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Questions and Answers

What is the mid-point of the line segment joining the points $\frac{5}{10}$ and $\frac{6}{10}$?

  • $\frac{3}{5}$
  • $\frac{11}{20}$ (correct)
  • $\frac{1}{5}$
  • $\frac{1}{2}$

How many rational numbers can be found between any two rational numbers?

  • None
  • Infinitely many (correct)
  • Only one
  • Exactly two

Which of the following represents a rational number between $\frac{2}{7}$ and $\frac{6}{7}$?

  • $\frac{7}{8}$
  • $\frac{4}{7}$ (correct)
  • $\frac{5}{7}$ (correct)
  • $\frac{1}{3}$

What can be concluded about the integers m and m + 1 where m is an integer?

<p>There is no integer between them (C)</p> Signup and view all the answers

If the points on the number line are $\frac{1}{10}$ and $\frac{1}{20}$, what is their mid-point?

<p>$\frac{1}{15}$ (C)</p> Signup and view all the answers

What is the denominator of the rational number that lies between $\frac{3}{5}$ and $\frac{4}{5}$?

<p>7 (C)</p> Signup and view all the answers

Which of the following best describes rational numbers in relation to integers?

<p>All integers are rational numbers (B), Some rational numbers are not integers (C)</p> Signup and view all the answers

Which of the following is an incorrect representation of a rational number between $\frac{-3}{4}$ and $\frac{5}{4}$?

<p>$\frac{5}{4}$ (A)</p> Signup and view all the answers

What fraction can be represented as a decimal by moving the decimal point two places to the left?

<p>1.350 (D)</p> Signup and view all the answers

Which of the following statements about adding zeros to decimal fractions is true?

<p>It keeps the value of the fraction the same. (B)</p> Signup and view all the answers

What is the first step to convert the fraction $\frac{7}{4}$ into a decimal?

<p>Perform the division to find the quotient. (A)</p> Signup and view all the answers

What will be the decimal representation for the rational number $\frac{11}{5}$?

<p>2.1 (B)</p> Signup and view all the answers

When multiplying a decimal fraction by 1000, where does the decimal point move?

<p>Three places to the right (A)</p> Signup and view all the answers

If 1.35 is expressed as 001.35, what is the decimal form of it?

<p>0.0135 (B)</p> Signup and view all the answers

Which process will lead to the correct conversion of $\frac{2}{5}$ into decimal form?

<p>Divide 2 by 5. (C)</p> Signup and view all the answers

What is the result of dividing a positive integer by a negative integer?

<p>Negative number (B)</p> Signup and view all the answers

What is the quotient of two negative integers?

<p>Positive number (B)</p> Signup and view all the answers

Which equation correctly explains the division of 7 by -2?

<p>$\frac{7}{-2} = -3.5$ (B)</p> Signup and view all the answers

What happens when zero is used as a denominator in a division?

<p>It results in an undefined value (D)</p> Signup and view all the answers

If -13 is divided by -2, what is the result?

<p>6.5 (D)</p> Signup and view all the answers

How is the division of a positive integer by a negative integer expressed?

<p>It can be written as a negative fraction with a positive denominator. (C)</p> Signup and view all the answers

What is the relationship between multiplication and division rules of integers according to the content?

<p>They have similar rules except for zero. (B)</p> Signup and view all the answers

Which of these statements is true regarding the quotient of two positive integers?

<p>It is always a positive number. (C)</p> Signup and view all the answers

What is the highest common factor (HCF) of the numbers 195, 312, and 546?

<p>39 (D)</p> Signup and view all the answers

Using the prime factorization method, what is the HCF of 10, 15, and 12?

<p>1 (D)</p> Signup and view all the answers

When finding the HCF of 60, 12, and 36, what prime factorization leads to the HCF?

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

What is the HCF of any two consecutive even numbers?

<p>2 (B)</p> Signup and view all the answers

In the division method for finding HCF of 144 and 252, what is the last divisor before the remainder becomes zero?

<p>36 (A)</p> Signup and view all the answers

To find the HCF of three numbers using prime factorization, what must be identified?

<p>The common factors (C)</p> Signup and view all the answers

Which statement about the HCF is true?

<p>It is the largest number that divides all the given numbers. (D)</p> Signup and view all the answers

What are opposite rays?

<p>Two rays that have the same origin and form a straight line. (B)</p> Signup and view all the answers

In figure (i), which angles are formed by ray BC and ray BA?

<p>Obtuse angle (B)</p> Signup and view all the answers

What is the sum of the measures of angles in a linear pair?

<p>180° (A)</p> Signup and view all the answers

What distinguishes adjacent angles from non-adjacent angles?

<p>Adjacent angles have a common arm and non-adjacent do not. (A)</p> Signup and view all the answers

Which of the following pairs of angles form a linear pair?

<p>Two angles that have a common arm and their other arms form a straight line. (C)</p> Signup and view all the answers

Which arms of angles ∠PQR and ∠RQS are not common?

<p>PR and QS (C)</p> Signup and view all the answers

Are ray PM and ray PT opposite rays?

<p>No, because they do not form a straight line. (C)</p> Signup and view all the answers

If the measure of angle ∠PQR is 70°, what is the measure of angle ∠RQS?

<p>110° (B)</p> Signup and view all the answers

What is an effect of converting rational numbers into equivalent fractions with larger denominators?

<p>It increases the number of rational numbers that can be expressed between them. (C)</p> Signup and view all the answers

If you multiply the numerator and denominator of a fraction by the same number, what happens to its value?

