BCT 105 MODULE 102

347.88 m2 15.6 × 22.3 = 347.88

Calculate the area of a rectangle that is 15.6 meters × 22.3 meters. 75.8 m3 75.8 m2 347.88 m2 347.88 m3

16 ft and 25 ft

English/metric measuring tapes commonly come in ______ lengths.

1 cubic yard = 27 cubic feet

How many cubic feet are there in 1 cubic yard?

Divisor

In a division problem, the number that is divided into another number is called the divisor. For example, in the problem 16 ÷ 8 = 2, 8 is the divisor.

Negative numbers

Numbers less than zero. For example, -1, -2, and -3 are negative numbers.

180' 212-32=180. On the Fahrenheit scale, water freezes at 32°F and boils at 212°F. On the Celsius scale, water freezes at 0°C and boils at 100°C.

On the Fahrenheit temperature scale, the difference between the freezing and boiling points of water is _________.

inch-pound system

The English ruler is used by people who use the _______.

Remainder

The amount left over in a division problem. For example, in the problem 34 ÷ 8, 8 goes into 34 four times (8 × 4 = 32) with 2 left over, so the remainder is 2

Area

The amount of space contained in a two-dimensional object, such as a rectangle, circle, or square.

Volume

The amount of space contained within a three-dimensional space.

Circumference

The distance around the curved line that forms the circle.

perimeter

The distance around the outside of a closed shape, such as a rectangle, circle, square, or any irregular shape is the _______.

Perimeter

The distance around the outside of a closed shape, such as a rectangle, circle, square, or any irregular shape.

Numerator

The part of a fraction above the dividing line. For example, the 1 in 1⁄2 is the numerator. It is equivalent to the dividend in a long division problem.

denominator

The part of a fraction below the dividing line. For example, the 2 in 1⁄2 is the denominator. It is equivalent to the divisor in a long division problem.

Decimal

The part of a number represented by digits to the right of a point, called a decimal point. For example, in the number 1.25, .25 is the decimal portion of the number. In this case, it represents the fraction 25⁄100.

To the left

When converting from a smaller metric unit to a larger one, the decimal point must move _________.

obtuse angle

An angle of 105° is a(n) _________.

Adjacent angles

Angles that have the same vertex and one side in common.

Square

(1) A special type of rectangle with four equal sides and four 90° angles. (2) The product of a number multiplied by itself. For example, 25 is the square of 5; 16 is the squareof 4.

3/2 - 5/16 = 24/16 - 5/16 = 19/16

1-1⁄2 - 5⁄16 = _________.

12/16 + 7/8 = 1-5/8

12⁄16 + 7⁄8 = _________.

1⁄6 × 1⁄2 = 1/12

1⁄6 × 1⁄2 = _________.

Straight angle

A 180° angle or flat line.

Circles

A closed curved line drawn at a constant distance around a central point. A circle measures 360°.

Triangle

A closed shape that has three sides and three angles.

Mixed number

A combination of a whole number with a fraction or decimal. Examples of mixed numbers are 3 7/16 and 1 1/4.

700 + 520 + 230 = 1,450

A contractor estimates $700 for lumber, $520 for roofing shingles, and $230 for hardware for a roofing bid. What is the total cost for the materials?

Rectangle

A four-sided shape with four 90° angles. Opposite sides of a rectangle are always parallel and the same length. Adjacent sides

Improper fraction

A fraction whose numerator is larger than its denominator. For example, 6∕3 is an improper fraction.

Pi

A mathematical constant value approximately equal to 3.14 (or 22⁄7) used to determine the area and circumference of circles. It is sometimes symbolized bythe Greek letter π.

Formula

A mathematical process used to solve a problem. For example, the formula for finding the area of a rectangle is Side A times Side B = Area, or A × B = Area.

Equation

A mathematical statement indicating that the value of two mathematical expressions, such as 2 × 2 and 1 × 4, are equal. An equation is written using the equal sign in this manner: 2 × 2 = 1 × 4.

Fraction

A portion of a whole number represented by two numbers. The upper number of a fraction is called the numerator, while the bottom number is called the denominator.

Force

A push or pull on a surface. In this module, a force is the weight of an object or a fluid.

Unit

A standardized quantity used for a particular kind of measurement.

Cube

A three-dimensional object whose sides are all the same length is a _______.

Cube

A three-dimensional object whose sides are all the same length.

Multiplying and Dividing Whole Numbers 100 ÷ 15 = 7

A trainee needs 100 special fasteners. The fasteners come in bags of 15. How many bags will the trainee need?

Equilateral triangle

A triangle that has three equal sides and three equal angles.

Isosceles triangle

A triangle that has two equal sides and two equal angles.

