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Questions and Answers
What is the product of (-15) and (-6)?
What is the product of (-15) and (-6)?
- 90 (correct)
- 21
- -90
- -21
What integer, when multiplied by -18, results in 126?
What integer, when multiplied by -18, results in 126?
- 18
- -14
- 7 (correct)
- -7
What is the result of 5 × (-6) × (+7) × (-8)?
What is the result of 5 × (-6) × (+7) × (-8)?
- -560
- 1680
- -1680 (correct)
- 560
Calculate the value of (-90) ÷ (-15).
Calculate the value of (-90) ÷ (-15).
What is the result of the expression -11 × 12 × (-7)?
What is the result of the expression -11 × 12 × (-7)?
What is the value of 240 ÷ (+4)?
What is the value of 240 ÷ (+4)?
What is the value of the expression $5/12 + 1/3 - 2/3 + 3/8$?
What is the value of the expression $5/12 + 1/3 - 2/3 + 3/8$?
Which of the following fractions is equal to 1?
Which of the following fractions is equal to 1?
What is the result of $13/36 - 7/36 - 5/36$?
What is the result of $13/36 - 7/36 - 5/36$?
Which unit of length is appropriate for representing the fraction $3/4$ on a number line?
Which unit of length is appropriate for representing the fraction $3/4$ on a number line?
If OA1 equals 4 cm, what is the label of the point at OA2 if points are marked consecutively in increments of 4 cm?
If OA1 equals 4 cm, what is the label of the point at OA2 if points are marked consecutively in increments of 4 cm?
What is the final result of the expression $2/3 + 9/14 - 13/21$?
What is the final result of the expression $2/3 + 9/14 - 13/21$?
What is the result of the sum (+212) + 86?
What is the result of the sum (+212) + 86?
How much is 0 - (-78)?
How much is 0 - (-78)?
What is the outcome of 500 - (+217)?
What is the outcome of 500 - (+217)?
What is the value of 66 - (-12)?
What is the value of 66 - (-12)?
How much is (-38) + (+80)?
How much is (-38) + (+80)?
What is the result of multiplying -7 and -2?
What is the result of multiplying -7 and -2?
Which statement is true about the product of -5 and 6?
Which statement is true about the product of -5 and 6?
What can be concluded from multiplying the integers -3 and 4?
What can be concluded from multiplying the integers -3 and 4?
When multiplying -8 by -5, which of the following is correct?
When multiplying -8 by -5, which of the following is correct?
What is the absolute value of the product of -2 and -9?
What is the absolute value of the product of -2 and -9?
What is the result of adding 5/12 + 5/12 + 5/12?
What is the result of adding 5/12 + 5/12 + 5/12?
Which of the following represents the result of 8/15 + 3/20?
Which of the following represents the result of 8/15 + 3/20?
What number should be added to 3/16 to get 1/8?
What number should be added to 3/16 to get 1/8?
What is the simplified result of 21/25 + 7/25 + 11/25?
What is the simplified result of 21/25 + 7/25 + 11/25?
What is the result of 6/14 - 5/14?
What is the result of 6/14 - 5/14?
When simplifying 2/5 - 5/16 + 3/16, what is the final result?
When simplifying 2/5 - 5/16 + 3/16, what is the final result?
Which of the following is the result of 15/20 + 7/25?
Which of the following is the result of 15/20 + 7/25?
What number should be subtracted from 4 to get 2/13?
What number should be subtracted from 4 to get 2/13?
What is the absolute value of -42?
What is the absolute value of -42?
Which statement correctly compares +23 and +32?
Which statement correctly compares +23 and +32?
Which expression equals 7?
Which expression equals 7?
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Study Notes
Addition and Subtraction of Fractions
- To add fractions, convert them to like fractions; sum is achieved by adding numerators and keeping the common denominator.
- Shortcut formula for addition: Sum = (numerator1 × (LCM of denominators / denominator1)) + (numerator2 × (LCM of denominators / denominator2)) / LCM of denominators.
- For subtraction, use the same method but replace the sum with difference in the first formula and "+" with "-" in the second.
- Negative fractions have negative numerators; operations are consistent with positive fractions.
Operations on Given Fractions
- Examples of fraction addition and subtraction provided.
- Simplifying results of operations to ensure clarity, especially in comparison problems.
Representation of Fractions on Number Line
- Fractions can be represented on the number line by marking points proportional to their denominators.
- Initial point O represents zero; subsequent fractions are plotted using an appropriate unit length based on the denominator.
Integers and Absolute Values
- Absolute value of an integer is the number without its sign, indicating its magnitude.
- When comparing integers, a greater absolute value indicates a larger number if both are positive, and smaller if both are negative.
- Positive integers are positioned right of zero on the number line while negatives to the left.
Exercise Snippets
- Detailed exercises given, focusing on sums and differences of integers and fractions.
- Practice problems designed to reinforce concepts of absolute values and comparisons.
Multiplication and Division of Integers
- Same-sign integer multiplication yields a positive integer; absolute values remain the same.
- Different-sign integer multiplication results in a negative integer.
- Division follows similar rules as multiplication, reinforcing the significance of signs.
Application of Mathematics in Problem-Solving
- Real-life scenarios illustrated through examples like profit/loss representations and displacement.
- Exercises challenge students to engage with addition, subtraction, multiplication, and division of both integers and fractions.
Summary of Solutions and Answers
- Answers provided for various problems to clarify operations and encourage self-checking.
- Example solutions encourage understanding of core concepts in math operations and their applications.
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