CTJan27 Online Year 7 - Rational Numbers

1

Which statement about rational numbers is FALSE?

A rational number can always be written as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q eq 0$. A rational number written in decimal form must be either terminating or repeating. The sum of a rational number and an irrational number is always rational. All integers are rational numbers.

2

Identify the number that is NOT rational:

$\sqrt{\frac{25}{36}}$ $-0.121212...$ $4 \pi$ $\frac{0}{-5}$

3

Which of the following fractions, when simplified, results in an integer?

$\frac{42}{5}$ $-\frac{54}{9}$ $\frac{1}{6}$ $\frac{101}{10}$

4

Which rational number is equivalent to $5.4 - 7/2$?

$1.9$ $3.5$ $2.4$ $1.8$

5

Which expression represents a rational number that is NOT an integer?

$\frac{18}{3}$ $\sqrt{121}$ $-1 \frac{5}{6}$ $15.000$

6

Convert the fraction $\frac{13}{80}$ to its decimal equivalent.

$0.138$ $0.1625$ $0.16\overline{25}$ $0.16$

7

Convert $\frac{4}{15}$ to its decimal form, using bar notation if necessary.

$0.26$ $0.\overline{26}$ $0.2\overline{6}$ $0.266$

8

Which of the following fractions will result in a terminating decimal?

$\frac{5}{24}$ $\frac{7}{60}$ $\frac{13}{40}$ $\frac{1}{18}$

9

The fraction $\frac{1}{13}$ results in a repeating decimal. What is the length of the repeating block (the period)?

$3$ $6$ $12$ $13$

10

Convert the mixed number $4 \frac{5}{16}$ to a decimal.

$4.3125$ $4.516$ $4.16$ $4.53125$

11

Which of the following inequalities is TRUE?

$-0.8 > -\frac{4}{5}$ $-1.15 < -1 \frac{1}{8}$ $\frac{5}{6} < 0.83$ $0.\overline{5} < 5/9$

12

Order the following rational numbers from smallest to largest: $\frac{2}{5}, 0.44, \frac{4}{9}$.

$\frac{4}{9}, 0.44, \frac{2}{5}$ $\frac{2}{5}, 0.44, \frac{4}{9}$ $0.44, \frac{2}{5}, \frac{4}{9}$ $\frac{2}{5}, \frac{4}{9}, 0.44$

13

Which of the following numbers is the greatest?

$-2.5$ $-2\frac{1}{3}$ $-2.3$ $-2.\overline{3}$

14

Identify the rational number that lies strictly between $\frac{5}{12}$ and $\frac{1}{2}$.

$\frac{11}{24}$ $\frac{4}{12}$ $0.55$ $\frac{5}{8}$

15

Order the following numbers from greatest to least: $-0.62, -3/5, -7/10$.

$-3/5, -0.62, -7/10$ $-7/10, -0.62, -3/5$ $-0.62, -3/5, -7/10$ $-7/10, -3/5, -0.62$

16

Point $Q$ is located exactly halfway between $-5/6$ and $-1/4$. What is the value of $Q$?

$-13/24$ $-7/12$ $-11/12$ $-1/2$

17

Between which two consecutive integers does the rational number $3 - \frac{15}{4}$ lie?

$-1$ and $0$ $0$ and $1$ $-2$ and $-1$ $-3$ and $-2$

18

A number line is marked with points every $0.25$ units. If you plot the fraction $\frac{1}{3}$, between which two marked points will it fall?

$0.0$ and $0.25$ $0.25$ and $0.5$ $0.5$ and $0.75$ $0.75$ and $1.0$

19

Which rational number is closest to $0$ on the number line?

$-0.11$ $-1/10$ $-1/9$ $-0.09$

20

Consider the location of $-3/8$ on the number line relative to $-1/2$. Which description is accurate?

$-3/8$ is to the left of $-1/2$. $-3/8$ is exactly halfway between $-1/2$ and $-1/4$. $-3/8$ is to the right of $-1/2$. $-3/8$ is equal to $-1/2$.

21

Which statement concerning the closure property for the set of rational numbers ($\mathbb{Q}$) is INCORRECT?

