The additive inverse of a number is another number that cancels it out to yield zero when both are added together. This concept applies to all integers. For example, the additive inverse of 7 is -7 because 7 + (-7) = 0. Similarly, the additive inverse of -5 is 5, since -5 + 5 = 0. This property is eRead more
The additive inverse of a number is another number that cancels it out to yield zero when both are added together. This concept applies to all integers. For example, the additive inverse of 7 is -7 because 7 + (-7) = 0. Similarly, the additive inverse of -5 is 5, since -5 + 5 = 0. This property is essential in arithmetic and algebra, allowing simplification of equations and balancing expressions by neutralizing terms.
Addition represents the combination of two movements on a number line. Starting from zero or another position, move a certain number of steps right for the first number, then continue moving for the second. For instance, starting at 0, moving 2 steps to the right, followed by 3 more steps, lands atRead more
Addition represents the combination of two movements on a number line. Starting from zero or another position, move a certain number of steps right for the first number, then continue moving for the second. For instance, starting at 0, moving 2 steps to the right, followed by 3 more steps, lands at 5, illustrating that 2 + 3 = 5. This visualization helps understand addition intuitively, as combining displacements to find a new position.
Subtraction on a number line is interpreted as finding the difference between two positions by moving left. Starting at the minuend's position, move steps equal to the subtrahend to the left. For instance, if you begin at 3 and subtract 2, move 2 steps left, arriving at 1, showing 3 - 2 = 1. This moRead more
Subtraction on a number line is interpreted as finding the difference between two positions by moving left. Starting at the minuend’s position, move steps equal to the subtrahend to the left. For instance, if you begin at 3 and subtract 2, move 2 steps left, arriving at 1, showing 3 – 2 = 1. This movement-based explanation makes subtraction tangible and connects it to physical displacement, aiding in understanding and solving arithmetic problems.
According to Brahmagupta’s rule, when two positive numbers are added, their values are simply combined, resulting in another positive number. For example, adding 4 and 6 yields 10, a positive result. This rule applies universally to positive integers and reflects their cumulative nature when combineRead more
According to Brahmagupta’s rule, when two positive numbers are added, their values are simply combined, resulting in another positive number. For example, adding 4 and 6 yields 10, a positive result. This rule applies universally to positive integers and reflects their cumulative nature when combined. It demonstrates that positive values grow larger when added together, forming the foundation for basic arithmetic operations and applications involving quantities or measurements.
When adding two negative numbers, Brahmagupta’s rule involves summing their absolute values and assigning a negative sign to the result. For example, adding -4 and -6 involves finding their absolute values (4 and 6), summing them to get 10, and then adding the negative sign, yielding -10. This methoRead more
When adding two negative numbers, Brahmagupta’s rule involves summing their absolute values and assigning a negative sign to the result. For example, adding -4 and -6 involves finding their absolute values (4 and 6), summing them to get 10, and then adding the negative sign, yielding -10. This method ensures the combined magnitude of negative values is correctly calculated and maintains their sign, aligning with mathematical principles of addition for negative numbers.
When adding a positive number and a negative number, compare their absolute values (ignoring signs). The result takes the sign of the number with the larger absolute value. For instance, adding -7 and 4 gives |-7| - |4| = 3, and the result is -3 because |-7| > |4|. This rule ensures that the overRead more
When adding a positive number and a negative number, compare their absolute values (ignoring signs). The result takes the sign of the number with the larger absolute value. For instance, adding -7 and 4 gives |-7| – |4| = 3, and the result is -3 because |-7| > |4|. This rule ensures that the overall value reflects the stronger magnitude between the positive and negative contributions in the operation.
Adding a number to its additive inverse yields zero because the positive and negative values cancel each other out. For example, 5 + (-5) = 0 and -8 + 8 = 0. This property is fundamental in mathematics, as it helps simplify equations and maintain balance in algebraic expressions. The concept of addiRead more
Adding a number to its additive inverse yields zero because the positive and negative values cancel each other out. For example, 5 + (-5) = 0 and -8 + 8 = 0. This property is fundamental in mathematics, as it helps simplify equations and maintain balance in algebraic expressions. The concept of additive inverses is crucial in arithmetic and algebra for solving problems involving opposites or neutralizing terms.
