Math Gr 8 Ch 1 SUM: Whole Numbers
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Questions and Answers

What is the commutative property of addition?

  • a + b = b + a (correct)
  • a + b = a / b
  • a + b = a - b
  • a + b = a × b

    • Which property does not apply to subtraction and division?

  • Commutative property (correct)
  • Additive property of 0
  • Distributive property
  • Associative property

    • What is the associative property of addition?

  • (a + b) + c = a + (b + c) (correct)
  • (a + b) + c = a + (b × c)
  • (a + b) + c = a + (b / c)
  • (a + b) + c = a + (b - c)

    • What is the distributive property of multiplication over addition?

    <p>a × (b + c) = a × b + a × c</p> Signup and view all the answers

    What is the additive property of 0?

    <p>a + 0 = a</p> Signup and view all the answers

    What is the purpose of using the distributive property?

    <p>To break down complex multiplications into simpler parts</p> Signup and view all the answers

    What is the benefit of using the commutative and associative properties?

    <p>To simplify calculations by changing the order of operations</p> Signup and view all the answers

    What is the purpose of using a summary table for multiplication?

    <p>To practice and reinforce the multiplication of various numbers</p> Signup and view all the answers

    What is the definition of a multiple of a number?

    <p>The product of that number and an integer</p> Signup and view all the answers

    What is the process of expressing a number as the product of its prime factors called?

    <p>Prime factorization</p> Signup and view all the answers

    What is the largest number that divides two or more numbers without leaving a remainder called?

    <p>Highest Common Factor</p> Signup and view all the answers

    How do you find the Least Common Multiple (LCM) of two or more numbers?

    <p>Take the highest power of each prime factor that appears in the factorization of each number</p> Signup and view all the answers

    What is a prime number?

    <p>A natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers</p> Signup and view all the answers

    What is the formula to find distance when given speed and time?

    <p>Distance = Speed x Time</p> Signup and view all the answers

    How do you calculate the number of items produced over different time periods when given a production rate?

    <p>Multiply the production rate by the new time period</p> Signup and view all the answers

    What is the definition of a factor?

    <p>A number that divides exactly into another number</p> Signup and view all the answers

    How do you find the Highest Common Factor (HCF) of two or more numbers?

    <p>Take the lowest power of each prime factor that appears in the factorization of each number</p> Signup and view all the answers

    What is the definition of rate?

    <p>Describes how one quantity changes in relation to another</p> Signup and view all the answers

    What is the primary purpose of estimating sums by rounding numbers to the nearest hundred?

    <p>To simplify the sum and make calculations easier</p> Signup and view all the answers

    When estimating products, what is the recommended method for quick approximation?

    <p>Round to the nearest thousand</p> Signup and view all the answers

    What is the main purpose of compensating in rounding off numbers?

    <p>To adjust for errors introduced by rounding</p> Signup and view all the answers

    What is the primary difference between column addition and expanded notation?

    <p>Column addition aligns numbers vertically, while expanded notation breaks down numbers into components</p> Signup and view all the answers

    What is the purpose of borrowing in column subtraction?

    <p>To subtract a larger digit from a smaller digit in a column</p> Signup and view all the answers

    What is the main advantage of multiplying in parts?

    <p>It breaks down the multiplication into smaller, manageable parts</p> Signup and view all the answers

    What is the primary purpose of long division?

    <p>To break down the division into smaller, manageable steps</p> Signup and view all the answers

    What is the result of not compensating for errors introduced by rounding?

    <p>The result is less accurate</p> Signup and view all the answers

    What is the primary advantage of using expanded notation for addition?

    <p>It helps to visualize the components of a number</p> Signup and view all the answers

    What is the main difference between column subtraction and subtraction by parts?

    <p>Column subtraction subtracts each column, while subtraction by parts subtracts corresponding parts</p> Signup and view all the answers

    What is the marked price of an article if the selling price is $80 and the discount is 20%?

    <p>$100</p> Signup and view all the answers

    A recipe calls for a 2:3 ratio of flour to sugar. If you want to make 12 servings, and the original recipe makes 4 servings, how much flour do you need?

    <p>6 units</p> Signup and view all the answers

    A car travels 240 miles in 4 hours. What is its speed?