The set $\mathbb{Q}$ is closed under addition. The set $\mathbb{Q}$ is closed under subtraction. The set $\mathbb{Q}$ is closed under division. The set $\mathbb{Q}$ is closed under multiplication.

22

The mathematical statement $\left( \frac{5}{8} \times 3 \right) = \left( 3 \times \frac{5}{8} \right)$ illustrates which fundamental property of rational numbers under multiplication?

Associative property of multiplication Closure property Distributive property Commutative property of multiplication

23

For any two rational numbers $a$ and $b$, how does the operation of subtraction ($a - b$) relate to the Closure and Commutative properties?

Fails Closure and satisfies Commutativity. Satisfies Closure and satisfies Commutativity. Fails Closure and fails Commutativity. Satisfies Closure and fails Commutativity.

24

If $a$ and $b$ are two non-zero rational numbers, which of the following expressions may result in a non-rational or undefined value?

$a \times (b - a)$ $\frac{a + b}{2}$ $a \div \frac{b}{a}$ $\frac{a}{a+b}$

25

Consider the four basic operations: addition ($+$), subtraction ($-$), multiplication ($\times$), and division ($\div$). How many of these operations satisfy BOTH the Closure property AND the Commutative property when applied to the set of rational numbers ($\mathbb{Q}$)?

1 2 3 4

26

Evaluate the expression $\left( \frac{3}{5} \times \left( -\frac{1}{2} \times \frac{10}{3} \right) \right)$. Which property allows you to simplify this calculation by regrouping it as $\left( \left( \frac{3}{5} \times \frac{10}{3} \right) \times \left( -\frac{1}{2} \right) \right)$?

Commutative Property of Multiplication Distributive Property Associative Property of Multiplication Identity Property of Multiplication

27

Given the equation $X \times \left( \frac{5}{8} \right) - X \times \left( \frac{1}{4} \right) = \frac{3}{4}$, use the Distributive Property to factor $X$ out and find its value.

$X = \frac{1}{2}$ $X = 2$ $X = \frac{1}{8}$ $X = 8$

28

Which of the following statements about the properties of rational numbers is FALSE?

The Associative Property holds true for the multiplication of rational numbers. The operation $a \div (b \div c) = (a \div b) \div c$ is generally true for non-zero rational numbers $a, b, c$. The expression $P \left( Q - R \right)$ is equivalent to $PQ - PR$ by the Distributive Property. For rational numbers, the Associative Property of Addition states that $(p+q)+r = p+(q+r)$.

29

Simplify the following expression using the Distributive Property: $-\frac{2}{3} \times \left( \frac{9}{4} - \frac{3}{2} \right)$.

$\frac{1}{2}$ $-\frac{1}{2}$ $1$ $-\frac{7}{6}$

30

Calculate the product $\left( \frac{5}{12} \times \frac{2}{7} \right) \times 24$. Which strategic application of the Associative Property significantly simplifies the calculation?

$\frac{10}{7}$ $\frac{20}{7}$ $\frac{4}{21}$ $\frac{48}{35}$

31

What is the sum of the additive inverse of $\frac{3}{4}$ and the multiplicative identity element?

$\frac{1}{4}$ $\frac{7}{4}$ $-\frac{3}{4}$ $0$

32

If $x$ is the multiplicative inverse of $2.5$, what is the additive inverse of $x$?

$-\frac{2}{5}$ $\frac{5}{2}$ $-\frac{5}{2}$ $\frac{2}{5}$

33

Which pair of properties is primarily illustrated by the steps in the equation: $$\left(-\frac{1}{2} + \frac{1}{2}\right) + (1 \times 9) = 0 + 9 = 9$$

Additive Inverse Property and Multiplicative Identity Property Associative Property and Commutative Property Additive Identity Property and Multiplicative Inverse Property Distributive Property and Closure Property

34

A number $z$ is defined as the additive inverse of $-4$. What is the multiplicative inverse of $z$?

$\frac{1}{4}$ $-4$ $-1$ $4$

35

What is the additive inverse of the multiplicative inverse of $-0.125$?

$8$ $-8$ $\frac{1}{8}$ $-\frac{1}{8}$

36

What is the Least Common Denominator (LCD) of the fractions $\frac{5}{18}$ and $\frac{7}{24}$?