<p>The value of the fraction remains unchanged. (B)</p> Signup and view all the answers

What is the result of converting the rational numbers $\frac{1}{2}$ and $\frac{3}{5}$ into equivalent fractions with a common denominator before identifying numbers between them?

<p>It makes the fractions easier to compare directly without altering their values. (C)</p> Signup and view all the answers

Which set of rational numbers lies between $\frac{7}{14}$ and $\frac{8}{14}$ when their denominators are increased to 140?

<p>$\frac{71}{140}$ and $\frac{79}{140}$ (D)</p> Signup and view all the answers

What is the general pattern observed when rational numbers are expressed with increasingly larger denominators?

<p>More rational numbers emerge between the two fractions. (B)</p> Signup and view all the answers

Flashcards

Dividing positive by negative integer

When a positive integer is divided by a negative integer, the result is a negative number.

Dividing negative by negative integer

When a negative integer is divided by a negative integer, the result is a positive number.

Division by zero

It's impossible to divide any number by zero.

Quotient of two positive integers

The result of dividing two positive integers is always positive.

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Quotient of two negative integers

The result of dividing two negative integers is always positive.

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Quotient of a positive and negative integer

The result of dividing a positive integer by a negative integer is always negative.

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Additive inverse

Two numbers that add up to zero.

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Integer division rules

The rules for dividing integers are similar to those for multiplying integers.

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Highest Common Factor (HCF)

The largest number that divides exactly into two or more given numbers.

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Finding HCF using Prime Factorization

Find the prime factors of each number; the HCF is the product of the prime factors common to all numbers, each taken to the lowest power.

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HCF of consecutive even numbers

The HCF of any two consecutive even numbers is 2.

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HCF of consecutive odd numbers

The HCF of any two consecutive odd numbers is 1.

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Division method for HCF

A method to find the HCF by successive divisions where the remainder is zero.

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Reducing a fraction to simplest form

Dividing both the numerator and denominator by their HCF to obtain the fraction in its most simplified form.

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Prime Factorization

Finding a number's decomposition into prime numbers.

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Example HCF Calculation

HCF example is a process of working out the HCF of several numbers using two methods: 1) prime factorization and 2) division method

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Rational Number Between Two Numbers

To find rational numbers between two given rational numbers, convert them into equivalent fractions with common denominators. Then, increase the denominators and numerators by the same factor. This creates more spaces between the numbers, revealing additional rational numbers.

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Equivalent Fractions

Fractions that represent the same value even though they have different numerators and denominators. Created by multiplying both the numerator and denominator by the same number.

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Consecutive Rational Numbers

Rational numbers that differ by a single rational number and can be represented with consecutive integers in the numerator with a common denominator.

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Increasing Denominators

Creating equivalent fractions with larger denominators by multiplying both numerator and denominator by the same factor, increasing the precision of the representation.

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Finding Rational Numbers

With larger denominators, more rational numbers appear between two given numbers. This is because equivalent fractions with increased denominators represent the same value, but with finer granularity, revealing more points on the number line.

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Opposite Rays

Two rays that share a common endpoint (origin) and form a straight line.

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Angle in Linear Pair

Two adjacent angles that share a common side and whose non-common sides form a straight line.

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Linear Pair

Two adjacent angles whose non-common sides form a straight line. The sum of their measures is 180 degrees.

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What are supplementary angles?

Two angles whose measures add up to 180 degrees.

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Angle in a Linear Pair: Property

Angles in a linear pair are always supplementary angles.

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Adjacent Angles

Two angles that share a common vertex and a common side.

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Complementary Angles

Two angles whose measures add up to 90 degrees.

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Non-Adjacent Angles

Two angles that do not share a common vertex or a common side.

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Finding middle number

To find the number exactly in the middle of two rational numbers, add them together and divide by 2.

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Rational number between 5/10 and 6/10

The rational number that lies exactly halfway between 5/10 and 6/10 is 11/20.

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Rational number between 2/7 and 6/7

To find a rational number between 2/7 and 6/7, add the two fractions and divide by 2.

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Finding three rational numbers

Given two rational numbers, you can find three rational numbers between them by repeatedly finding the middle number.

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Rational number between -3/4 and +5/4

To find a rational number between -3/4 and +5/4, find the average.

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Rational number between 0 and -3

To find a rational number between 0 and -3, think of dividing the space between 0 and -3 into smaller parts.

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Consecutive integers

Consecutive integers are integers that follow each other in order, with a difference of 1 between them.

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Decimal form of a fraction

Representing a fraction as a decimal number, where the numerator is divided by the denominator. This results in a number with a whole part and a decimal part.

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Decimal point movement in division

Dividing a decimal number by 10, 100, 1000, etc., shifts the decimal point to the left by the same number of places as the number of zeros in the divisor.

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Decimal point movement in multiplication

Multiplying a decimal number by 10, 100, 1000, etc., shifts the decimal point to the right by the same number of places as the number of zeros in the multiplier.

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Adding zeros to a decimal

Adding zeros to the right of a decimal number after the fractional part does not change its value.

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Adding zeros to the left of a decimal

Adding zeros to the left of a decimal number before the integer part does not change its value.

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Rational number decimal form

Every rational number can be expressed as a decimal that either terminates (ends) or repeats.

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Finding rational numbers between two given numbers

To find rational numbers between two given rational numbers, express them as fractions with the same denominator. Then, increase the numerator and denominator of both fractions by the same factor to create new fractions in between.

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Rational numbers are infinite

Between any two rational numbers, there are infinitely many more rational numbers.

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