Mathematics Concepts: Rational Numbers & Angles

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Questions and Answers

What is the sum of $8 + 3$?

$10$ (correct)

$12$

$11$

$9$

If the ratio of two supplementary angles is $5:7$, what is the measure of the smaller angle?

$55^ ext{o}$ (correct)

$70^ ext{o}$

$100^ ext{o}$

$45^ ext{o}$

How much water did Manoj consume if Vidya consumed $rac{1}{2}$ of the total 8 litres and Pratap consumed $rac{3}{8}$?

4 litres

2 litres (correct)

1 litre

3 litres

What is the result of $6.34 imes 1.27$?

$7.14$ Signup and view all the answers

What is the value of $(-87)$ subtracted from $157$?

$244$ Signup and view all the answers

What is the quotient of $543.213$ divided by $3.1$?

$175.005$ Signup and view all the answers

If a committee buys $43.7$ Kg of wheat at ₹12 per kg, how much total money did they spend?

₹524.40 Signup and view all the answers

What is the simplified result of $[(-847) × 17 + (-847) × 70 + (-847) × 13]$?

$-847 × 100$ Signup and view all the answers

What is the length of cloth used for making one shirt if 25 shirts are prepared from 30 m of cloth?

1.2 m Signup and view all the answers

What should be added to 5.76 - 5.2 to get 1?

0.24 Signup and view all the answers

If 3 kg of sweets are shared equally among 4 students, how many grams does each child receive?

500 g Signup and view all the answers

Which product is greater, 5.1 × 2.4 or 1.5 × 6.2?

1.5 × 6.2 Signup and view all the answers

What is the result of finding $46 × 0.093$ given that $46 × 93 = 4278$?

42.78 Signup and view all the answers

Which of the following is a negative rational number?

-3 Signup and view all the answers

What is the complement of an angle measuring 51 degrees?

49 degrees Signup and view all the answers

How many decimal places are in the product of 99.02 and 6.3?

2 Signup and view all the answers

What is the improper fraction for the whole number 2?

16/8 Signup and view all the answers

Which property is used in the expression -5 + [9 + (-6)] = [(-5) + 9] + (-6)?

Associative property Signup and view all the answers

What is the value of |−17| − |−4|?

13 Signup and view all the answers

What is the reciprocal of 5?

1/5 Signup and view all the answers

What is the result of 0.125 × 100?

12.5 Signup and view all the answers

Study Notes

Rational Numbers

A rational number is any number that can be written as a fraction, where both the numerator and denominator are integers
Example: -3/7 is a negative rational number
Example: 9/83 is a positive rational number
Example: 5/-8 is a negative rational number

Complementary Angles

Complementary angles are two angles that add up to 90 degrees
Example: 51 degrees and 39 degrees are complementary angles because 51 + 39 = 90

Decimal Places

The number of decimal places in a product is equal to the total number of decimal places in the numbers being multiplied
Example: 99.02 has two decimal places, and 6.3 has one decimal place. The product will have three decimal places

Improper Fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator
Example: 16/8 is an improper fraction because 16 is greater than 8

Associative Property

The associative property states that the way numbers are grouped in addition or multiplication does not affect the result
Example: -5 + (9 + -6) = (-5 + 9) + -6

Absolute Value

The absolute value of a number is its distance from zero, regardless of direction
Example: | -17| = 17 and |-4| = 4

Linear Pair

A linear pair is a pair of adjacent angles that have a common side and whose non-common sides are opposite rays.
Example: The angles BAG and BAT are a linear pair, and since the angles in a linear pair add up to 180 degrees, BAT = 180 - BAG = 180 - 55 = 125 degrees.

Reciprocal

To find the reciprocal of a number, divide 1 by that number
Example: The reciprocal of 5/6 is 6/5

Number Line

A number line is a line that represents numbers as points
The further to the right that a point is on the number line, the larger the number represented by that point
The further to the left that a point is on the number line, the smaller the number represented by that point
Example: -5/8 can be represented on the number line by placing a point located 5/8 of the distance between -1 and 0

Adjacent Angles

Adjacent angles are two angles that share a common vertex and a common side.
The two common sides of adjacent angles form a straight line
Example: In a quadrilateral, two angles sharing a side are adjacent

Equivalent Fractions

Equivalent fractions represent the same value, even though they have different numerators and denominators.
Example: 1/2, 2/4, 3/6, 6/12, 9/18 are all equivalent fractions.

Ascending and Descending Order

Ascending order means arranging from smallest to largest
Descending order means arranging from largest to smallest

Adding Fractions

To add fractions with the same denominator, add the numerators and keep the same denominator
Example: 8/2 + 3/2 = (8 + 3)/2 = 11/2

Subtracting Decimals

Line up the decimals and subtract vertically, borrowing if necessary

Dividing Decimals

Convert the divisor to a whole number by moving the decimal point as many places to the right as necessary
Move the decimal point in the dividend the same number of places to the right

Ratio

A ratio is a comparison of two quantities by division
Example: If the ratio of two supplementary angles is 5:7, then the angles are 5x and 7x. We know that the sum of supplementary angles is 180 degrees. So, 5x + 7x = 180, or x = 15. So, the angles are 515 = 75 degrees and 715 = 105 degrees

Product and Quotient

The product of two numbers is the result of their multiplication.
The quotient of two numbers is the result of their division

Case Study - Decimals

The sum of 5.76 (decimal places: two) and 5.2 (decimal places: one) is 10.96 (decimal places: two).
5.1 (decimal places: one) times 2.4 (decimal places: one) is 12.24 (decimal places: two).
1.5 (decimal places: one) times 6.2 (decimal places: one) is 9.3 (decimal places: one).
Since 12.24 is larger than 9.3, then 5.1 × 2.4 is greater than 1.5 × 6.2
To find 46 × 0.093, we can write 0.093 as 93/1000. So, 46 x 0.093 = 46 x 93/1000. Since we know that 46 x 93 = 4278, then 46 x 0.093 = 4278/1000 = 4.278

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Description

This quiz covers essential mathematics concepts including rational numbers, complementary angles, decimal places, improper fractions, and the associative property. Test your understanding and enhance your skills in these foundational topics. Perfect for students looking to solidify their math knowledge.