36 48 72 144

37

Find the LCD for the set of rational numbers: $\frac{1}{6}, \frac{3}{10},$ and $\frac{5}{9}$.

30 60 90 180

38

Order the following fractions from least to greatest: $\frac{2}{3}, \frac{5}{8}, \frac{7}{12}$.

$\frac{7}{12}, \frac{5}{8}, \frac{2}{3}$ $\frac{5}{8}, \frac{7}{12}, \frac{2}{3}$ $\frac{2}{3}, \frac{5}{8}, \frac{7}{12}$ $\frac{7}{12}, \frac{2}{3}, \frac{5}{8}$

39

Calculate: $\frac{7}{4} + \frac{5}{6}$. Express the answer as an improper fraction.

$\frac{12}{10}$ $\frac{31}{12}$ $\frac{12}{24}$ $3 \frac{1}{12}$

40

Calculate: $\frac{1}{3} - \left(-\frac{3}{8}\right)$.

$\frac{1}{24}$ $-\frac{1}{24}$ $\frac{17}{24}$ $\frac{7}{8}$

41

Calculate: $\frac{5}{9} - \frac{4}{3}$.

$\frac{7}{9}$ $-\frac{1}{9}$ $-\frac{7}{9}$ $1 \frac{2}{9}$

42

Evaluate the expression: $\frac{1}{2} + \frac{1}{4} - \frac{5}{6}$.

$\frac{1}{12}$ $-\frac{1}{12}$ $\frac{1}{3}$ $-\frac{1}{6}$

43

Calculate: $-\frac{11}{10} - \frac{3}{5}$.

$-\frac{8}{10}$ $-\frac{14}{15}$ $-\frac{17}{10}$ $1 \frac{7}{10}$

44

Simplify: $-\frac{9}{4} - \left(-\frac{5}{2}\right)$.

$-\frac{19}{4}$ $\frac{1}{4}$ $-\frac{1}{4}$ $\frac{19}{4}$

45

Calculate the sum: $2 \frac{3}{5} + 1 \frac{3}{4}$.

$3 \frac{6}{9}$ $4 \frac{7}{20}$ $3 \frac{27}{20}$ $4 \frac{1}{20}$

46

Subtract: $5 \frac{1}{6} - 2 \frac{2}{3}$.

$3 \frac{5}{6}$ $3 \frac{1}{2}$ $2 \frac{1}{2}$ $2 \frac{5}{6}$

47

Calculate: $4 \frac{1}{2} - 1 \frac{7}{8}$.

$3 \frac{3}{8}$ $2 \frac{5}{8}$ $3 \frac{1}{2}$ $2 \frac{3}{8}$

48

Evaluate: $1 \frac{1}{4} + \left(-3 \frac{1}{2}\right)$.

$4 \frac{3}{4}$ $-2 \frac{1}{4}$ $-2 \frac{3}{4}$ $2 \frac{1}{4}$

49

Calculate: $8 - 3 \frac{5}{7}$.

$5 \frac{2}{7}$ $4 \frac{2}{7}$ $4 \frac{5}{7}$ $5 \frac{5}{7}$

50

Evaluate: $-5 \frac{1}{3} + 2 \frac{5}{6}$.

$-3 \frac{1}{6}$ $3 \frac{1}{2}$ $-2 \frac{1}{2}$ $2 \frac{1}{6}$

51

Simplify: $-\left( -\frac{2}{3} \right) + \left( -\frac{1}{6} \right)$.

$\frac{5}{6}$ $\frac{1}{2}$ $-\frac{1}{2}$ $\frac{1}{3}$

52

Find the absolute value of the expression: $\left| -\frac{3}{4} - \frac{1}{8} \right|$.

$-\frac{5}{8}$ $\frac{7}{8}$ $-\frac{7}{8}$ $\frac{5}{8}$

53

Calculate: $\frac{5}{14} + \left(-\frac{9}{7}\right) - \left(-\frac{1}{2}\right)$.

$-\frac{1}{14}$ $\frac{3}{7}$ $-\frac{3}{7}$ $\frac{5}{14}$

54

Let $A = -2 \frac{1}{5}$ and $B = 1 \frac{3}{10}$. Which operation yields the largest result?

$A + B$ $A - B$ $B - A$ $|A| - B$

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