Math Gr 8 Term 1 Test

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

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

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

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

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

<p>To write down the last digit of the product and carry over any extra value to the next column</p> Signup and view all the answers

<p>A number that has exactly two distinct positive divisors: 1 and itself</p> Signup and view all the answers

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

<p>To find a common denominator for adding fractions</p> Signup and view all the answers

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

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

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

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

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

<p>To find the time required to complete a task</p> Signup and view all the answers

<p>To make quick decisions and check the reasonableness of results</p> Signup and view all the answers

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

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

<p>Expanded Notation</p> Signup and view all the answers

<p>Column Subtraction</p> Signup and view all the answers

<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

<p>Multiplication in Parts</p> Signup and view all the answers

<p>Long Division</p> Signup and view all the answers

<p>The remainder</p> Signup and view all the answers

<p>The sum of the errors introduced by rounding each number</p> Signup and view all the answers

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

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

<p>&gt;</p> Signup and view all the answers

<p>Depends on the integers</p> Signup and view all the answers

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

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

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

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

<p>Both positive and negative</p> Signup and view all the answers

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

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

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

<p>A number that is subtracted from the integer to get 0</p> Signup and view all the answers

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

<p>To express the total amount to be shared in the ratio of hours worked</p> Signup and view all the answers

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

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

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

<p>The additive inverse of the integer</p> Signup and view all the answers

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

<p>A positive integer</p> Signup and view all the answers

<p>The distance between the number and 0 on the number line</p> Signup and view all the answers

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

<p>To scale up or down the quantities of ingredients as needed</p> Signup and view all the answers

<p>The distance between the number and zero on the number line</p> Signup and view all the answers

<p>To represent the same value</p> Signup and view all the answers

<p>The value increases</p> Signup and view all the answers

<p>A positive integer</p> Signup and view all the answers

<p>By finding the difference between the selling price and the cost price, dividing by the cost price, and multiplying by 100</p> Signup and view all the answers

<p>A negative integer</p> Signup and view all the answers

<p>Dividing both the numerator and the denominator by their greatest common divisor</p> Signup and view all the answers

<p>( \frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d} )</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>A combination of a whole number and a fraction</p> Signup and view all the answers

<p>( \text{Percentage} = \frac{a}{b} \times 100 )</p> Signup and view all the answers

<p>Equivalent fractions</p> Signup and view all the answers

<p>( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} )</p> Signup and view all the answers

<p>Multiplying the fractions together</p> Signup and view all the answers

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

<p>( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} )</p> Signup and view all the answers

<p>(Part ÷ Whole) × 100</p> Signup and view all the answers

<p>Align the decimal points</p> Signup and view all the answers

<p>To eliminate the decimals</p> Signup and view all the answers

<p>Convert the divisor to a whole number</p> Signup and view all the answers

<p>To adjust the decimal place correctly</p> Signup and view all the answers

<p>Convert the total amount to a decimal and divide</p> Signup and view all the answers

<p>To find the total weight</p> Signup and view all the answers

<p>Aligning decimal points</p> Signup and view all the answers

<p>To find the total cost</p> Signup and view all the answers

<p>Adjust the result by dividing by the appropriate power of 10</p> Signup and view all the answers

<p>$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$</p> Signup and view all the answers

<p>$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$</p> Signup and view all the answers

<p>Dividing both the numerator and denominator by their greatest common divisor</p> Signup and view all the answers

<p>$\frac{a}{b} = \frac{a}{b} \times 100$</p> Signup and view all the answers

<p>$\left( \frac{a}{b} \right) \times \text{Number}$</p> Signup and view all the answers

<p>Add the percentage of the original number to the original number</p> Signup and view all the answers

<p>$\left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$</p> Signup and view all the answers

<p>To represent parts of a whole</p> Signup and view all the answers

<p>A fraction of 100</p> Signup and view all the answers

<p>$\frac{\text{Percentage}}{100}$</p> Signup and view all the answers

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

<p>To regroup numbers when adding or multiplying</p> Signup and view all the answers

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

<p>Changing the order of numbers in addition does not change the result</p> Signup and view all the answers

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

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

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

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

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

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

<p>To write down the last digit of the product</p> Signup and view all the answers

<p>Take the highest power of each prime factor</p> Signup and view all the answers

<p>To compare the time taken by different machines</p> Signup and view all the answers

<p>As a fraction in its lowest terms</p> Signup and view all the answers

<p>It has exactly two distinct positive divisors: 1 and itself</p> Signup and view all the answers

