What is the first step when simplifying (30 - 24 - 6) - 8?

We first operate on the terms inside the brackets: (30 - 24 - 6) = 0. This is because brackets are performed before subtraction.

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What happens if there's no sign after a number in a calculation?

It implies multiplication. For example, 4(5-3) is the same as 4 x (5 - 3).

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What does 'of' mean in a mathematical expression?

'Of' means multiplication. For example, 4 of 21 is the same as 4 x 21.

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How do we solve expressions with repeated subtractions or divisions?

We solve them step by step from left to right. For example, for 10 - 3 - 5, we first subtract 3 from 10, then subtract 5 from the result.

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What is the difference between (16 - 4)(5 - 3) and 16 - 4(5 - 3)?

(16 - 4)(5 - 3) means we first calculate (16 - 4) and (5 - 3) and then multiply the results. 16 - 4(5 - 3) means we first calculate 4(5 - 3) and then subtract the result from 16.

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How do we simplify (40 ÷ 5) ÷ 4(5 - 3) ?

We first simplify the expression inside the brackets, then division and multiplication from left to right. So it becomes (40 ÷ 5) ÷ 4(2) = 8 ÷ 8 = 1.

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Why is 8 ÷ 4 × 2 = 4 and NOT 1?

Division and multiplication have equal priority in BODMAS. We solve them from left to right. So 8 ÷ 4 = 2, then 2 × 2 = 4.

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Study Notes

Book Title and Class

  • GANITPRABHA
  • Class VI

Publication Information

  • Eighth Edition : December, 2020
  • West Bengal Board of Secondary Education
  • Published by Smt. Paromita Roy
  • Secretary-in-charge
  • West Bengal Board of Secondary Education
  • 77/2, Park Street, Kolkata - 700016
  • Printed at West Bengal Text Book Corporation Limited (Government of West Bengal Enterprise)
  • Kolkata-700 056

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Ganit Prabha Class VI Mathematics Textbook PDF

Description

Test your knowledge on the highest common factor (HCF) and least common multiple (LCM). This quiz explores their definitions, relationships, calculations, and real-life applications. Enhance your understanding of these fundamental mathematical concepts.

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