    <p>60 miles per hour</p> Signup and view all the answers

    If a shirt has a 15% discount, and the marked price is $50, what is the selling price?

    <p>$42.50</p> Signup and view all the answers

    A store buys a product for $120 and sells it for $150. What is the profit percentage?

    <p>20%</p> Signup and view all the answers

    If you want to decrease a quantity in a ratio by 25%, what do you multiply it by?

    <p>0.75</p> Signup and view all the answers

    What is the formula for simple interest?

    <p>Interest = Principal × Rate × Time</p> Signup and view all the answers

    If you want to divide a quantity in a ratio of 2:3, what do you do?

    <p>Sum the parts and divide the total by the sum</p> Signup and view all the answers

    What is the purpose of scaling quantities in a recipe?

    <p>To ensure the right amount of ingredients for a specific number of servings</p> Signup and view all the answers

    How do you calculate the selling price of an item after a discount?

    <p>Subtract the discount amount from the marked price</p> Signup and view all the answers

    What is the formula for calculating simple interest?

    <p>Interest = Principal × Rate × Time</p> Signup and view all the answers

    How do you increase a quantity in a ratio?

    <p>Multiply the quantity by the factor</p> Signup and view all the answers

    What is the purpose of rounding off numbers in calculations?

    <p>To simplify calculations and make them easier</p> Signup and view all the answers

    What is the purpose of comparing ratios?

    <p>To determine which shapes or objects are more similar</p> Signup and view all the answers

    When estimating products, what is the recommended method for quick approximation?

    <p>Rounding to the nearest thousand</p> Signup and view all the answers

    How do you calculate the profit percentage of an item?

    <p>Find the difference between the selling price and the cost price, then divide by the cost price and multiply by 100</p> Signup and view all the answers

    What is the main purpose of compensating in rounding off numbers?

    <p>To correct for errors introduced by rounding</p> Signup and view all the answers

    What is the primary difference between column addition and expanded notation?

    <p>Column addition is used for adding multiple numbers, while expanded notation is used for adding two numbers</p> Signup and view all the answers

    What is the purpose of dividing quantities in a ratio?

    <p>To distribute the total quantity among the parts in the correct proportion</p> Signup and view all the answers

    What is the purpose of borrowing in column subtraction?

    <p>To allow for subtraction of larger numbers from smaller numbers</p> Signup and view all the answers

    How do you rank entities based on their speeds?

    <p>Calculate the speed of each entity by dividing the time by the distance, then rank them from fastest to slowest</p> Signup and view all the answers

    What is the main advantage of multiplying in parts?

    <p>It simplifies calculations and makes them easier</p> Signup and view all the answers

    What is the primary purpose of long division?

    <p>To find the remainder of a division problem</p> Signup and view all the answers

    What is the result of not compensating for errors introduced by rounding?

    <p>The results are less accurate</p> Signup and view all the answers

    What is the primary advantage of using expanded notation for addition?

    <p>It simplifies calculations and makes them easier</p> Signup and view all the answers

    What is the main difference between column subtraction and subtraction by parts?

    <p>Column subtraction is used for subtracting multiple numbers, while subtraction by parts is used for subtracting two numbers</p> Signup and view all the answers

    What is the purpose of finding the prime factorization of a number?

    <p>To express the number as a product of its prime factors</p> Signup and view all the answers

    What is the relationship between the number of factors of a prime number and a composite number?

    <p>A prime number has exactly two factors, while a composite number has more than two factors</p> Signup and view all the answers

    What is the purpose of finding the least common multiple (LCM) of two or more numbers?

    <p>To find the smallest multiple that the numbers have in common</p> Signup and view all the answers

    What is the method used to determine if a number is prime?

    <p>Check if the number can be divided evenly by any prime numbers smaller than its square root</p> Signup and view all the answers

    What is the formula used to calculate distance when given speed and time?

    <p>Distance = Speed × Time</p> Signup and view all the answers

    What is the purpose of calculating the rate of production?

    <p>To compare the outputs of different machines</p> Signup and view all the answers

    What is the method used to describe a pattern in terms of a ratio?

    <p>Identify the relationship between quantities and express it as a fraction</p> Signup and view all the answers

    What is the purpose of finding the highest common factor (HCF) of two or more numbers?