<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

<p>To calculate the time taken to travel a certain distance</p> Signup and view all the answers

<p>It allows you to divide numbers step-by-step, starting with the leftmost digits</p> Signup and view all the answers

<p>Multiplying the number of ingredients by the ratio of ingredients to servings</p> Signup and view all the answers

<p>By comparing their ratios</p> Signup and view all the answers

<p>Profit percentage = (selling price - cost price) / cost price * 100</p> Signup and view all the answers

<p>May be positive or negative</p> Signup and view all the answers

<p>To find the value of one part</p> Signup and view all the answers

<p>Simple interest = principal * rate * time</p> Signup and view all the answers

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

<p>To determine which entity is the fastest</p> Signup and view all the answers

<p>Always positive</p> Signup and view all the answers

<p>To find the distance between the number and zero on the number line</p> Signup and view all the answers

<p>To check the reasonableness of results</p> Signup and view all the answers

<p>Subtract the error from the rounded result</p> Signup and view all the answers

<p>Expanded notation</p> Signup and view all the answers

<p>To make subtraction easier</p> Signup and view all the answers

<p>Multiplication in parts</p> Signup and view all the answers

<p>Long division</p> Signup and view all the answers

<p>The remainder</p> Signup and view all the answers

<p>The sum of the errors introduced by rounding each number</p> Signup and view all the answers

<p>To simplify addition by aligning numbers by their place values</p> Signup and view all the answers

<p>Column subtraction</p> Signup and view all the answers

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

<p>It decreases the value</p> Signup and view all the answers

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

<p>Depends on the values of the integers</p> Signup and view all the answers

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

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

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

<p>A negative version of the integer</p> Signup and view all the answers

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

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

<p>a/b ÷ c/d = ad/bc</p> Signup and view all the answers

<p>The product of the numerators divided by the product of the denominators</p> Signup and view all the answers

<p>a/b = a ÷ GCD(a, b)/b ÷ GCD(a, b)</p> Signup and view all the answers

<p>Percentage = a/b × 100</p> Signup and view all the answers

<p>Percentage of a number = (Percentage/100) × Number</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>Increased Value = Original Number + (Percentage/100) × Original Number</p> Signup and view all the answers

<p>To find a common denominator</p> Signup and view all the answers

<p>Percentage Change = (New Value - Original Value)/Original Value × 100</p> Signup and view all the answers

<p>Multiply the fractions together</p> Signup and view all the answers

<p>A fraction with the same numerator and a new denominator</p> Signup and view all the answers

<p>Fraction = Percentage/100</p> Signup and view all the answers

<p>Percentage = (a/b) × 100</p> Signup and view all the answers

<p>A fraction with the product of the numerators and denominators</p> Signup and view all the answers

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

<p>The original fraction</p> Signup and view all the answers

<p>To make it easier to work with</p> Signup and view all the answers

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

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

<p>Its negative counterpart</p> Signup and view all the answers

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

<p>1</p> Signup and view all the answers

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

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

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

<p>To make it easier to work with in calculations</p> Signup and view all the answers

<p>To multiply a number by a sum of numbers</p> Signup and view all the answers

<p>Its distance from zero on the number line</p> Signup and view all the answers

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

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

<p>(Part / Whole) × 100</p> Signup and view all the answers

<p>Align the decimal points</p> Signup and view all the answers

<p>To eliminate the decimals</p> Signup and view all the answers

<p>Convert the divisor to a whole number by multiplying both numbers by a power of 10</p> Signup and view all the answers

<p>To divide the amount equally among the people</p> Signup and view all the answers

<p>Convert the numbers to whole numbers, multiply, and then adjust the result</p> Signup and view all the answers

<p>To adjust the decimal place to its correct position</p> Signup and view all the answers

<p>Convert the divisor to a whole number by multiplying both numbers by a power of 10</p> Signup and view all the answers

<p>To make the division easier to perform</p> Signup and view all the answers

<p>Align the decimal points</p> Signup and view all the answers

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

<p>(2 × 3) × 4</p> Signup and view all the answers

<p>3 × 4 + 3 × 2</p> Signup and view all the answers

<p>Adding 0 to a number does not change the result.</p> Signup and view all the answers

<p>2 + (3 + 4)</p> Signup and view all the answers

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

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

<p>Multiplying a number by 1 does not change the result.</p> Signup and view all the answers

<p>To make quick decisions and check the reasonableness of results</p> Signup and view all the answers

<p>It breaks down numbers into their component parts</p> Signup and view all the answers