Zero is the identity element for addition, meaning that adding it to any number leaves the number unchanged. For example, 12 + 0 = 12 and -7 + 0 = -7. This property ensures that zero has no effect on the sum, making it a unique and essential number in arithmetic. Its role is crucial in maintaining tRead more
Zero is the identity element for addition, meaning that adding it to any number leaves the number unchanged. For example, 12 + 0 = 12 and -7 + 0 = -7. This property ensures that zero has no effect on the sum, making it a unique and essential number in arithmetic. Its role is crucial in maintaining the integrity of mathematical operations and simplifying expressions where it appears.
Subtraction of integers can be interpreted by converting the operation into addition of the additive inverse. For example, 10 - 6 becomes 10 + (-6), yielding 4. This method transforms subtraction into addition, simplifying calculations and aligning with standard rules for combining integers. It is pRead more
Subtraction of integers can be interpreted by converting the operation into addition of the additive inverse. For example, 10 – 6 becomes 10 + (-6), yielding 4. This method transforms subtraction into addition, simplifying calculations and aligning with standard rules for combining integers. It is particularly useful in algebra and problem-solving, where subtraction can be eliminated and operations streamlined by replacing them with equivalent addition processes involving inverse values.
Arranging the integers -3, -1, 2, 0, -2, and 3 in ascending order involves placing smaller values first. Negative numbers (-3, -2, -1) are ordered by their decreasing magnitude, followed by zero, and then positive numbers (2, 3). The final order is -3, -2, -1, 0, 2, 3. This arrangement reflects theRead more
Arranging the integers -3, -1, 2, 0, -2, and 3 in ascending order involves placing smaller values first. Negative numbers (-3, -2, -1) are ordered by their decreasing magnitude, followed by zero, and then positive numbers (2, 3). The final order is -3, -2, -1, 0, 2, 3. This arrangement reflects the number line’s structure, where values increase as they move rightward.
What is the additive inverse of a number? Give an example.
The additive inverse of a number is another number that cancels it out to yield zero when both are added together. This concept applies to all integers. For example, the additive inverse of 7 is -7 because 7 + (-7) = 0. Similarly, the additive inverse of -5 is 5, since -5 + 5 = 0. This property is eRead more
The additive inverse of a number is another number that cancels it out to yield zero when both are added together. This concept applies to all integers. For example, the additive inverse of 7 is -7 because 7 + (-7) = 0. Similarly, the additive inverse of -5 is 5, since -5 + 5 = 0. This property is essential in arithmetic and algebra, allowing simplification of equations and balancing expressions by neutralizing terms.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
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Explain how addition can be interpreted as a combination of movements.
Addition represents the combination of two movements on a number line. Starting from zero or another position, move a certain number of steps right for the first number, then continue moving for the second. For instance, starting at 0, moving 2 steps to the right, followed by 3 more steps, lands atRead more
Addition represents the combination of two movements on a number line. Starting from zero or another position, move a certain number of steps right for the first number, then continue moving for the second. For instance, starting at 0, moving 2 steps to the right, followed by 3 more steps, lands at 5, illustrating that 2 + 3 = 5. This visualization helps understand addition intuitively, as combining displacements to find a new position.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
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How can subtraction be interpreted using positions on a number line?
Subtraction on a number line is interpreted as finding the difference between two positions by moving left. Starting at the minuend's position, move steps equal to the subtrahend to the left. For instance, if you begin at 3 and subtract 2, move 2 steps left, arriving at 1, showing 3 - 2 = 1. This moRead more
Subtraction on a number line is interpreted as finding the difference between two positions by moving left. Starting at the minuend’s position, move steps equal to the subtrahend to the left. For instance, if you begin at 3 and subtract 2, move 2 steps left, arriving at 1, showing 3 – 2 = 1. This movement-based explanation makes subtraction tangible and connects it to physical displacement, aiding in understanding and solving arithmetic problems.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
State Brahmagupta’s rule for adding two positive numbers.
According to Brahmagupta’s rule, when two positive numbers are added, their values are simply combined, resulting in another positive number. For example, adding 4 and 6 yields 10, a positive result. This rule applies universally to positive integers and reflects their cumulative nature when combineRead more
According to Brahmagupta’s rule, when two positive numbers are added, their values are simply combined, resulting in another positive number. For example, adding 4 and 6 yields 10, a positive result. This rule applies universally to positive integers and reflects their cumulative nature when combined. It demonstrates that positive values grow larger when added together, forming the foundation for basic arithmetic operations and applications involving quantities or measurements.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
How do you add two negative numbers according to Brahmagupta’s rules?