    <p>To find the largest number that divides the numbers without leaving a remainder</p> Signup and view all the answers

    What is the relationship between the rate of production and the time required to produce a certain amount of items?

    <p>The rate of production is inversely proportional to the time required to produce a certain amount of items</p> Signup and view all the answers

    What is the purpose of calculating the ratio of hours worked to share a total amount?

    <p>To find the individual shares of each person</p> Signup and view all the answers

    What is the result of changing the order of numbers in addition or multiplication?

    <p>The result remains the same.</p> Signup and view all the answers

    Which of the following properties is used to simplify complex multiplications?

    <p>Distributive Property</p> Signup and view all the answers

    What is the purpose of using the associative property of addition and multiplication?

    <p>To simplify complex calculations.</p> Signup and view all the answers

    What is the result of adding 0 to any whole number?

    <p>The number remains the same.</p> Signup and view all the answers

    What is the purpose of using a summary table for multiplication?

    <p>To practice and reinforce multiplication facts.</p> Signup and view all the answers

    What is the benefit of using the properties of whole numbers in calculations?

    <p>It makes calculations simpler and more efficient.</p> Signup and view all the answers

    What is the purpose of estimating sums by rounding numbers to the nearest hundred?

    <p>To get a close approximation of the answer.</p> Signup and view all the answers

    What is the benefit of using estimating, approximating, and rounding in calculations?

    <p>It makes calculations simpler and faster.</p> Signup and view all the answers

    Which property allows you to change the order of numbers in an operation without changing the result?

    <p>Commutative Property</p> Signup and view all the answers

    What is the purpose of the summary table for multiplication?

    <p>To practice and reinforce multiplication of various numbers</p> Signup and view all the answers

    When using the distributive property, what is being broken down?

    <p>Complex multiplications into simpler parts</p> Signup and view all the answers

    What is the result of not compensating for errors introduced by rounding?

    <p>An answer that is slightly off</p> Signup and view all the answers

    What is the main benefit of using the associative property of addition?

    <p>To group numbers in a way that does not affect the result</p> Signup and view all the answers

    What is the purpose of estimating sums by rounding numbers to the nearest hundred?

    <p>To get a quick approximation</p> Signup and view all the answers

    What is the primary purpose of using the commutative and associative properties?

    <p>To group numbers in a way that does not affect the result</p> Signup and view all the answers

    What is the benefit of using the distributive property of multiplication?

    <p>To break down complex multiplications into simpler parts</p> Signup and view all the answers

    What is the purpose of rounding off numbers in calculations?

    <p>To simplify numbers and make calculations easier</p> Signup and view all the answers

    What is the main difference between column addition and expanded notation?

    <p>Column addition aligns numbers by place value, while expanded notation breaks down numbers into parts</p> Signup and view all the answers

    What is the purpose of compensating in rounding off numbers?

    <p>To adjust for errors introduced by rounding</p> Signup and view all the answers

    What is the primary advantage of multiplying in parts?

    <p>It breaks down the multiplication into smaller parts, making it easier to calculate</p> Signup and view all the answers

    What is the purpose of borrowing in column subtraction?

    <p>To adjust for errors introduced by borrowing from the next left column</p> Signup and view all the answers

    What is the primary purpose of long division?

    <p>To break down the division into smaller, manageable steps</p> Signup and view all the answers

    What is the result of not compensating for errors introduced by rounding?

    <p>The final answer becomes less accurate</p> Signup and view all the answers

    What is the primary advantage of using expanded notation for addition?

    <p>It breaks down numbers into parts, making it easier to add</p> Signup and view all the answers

    What is the main difference between column subtraction and subtraction by parts?

    <p>Column subtraction aligns numbers by place value, while subtraction by parts breaks down numbers into parts</p> Signup and view all the answers

    What is the purpose of estimating sums by rounding numbers to the nearest hundred?

    <p>To simplify sums and make calculations easier</p> Signup and view all the answers

    What is the primary purpose of finding the Least Common Multiple (LCM) of two or more numbers?

    <p>To add fractions with different denominators.</p> Signup and view all the answers

    What is the relationship between the factors of a number?