<p>To rearrange parts to make subtraction easier</p> Signup and view all the answers

<p>It adjusts for the errors introduced by rounding</p> Signup and view all the answers

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

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

<p>To align numbers by their place values and add each column</p> Signup and view all the answers

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

<p>To simplify the calculation by making it easier to add or subtract</p> Signup and view all the answers

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

<p>A negative integer</p> Signup and view all the answers

<p>A negative integer</p> Signup and view all the answers

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

<p>A positive integer</p> Signup and view all the answers

<p>The sum is always zero</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

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

<p>A negative integer</p> Signup and view all the answers

<p>The product is always positive</p> Signup and view all the answers

<p>A negative integer</p> Signup and view all the answers

<p>To adjust the quantity of ingredients for a specific number of servings</p> Signup and view all the answers

<p>Interest is calculated on the principal only</p> Signup and view all the answers

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

<p>Always negative</p> Signup and view all the answers

<p>To find the value of each part of the ratio</p> Signup and view all the answers

<p>Profit is calculated as a percentage of the cost price</p> Signup and view all the answers

<p>To determine the distance of the number from zero</p> Signup and view all the answers

<p>Interest is calculated on the principal and any accrued interest</p> Signup and view all the answers

<p>Always zero</p> Signup and view all the answers

<p>To find the selling price of the article</p> Signup and view all the answers

<p>Every composite number can be expressed as a product of its prime factors, and this representation is unique, apart from the order of the factors.</p> Signup and view all the answers

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

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

<p>Multiples of a number form a sequence where each term is that number multiplied by an integer.</p> Signup and view all the answers

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

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

<p>Step-by-step division</p> Signup and view all the answers

<p>The LCM is the largest number that divides two or more numbers without leaving a remainder.</p> Signup and view all the answers

<p>To find the common denominator for adding fractions.</p> Signup and view all the answers

<p>Partial products</p> Signup and view all the answers

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

<p>Always negative</p> Signup and view all the answers

<p>To change the sign of an integer</p> Signup and view all the answers

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

<p>Always zero</p> Signup and view all the answers

<p>To ensure accurate placement of the decimal point in the result</p> Signup and view all the answers

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

<p>Always negative</p> Signup and view all the answers

<p>Convert the total amount to a decimal</p> Signup and view all the answers

<p>To multiply a number by a sum of numbers</p> Signup and view all the answers

<p>To make the divisor a whole number</p> Signup and view all the answers

<p>Divide the result by the power of 10</p> Signup and view all the answers

<p>Always positive</p> Signup and view all the answers

<p>The distance between the number and zero on the number line</p> Signup and view all the answers

<p>Align decimal points, add corresponding digits, place the decimal point</p> Signup and view all the answers

<p>To calculate the cost per unit weight</p> Signup and view all the answers

<p>Convert the divisor to a whole number</p> Signup and view all the answers

<p>(Part/Whole) × 100</p> Signup and view all the answers

<p>To ensure accurate placement of the decimal point</p> Signup and view all the answers

<p>Multiply both by the same power of 10</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>Fraction × 100</p> Signup and view all the answers

<p>The numerator and denominator are divided by 2</p> Signup and view all the answers

<p>Percentage × Number</p> Signup and view all the answers

<p>The number is decreased by 5%</p> Signup and view all the answers

<p>((New Value - Original Value) ÷ Original Value) × 100</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>Percentage ÷ 100</p> Signup and view all the answers

<p>The quotient of the two fractions</p> Signup and view all the answers

<p>First Fraction × Second Fraction</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>Divide both the numerator and the denominator by their greatest common divisor</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>Divide the numerator by the denominator and multiply by 100</p> Signup and view all the answers

<p>0</p> Signup and view all the answers

<p>Multiply both the numerator and the denominator by a non-zero integer</p> Signup and view all the answers

<p>2 times the original fraction</p> Signup and view all the answers

<p>Multiply the whole number part by the denominator and add the numerator</p> Signup and view all the answers

<p>The original fraction multiplied by the whole number</p> Signup and view all the answers

<p>Multiply the fractions together</p> Signup and view all the answers

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

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

<p>2 × 3 + 2 × 4</p> Signup and view all the answers

<p>Associative property of addition</p> Signup and view all the answers

<p>2 × 3 - 2 × 4</p> Signup and view all the answers

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

<p>Distributive property of multiplication over addition</p> Signup and view all the answers