Right triangle

A triangle that includes one 90° angle.

Scalene triangle

A triangle with sides of unequal lengths.

Degree

A unit of measurement for angles. For example, a right angle measures 90°.

Stud

A vertical support inside a wall to which the wall finish material attaches. The base of a stud rests on a horizontal baseplate, and a horizontal cap plate rests on top of a series of studs.

Right angle

An angle that measures 90°. The two lines that form a right angle are perpendicular to each other. This is the angle most used in the crafts.

Acute angle

Any angle greater than 0° and less than 90°.

Obtuse angle

Any angle greater than 90° and less than 180°.

Digit

Any of the numerical symbols 0 to 9.

Base

As it relates to triangles, the base is the line forming the bottom of the triangle.

704 ft3 32 × 11 × 2 = 704

Calculate the volume of a shipping container that is 32' long × 11' wide × 2' deep. 704 ft2 704 ft3 352 ft3 320 ft2

Loadbearing

Carrying a significant amount of weight and/or providing necessary structural support. A loadbearing wall typically carries some portion of the roof's weight and cannot be removed without risking structural failure or collapse.

Whole numbers

Complete number units without fractions or decimal.

Equivalent fractions

Fractions having different numerators and denominators but still having equal values, such as the fractions 1⁄2 and 2⁄4.

Multiplying and Dividing Whole Numbers (10 feet × 12 inch/feet) × (2 feet ×12 inch/feet) ÷ (6 inch x 12 inch) = 40

How many concrete blocks with a height of 6", width of 6", and length of 12" are required to erect a 2' high, 10' long wall?

Dividend

In a division problem, the number being divided is the dividend. For example, in the problem 16 ÷ 8 = 2, 16 is the dividend.

Joists

Lengths of wood or steel that usually support floors, ceilings, or a roof are called _______.

Joists

Lengths of wood or steel that usually support floors, ceilings, or a roof. Roof joists will be at the same angle as the roof itself, while floor and ceiling joists are usually horizontal.

Diagonal

Line drawn from one corner of a rectangle or square to the farthest opposite corner.

True

Metric-only tapes are common outside of the United States. True or False

MDAS

Multiplication, division, addition, subtraction

Positive numbers

Numbers greater than zero. For example, 1, 2, and 3 are positive numbers. Except for zero, any number without a negative (-) sign in front of it is treated as a positive number.

Radius

The distance from a circle's center point to any point on the curved line, or half the width (diameter) of the circle.

diameter

The formula for finding circumference is pi (3.14) × _________. radius area diameter radius × 3

45/32 = 1 13⁄32.

The improper fraction 45⁄32 converts to the mixed number 1 13⁄32.

Diameter

The length of a straight line that crosses from one side of a circle, through the center point, to a point on the opposite side. The diameter is the longest straight line that can be drawn inside a circle.

Solid geometry

The mathematical study of three-dimensional shapes.

Plane geometry

The mathematical study of two-dimensional (flat) shapes.

Vertex

The point at which two or more lines or curves come together.

Mass

The quantity of matter present.

Quotient

The result of a division problem. For example, when dividing 6 by 2, the quotient is 3.

Product

The result of a multiplication problem. For example, the product of 6 × 6 is 36.

Sum

The result of an addition problem. For example, in the problem 7 + 8 = 15, 15 is the sum.

Difference

The result of subtracting one number from another. For example, in the problem 8 - 3 = 5, 5 is the difference between the two numbers.

Angle

The shape made by two straight lines coming together at a point. The space between those two lines is measured in degrees.

Place Value

The value that a digit represents in a whole number, determined by its place within the whole number or by its position relative to the decimal point. In the number 124, the number 2 represents 20, since it is in the tens position.

Bisect

To divide into two equal parts. For example, when an angle is bisected, the two resulting angles are equal.

Invert

To reverse the order or position of numbers. In fractions, inverting means reversing the positions of the numerator and denominator, so 3⁄4 becomes 4⁄3. When dividing by fractions, one fraction is inverted.

Opposite angles

Two angles that are formed by two straight lines crossing. They are always equal.

loadbearing

Walls that carry a significant amount of weight and/or provide necessary structural support are called _______.

35 FEET, 12X2 +23X2=70

What is the distance around a rectangular room with two walls measuring 12 feet and two walls measuring 23 feet?

Finding Equivalent Fractions 1⁄4 = 8/32

Which of the following fraction pairs are equivalent fractions? 1⁄4 and 8⁄32 1⁄4 and 32⁄64 1⁄4 and 3⁄8 1⁄4 and 42⁄128

Weight

______ is the force that an object exerts on a surface due to its mass and the pull of the Earth's gravity.