    <p>They come in pairs, and each pair multiplies to give the original number.</p> Signup and view all the answers

    What is the process of expressing a number as the product of its prime factors?

    <p>Prime factorization</p> Signup and view all the answers

    What is the largest number that divides two or more numbers without leaving a remainder?

    <p>Highest Common Factor (HCF)</p> Signup and view all the answers

    What is the formula to calculate distance when given speed and time?

    <p>Distance = Speed × Time</p> Signup and view all the answers

    How do you determine if a number is prime?

    <p>By checking if it can be divided evenly by any prime numbers smaller than its square root.</p> Signup and view all the answers

    What is the purpose of finding the Highest Common Factor (HCF) of two or more numbers?

    <p>To simplify fractions to their lowest terms.</p> Signup and view all the answers

    What is the primary purpose of using ratios in pattern recognition?

    <p>To identify the relationship between quantities in patterns.</p> Signup and view all the answers

    What is the primary purpose of using rate in problem-solving?

    <p>To describe how one quantity changes in relation to another.</p> Signup and view all the answers

    What is the primary purpose of comparing ratios?

    <p>To determine the equivalent ratio of two quantities.</p> Signup and view all the answers

    What is the purpose of scaling quantities in a recipe?

    <p>To adjust the quantity of ingredients based on the number of servings</p> Signup and view all the answers

    How do you calculate the discount amount of an item?

    <p>Multiply the marked price by the discount rate and divide by 100</p> Signup and view all the answers

    What is the formula for calculating simple interest?

    <p>Interest = Principal × Rate × Time</p> Signup and view all the answers

    How do you increase a quantity in a ratio?

    <p>Multiply the quantity by the factor needed to reach the desired ratio</p> Signup and view all the answers

    What is the purpose of comparing ratios?

    <p>To determine which objects are more similar</p> Signup and view all the answers

    How do you calculate the profit percentage of an item?

    <p>Profit percentage = (Selling price - Cost price) / Cost price × 100</p> Signup and view all the answers

    What is the purpose of dividing quantities in a ratio?

    <p>To distribute a quantity into parts according to a given ratio</p> Signup and view all the answers

    How do you rank entities based on their speeds?

    <p>By comparing the speeds of each entity from fastest to slowest</p> Signup and view all the answers

    What is the correct method to scale up a recipe that serves 4 people to serve 12 people?

    <p>Multiply the quantity of each ingredient by 3</p> Signup and view all the answers

    A store buys a product for $100 and sells it for $120. What is the profit percentage?

    <p>20%</p> Signup and view all the answers

    A car travels 300 miles in 5 hours. What is its speed?

    <p>60 miles per hour</p> Signup and view all the answers

    What is the selling price of an article if the marked price is $60 and the discount is 25%?

    <p>$45</p> Signup and view all the answers

    What is the correct method to decrease a quantity in a ratio by 20%?

    <p>Multiply the quantity by 0.8</p> Signup and view all the answers

    What is the formula for calculating compound interest?

    <p>Interest = Principal x (1 + Rate)^Time</p> Signup and view all the answers

    A recipe has a ratio of 3:5 of flour to sugar. If you want to make 10 servings, and the original recipe makes 2 servings, how much flour do you need?

    <p>15 units of flour</p> Signup and view all the answers

    What is the correct method to find the value of one part in a ratio?

    <p>Divide the total quantity by the sum of the parts of the ratio</p> Signup and view all the answers

    What is the primary purpose of finding the highest common factor of two or more numbers?

    <p>To simplify fractions to their lowest terms</p> Signup and view all the answers

    A factory produces 480 units of a product in 8 hours. What is the production rate of the factory?

    <p>48 units per hour</p> Signup and view all the answers

    What is the least common multiple of 12 and 15?

    <p>60</p> Signup and view all the answers

    A car travels 360 miles in 6 hours. What is its speed in miles per minute?

    <p>2 miles per minute</p> Signup and view all the answers

    What is the prime factorization of 42?

    <p>2 × 3 × 7</p> Signup and view all the answers

    What is the highest common factor of 24 and 30?

    <p>6</p> Signup and view all the answers

    A bakery sells 240 loaves of bread in 4 hours. What is the rate of sale of bread in loaves per minute?