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

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

<p>390</p> Signup and view all the answers

<p>Column Subtraction</p> Signup and view all the answers

<p>To make subtraction easier by borrowing from higher place values</p> Signup and view all the answers

<p>Multiplication in Parts</p> Signup and view all the answers

<p>A negative integer</p> Signup and view all the answers

<p>The sum of the errors introduced by rounding each number</p> Signup and view all the answers

<p>$2b$</p> Signup and view all the answers

<p>To make the division easier to understand</p> Signup and view all the answers

<p>A remainder</p> Signup and view all the answers

<p>A positive integer</p> Signup and view all the answers

<p>$-ab$</p> Signup and view all the answers

<p>To make the calculation easier and faster</p> Signup and view all the answers

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

<p>Expanded Notation</p> Signup and view all the answers

<p>$-a - b$</p> Signup and view all the answers

<p>A positive integer</p> Signup and view all the answers

<p>$a^2 - b^2$</p> Signup and view all the answers

<p>A negative integer</p> Signup and view all the answers

<p>$2a$</p> Signup and view all the answers

<p>The product will be incorrect</p> Signup and view all the answers

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

<p>The quotient will be 1</p> Signup and view all the answers

<p>The LCM is always greater than the HCF</p> Signup and view all the answers

<p>To find the time required to complete a task</p> Signup and view all the answers

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

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

<p>To find the common denominator for adding fractions</p> Signup and view all the answers

<p>The result is always 1</p> Signup and view all the answers

<p>To find the distance traveled given the speed and time</p> Signup and view all the answers

<p>The ratio of the hours worked by each person to the total hours worked</p> Signup and view all the answers

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

<p>4:9</p> Signup and view all the answers

<p>2:1</p> Signup and view all the answers

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

<p>$90</p> Signup and view all the answers

<p>$96</p> Signup and view all the answers

<p>3%</p> Signup and view all the answers

<p>5 or -5</p> Signup and view all the answers

<p>One is positive and the other is negative</p> Signup and view all the answers

<p>A positive integer</p> Signup and view all the answers

<p>$-c$</p> Signup and view all the answers

<p>A positive integer</p> Signup and view all the answers

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

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

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

<p>A negative integer</p> Signup and view all the answers

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

<p>A negative integer</p> Signup and view all the answers

<p>A positive integer</p> Signup and view all the answers

<p>A fraction with a numerator equal to the product of the numerators and a denominator equal to the product of the denominators</p> Signup and view all the answers

<p>To find the common denominator</p> Signup and view all the answers

<p>A fraction with a numerator equal to the product of the numerators and a denominator equal to the product of the denominators</p> Signup and view all the answers

<p>To reduce the fraction to its simplest form</p> Signup and view all the answers

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

<p>To express the fraction as a part of a whole</p> Signup and view all the answers

<p>A fraction with the same value</p> Signup and view all the answers

<p>To add or subtract fractions</p> Signup and view all the answers

<p>A fraction with a value of 1</p> Signup and view all the answers

<p>A fraction with a value of 1</p> Signup and view all the answers

<p>Convert only the divisor to a whole number, then divide and adjust the result.</p> Signup and view all the answers

<p>To eliminate the decimals from the numbers.</p> Signup and view all the answers

<p>Align the decimal points, then add corresponding digits.</p> Signup and view all the answers

<p>(Part ÷ Whole) × 100</p> Signup and view all the answers

<p>To ensure the correct placement of the decimal point in the result.</p> Signup and view all the answers

<p>Use the correct techniques for addition, subtraction, multiplication, and division of decimal fractions.</p> Signup and view all the answers

<p>To adjust the decimal place in the result to the correct position.</p> Signup and view all the answers

<p>Convert the total amount to a decimal, then divide.</p> Signup and view all the answers

<p>To eliminate the decimals from the divisor.</p> Signup and view all the answers

<p>Multiply the volume by the weight per unit volume, then multiply by the cost per unit weight.</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>( \frac{a}{b} \times 100 )</p> Signup and view all the answers

<p>Multiplying the fractions</p> Signup and view all the answers

<p>( \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)} )</p> Signup and view all the answers

<p>( \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 )</p> Signup and view all the answers

<p>( \frac{\text{Percentage}}{100} )</p> Signup and view all the answers

<p>( \left( \frac{\text{Percentage}}{100} \right) \times \text{Whole} )</p> Signup and view all the answers

<p>( \text{Original Number} + \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right) )</p> Signup and view all the answers

<p>( \text{Original Number} - \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right) )</p> Signup and view all the answers

<p>( \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 )</p> Signup and view all the answers