Addition and Subtraction of Rational Numbers

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What are rational numbers?

Rational numbers are numbers that can be expressed as a fraction or quotient of two integers, where the denominator is not zero.

What is the sum of -5/8 and 1/2 in rational numbers?

To find the sum, convert the fractions to a common denominator: -5/8 + 4/8 = (-5 + 4)/8 = -1/8.

How can you subtract rational numbers?

To subtract rational numbers, find a common denominator and subtract the numerators.

What is the result of adding 3/7 and -2/7?

To add the fractions, combine the numerators: (3 - 2)/7 = 1/7.

What must you remember about the sign when subtracting rational numbers?

Remember to change the sign of the number being subtracted, which is equivalent to adding its opposite.

Calculate the sum of 2/3 and (-5/6).

Find a common denominator: 4/6 + (-5/6) = (4 - 5)/6 = -1/6.

What is the difference between 7/9 and 1/9?

The difference is (7 - 1)/9 = 6/9, which simplifies to 2/3.

Explain the process of finding a common denominator.

A common denominator is a shared multiple of the denominators of the fractions involved. It allows you to add or subtract fractions easily by bringing them to equivalent terms.

What is the sum of -3/4 and -1/8?

Convert to a common denominator: -6/8 + -1/8 = (-6 - 1)/8 = -7/8.

What is the simplified form of the difference between 11/12 and 7/12?

(11 - 7)/12 = 4/12, which simplifies to 1/3.

What happens to the signs of numbers in subtraction?

In subtraction, you switch to addition by adding the opposite of the number being subtracted.

Calculate 5/6 - (-2/3).

Convert -2/3 to an addition term: 5/6 + 4/6 = 9/6 = 3/2.

What is the result of subtracting 3/5 from 9/10?

Bring to common denominators: 9/10 - 6/10 = 3/10.

How do you add two positive rational numbers?

Add the numerators if the denominators are the same, otherwise find a common denominator and then add.

What is the key rule for changing subtraction to addition when working with rational numbers?

Change subtraction to addition of the opposite by inverting the sign of the second number.





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1. What are rational numbers?

Rational numbers are real numbers that cannot be expressed as the square root of any positive integer.

Rational numbers are numbers that can be expressed as a fraction or quotient of two integers, where the denominator is not zero.

Rational numbers are numbers that can be expressed as an infinite decimal sequence.

Rational numbers are only positive integers that can be divided by 1.

2. What is the sum of -5/8 and 1/2 in rational numbers?

1/8

-5/4

-1/8

7/8

3. How can you subtract rational numbers?

To subtract rational numbers, find a common denominator and subtract the numerators.

Subtract the numerators directly without considering the denominators.

Divide the denominators and then multiply the numerators.

Add the rational numbers with opposite signs.

4. What is the result of adding 3/7 and -2/7?

5/7

-1

3/49

1/7

5. What must you remember about the sign when subtracting rational numbers?

Ignore the signs and perform regular subtraction.

Remember to change the sign of the number being subtracted, which is equivalent to adding its opposite.

Convert both numbers to positive before subtracting.

Always subtract smaller magnitude from larger regardless of sign.

6. Calculate the sum of 2/3 and (-5/6).

1/2

-1/6

7/6

1/6

7. What is the difference between 7/9 and 1/9?

2/3

6/18

0

4/9

8. Explain the process of finding a common denominator.

Double the numerators and find the smallest common result.

Use any number larger than the numerators.

A common denominator is a shared multiple of the denominators of the fractions involved. It allows you to add or subtract fractions easily by bringing them to equivalent terms.

Multiply the numerators and denominators directly.

9. What is the sum of -3/4 and -1/8?

-7/8

-5/8

1/4

-9/8

10. What is the simplified form of the difference between 11/12 and 7/12?

1/4

2/3

3/4

1/3

11. What happens to the signs of numbers in subtraction?

In subtraction, you switch to addition by adding the opposite of the number being subtracted.

The signs remain unchanged, and you add both numbers.

You always switch signs for both numbers.

Subtract as if numbers are neutral, ignoring signs.

12. Calculate 5/6 - (-2/3).

1/2

3/6

-1/2

3/2

13. What is the result of subtracting 3/5 from 9/10?

3/10

9/10

6/10

1/2

14. How do you add two positive rational numbers?

Add the numerators if the denominators are the same, otherwise find a common denominator and then add.

Add the denominators first, then the numerators.

Find a common multiple of the numerators.

Multiply both numbers and divide by their common denominator.

15. What is the key rule for changing subtraction to addition when working with rational numbers?

Subtract the smallest number from the largest regardless of their order.

Change subtraction to addition of the opposite by inverting the sign of the second number.

Always switch the signs of both numbers.

Ignore the signs and perform addition directly.