    <p>2 loaves per minute</p> Signup and view all the answers

    What is the prime factorization of 90?

    <p>2 × 3 × 3 × 5</p> Signup and view all the answers

    A car travels 420 miles in 7 hours. What is its speed in kilometers per hour?

    <p>70 km per hour</p> Signup and view all the answers

    What is the least common multiple of 9 and 12?

    <p>36</p> Signup and view all the answers

    Which of the following properties is used to simplify the calculation of $(a + b) + c$?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the result of applying the commutative property of multiplication to the equation $a imes b = c$?

    <p>b imes a = c</p> Signup and view all the answers

    Which of the following expressions is an example of the distributive property of multiplication over subtraction?

    <p>a imes (b - c) = a imes b - a imes c</p> Signup and view all the answers

    What is the purpose of using a summary table for multiplication?

    <p>To practice and reinforce the multiplication of various numbers</p> Signup and view all the answers

    Which of the following is an example of using the associative property of addition to simplify a calculation?

    <p>(a + b) + c = a + (b + c)</p> Signup and view all the answers

    What is the benefit of using the commutative and associative properties in calculations?

    <p>It simplifies complex calculations by changing the order of operations</p> Signup and view all the answers

    Which of the following is an example of estimating a sum by rounding numbers to the nearest hundred?

    <p>Rounding 247 to 250</p> Signup and view all the answers

    What is the purpose of using the distributive property in calculations?

    <p>To simplify complex calculations by breaking down multiplications into simpler parts</p> Signup and view all the answers

    What is the primary purpose of using the column addition method?

    <p>To simplify the calculation by breaking down the numbers into smaller parts</p> Signup and view all the answers

    What is the benefit of using the expanded notation method for addition?

    <p>It breaks down numbers into smaller parts, making addition easier</p> Signup and view all the answers

    What is the primary purpose of the borrowing technique in subtraction?

    <p>To increase the top digit by 10 while decreasing the digit in the column from which you borrowed by 1</p> Signup and view all the answers

    What is the main advantage of using the multiplication in parts method?

    <p>It breaks down the multiplication into smaller parts, making it easier to calculate</p> Signup and view all the answers

    What is the primary purpose of long division?

    <p>To divide the dividend by the divisor step-by-step, writing down the quotient and remainder</p> Signup and view all the answers

    What is the result of not compensating for errors introduced by rounding numbers?

    <p>The calculation becomes less accurate</p> Signup and view all the answers

    What is the primary purpose of rounding off numbers in calculations?

    <p>To simplify the calculation by approximating the numbers</p> Signup and view all the answers

    What is the main advantage of using expanded notation for addition?

    <p>It breaks down numbers into smaller parts, making addition easier</p> Signup and view all the answers

    What is the primary difference between column subtraction and subtraction by parts?

    <p>Column subtraction aligns numbers by place value, while subtraction by parts subtracts corresponding parts separately</p> Signup and view all the answers

    What is the primary purpose of compensating in rounding off numbers?

    <p>To adjust for errors introduced by rounding numbers</p> Signup and view all the answers

    What is the primary purpose of finding the highest common factor of two numbers?

    <p>To simplify fractions to their lowest terms</p> Signup and view all the answers

    A machine can produce 120 units of a product in 4 hours. What is the ratio of the number of units produced to the time taken?

    <p>30:4</p> Signup and view all the answers

    What is the smallest multiple that 12 and 15 have in common?

    <p>180</p> Signup and view all the answers

    A number is divided into two parts in a ratio of 3:5. If the smaller part is 18, what is the larger part?

    <p>30</p> Signup and view all the answers

    What is the prime factorization of 42?

    <p>2 × 3 × 7</p> Signup and view all the answers

    A car travels from City A to City B at an average speed of 60 km/h. If the distance between the two cities is 240 km, how long does the journey take?

    <p>4 hours</p> Signup and view all the answers

    What is the largest number that divides 24 and 30 without leaving a remainder?

    <p>6</p> Signup and view all the answers

    A recipe calls for a 3:4 ratio of sugar to flour. If you need 12 cups of sugar, how much flour do you need?

    <p>16 cups</p> Signup and view all the answers

    What is the result of dividing a number by its highest common factor?