When adding two negative numbers, Brahmagupta’s rule involves summing their absolute values and assigning a negative sign to the result. For example, adding -4 and -6 involves finding their absolute values (4 and 6), summing them to get 10, and then adding the negative sign, yielding -10. This methoRead more
When adding two negative numbers, Brahmagupta’s rule involves summing their absolute values and assigning a negative sign to the result. For example, adding -4 and -6 involves finding their absolute values (4 and 6), summing them to get 10, and then adding the negative sign, yielding -10. This method ensures the combined magnitude of negative values is correctly calculated and maintains their sign, aligning with mathematical principles of addition for negative numbers.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
When adding a positive number and a negative number, which number’s sign is assigned to the result?
When adding a positive number and a negative number, compare their absolute values (ignoring signs). The result takes the sign of the number with the larger absolute value. For instance, adding -7 and 4 gives |-7| - |4| = 3, and the result is -3 because |-7| > |4|. This rule ensures that the overRead more
When adding a positive number and a negative number, compare their absolute values (ignoring signs). The result takes the sign of the number with the larger absolute value. For instance, adding -7 and 4 gives |-7| – |4| = 3, and the result is -3 because |-7| > |4|. This rule ensures that the overall value reflects the stronger magnitude between the positive and negative contributions in the operation.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
What is the result of adding a number to its additive inverse?
Adding a number to its additive inverse yields zero because the positive and negative values cancel each other out. For example, 5 + (-5) = 0 and -8 + 8 = 0. This property is fundamental in mathematics, as it helps simplify equations and maintain balance in algebraic expressions. The concept of addiRead more
Adding a number to its additive inverse yields zero because the positive and negative values cancel each other out. For example, 5 + (-5) = 0 and -8 + 8 = 0. This property is fundamental in mathematics, as it helps simplify equations and maintain balance in algebraic expressions. The concept of additive inverses is crucial in arithmetic and algebra for solving problems involving opposites or neutralizing terms.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
What happens when zero is added to any number?
Zero is the identity element for addition, meaning that adding it to any number leaves the number unchanged. For example, 12 + 0 = 12 and -7 + 0 = -7. This property ensures that zero has no effect on the sum, making it a unique and essential number in arithmetic. Its role is crucial in maintaining tRead more
Zero is the identity element for addition, meaning that adding it to any number leaves the number unchanged. For example, 12 + 0 = 12 and -7 + 0 = -7. This property ensures that zero has no effect on the sum, making it a unique and essential number in arithmetic. Its role is crucial in maintaining the integrity of mathematical operations and simplifying expressions where it appears.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
How can subtraction of integers be interpreted using addition rules?
Subtraction of integers can be interpreted by converting the operation into addition of the additive inverse. For example, 10 - 6 becomes 10 + (-6), yielding 4. This method transforms subtraction into addition, simplifying calculations and aligning with standard rules for combining integers. It is pRead more
Subtraction of integers can be interpreted by converting the operation into addition of the additive inverse. For example, 10 – 6 becomes 10 + (-6), yielding 4. This method transforms subtraction into addition, simplifying calculations and aligning with standard rules for combining integers. It is particularly useful in algebra and problem-solving, where subtraction can be eliminated and operations streamlined by replacing them with equivalent addition processes involving inverse values.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/
Arrange the following integers in ascending order: -3, -1, 2, 0, -2, 3.
Arranging the integers -3, -1, 2, 0, -2, and 3 in ascending order involves placing smaller values first. Negative numbers (-3, -2, -1) are ordered by their decreasing magnitude, followed by zero, and then positive numbers (2, 3). The final order is -3, -2, -1, 0, 2, 3. This arrangement reflects theRead more
Arranging the integers -3, -1, 2, 0, -2, and 3 in ascending order involves placing smaller values first. Negative numbers (-3, -2, -1) are ordered by their decreasing magnitude, followed by zero, and then positive numbers (2, 3). The final order is -3, -2, -1, 0, 2, 3. This arrangement reflects the number line’s structure, where values increase as they move rightward.
For more NCERT Solutions for Class 6 Math Chapter 10 The Other Side of Zero Extra Questions and Answer:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-6/maths/