    <p>A smaller number</p> Signup and view all the answers

    What is the purpose of finding the prime factorization of a number?

    <p>To express a composite number as a product of prime factors</p> Signup and view all the answers

    What is the purpose of using the commutative and associative properties of addition and multiplication?

    <p>To simplify calculations by changing the order or grouping of operations</p> Signup and view all the answers

    What is the benefit of using the distributive property of multiplication over addition?

    <p>It allows us to break down complex multiplications into simpler parts</p> Signup and view all the answers

    What is the purpose of using a summary table for multiplication?

    <p>To practice and reinforce the multiplication of various numbers</p> Signup and view all the answers

    What is the outcome of not compensating for errors introduced by rounding?

    <p>The result may be inaccurate or approximate</p> Signup and view all the answers

    What is the main advantage of using expanded notation for addition?

    <p>It allows for easier rearrangement of numbers</p> Signup and view all the answers

    What is the purpose of estimating sums by rounding numbers to the nearest hundred?

    <p>To get a close approximation of the result without doing the exact calculation</p> Signup and view all the answers

    What is the main purpose of using the associative property of multiplication?

    <p>To simplify complex multiplications by changing the order of operations</p> Signup and view all the answers

    What is the purpose of using the additive property of 0?

    <p>To verify that a number remains unchanged when 0 is added to it</p> Signup and view all the answers

    When using the compensation method in rounding off numbers, what is the primary reason for adjusting the rounded sum or difference?

    <p>To correct for the error introduced by rounding each number.</p> Signup and view all the answers

    What is the primary advantage of using the expanded notation method for addition?

    <p>It enables the calculation of partial sums before adding them up.</p> Signup and view all the answers

    When using the borrowing technique in column subtraction, what happens to the digit in the top number when borrowing from the next left column?

    <p>It is increased by 10.</p> Signup and view all the answers

    What is the primary purpose of multiplying in parts when using the multiplication in parts method?

    <p>To simplify the calculation by breaking it down into smaller parts.</p> Signup and view all the answers

    When using the step-by-step division method, what is the primary purpose of dividing the number step-by-step?

    <p>To break down the division into smaller, manageable steps.</p> Signup and view all the answers

    What is the primary advantage of using column addition when adding numbers?

    <p>It allows for easier carrying over of values to the next column.</p> Signup and view all the answers

    When using the estimation method for calculating sums, what is the primary purpose of rounding numbers to the nearest hundred?

    <p>To obtain a quick approximation of the sum.</p> Signup and view all the answers

    What is the primary difference between column subtraction and subtraction by parts?

    <p>Column subtraction aligns numbers by place value, while subtraction by parts breaks down numbers into their components.</p> Signup and view all the answers

    When using the multiplication in parts method, what is the primary purpose of carrying over values to the next column?

    <p>To write down the partial product and carry over extra values to the next column.</p> Signup and view all the answers

    What is the primary purpose of using the rounding off method for calculating products?

    <p>To obtain a quick approximation of the product.</p> Signup and view all the answers

    A bakery wants to make 18 servings of a cake. The original recipe makes 6 servings and requires a 3:4 ratio of flour to sugar. How much flour do they need?

    <p>9 units of flour</p> Signup and view all the answers

    A shirt has a marked price of $60 and a discount of 25%. What is the selling price?

    <p>$45</p> Signup and view all the answers

    A store buys a product for $80 and sells it for $120. What is the profit percentage?

    <p>30%</p> Signup and view all the answers

    A car travels 360 miles in 6 hours. How does its speed compare to a bike that travels 120 miles in 4 hours?

    <p>The car is faster</p> Signup and view all the answers

    A recipe has a 2:5 ratio of flour to sugar. If you want to decrease the quantity of flour by 20%, what factor do you multiply it by?

    <p>0.8</p> Signup and view all the answers

    A book has a marked price of $100 and a discount of 15%. What is the selling price?

    <p>$85</p> Signup and view all the answers

    A store buys a product for $90 and sells it for $108. What is the profit percentage?

    <p>20%</p> Signup and view all the answers

    A car travels 240 miles in 4 hours. If it travels at the same speed, how far will it travel in 6 hours?

    <p>360 miles</p> Signup and view all the answers

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