Transcript Fractions, Shapes and Perimeter

Fractions, Shapes and
Perimeter
Math 10-3
Ch.3 Measurement
Changing Mixed Numbers to Improper
Fractions
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Remember mixed numbers? A mixed number is a whole number plus a
fraction part.
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An improper fraction is where the number in the numerator is larger
than the number in the denominator.
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To change from a mixed fraction to an improper fraction, use the
following steps:
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1) Multiply the denominator and the whole number together
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2) Add the numerator to this number
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3) Write your answer over the original denominator.
Ex1. Write the following mixed number as
an improper fraction.
3
8
4
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4 x 8 = 32
32 + 3 = 35
Answer:
35
4
How do we go from improper fractions
back to mixed numbers?

1) Divide the numerator by the denominator on your
calculator. The number in front of the decimal is the
whole number. This number goes in front of your
fraction.
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2) Multiply the denominator by the whole number.
Subtract the original numerator from your answer.
This is the numerator of your mixed number.
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3) Write out your answer with the original
denominator.
Ex.2 Write the following improper fraction
as a mixed number
56
5
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56 5 = 11.2  11 is the whole number.
11 x 5 = 55
56 – 55 = 1  1 is the remainder
Answer:
1
11
5
Being able to divide fractions is an important skill in many trades. To
divide fractions by fractions, use the following steps:

1) Find the reciprocal of the SECOND fraction.
Reciprocal means to “flip” the numerator and
denominator
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2) Multiply the two fractions together. numerator x
numerator OVER denominator X denominator
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3) Reduce the answer as needed.
Ex3. Solve the following…
1 2

4 3
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Find the reciprocal of the second fraction and
then multiply.
1 3
x
4 2
1x3 3

4 x2 8
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People who work in the trades, such as
carpenters, plumbers and electricians often
use measurements to solve problems. There
are usually many 2-D and 3-D shapes
involved in measurements.

2-D means “two-dimensional”; These
shapes are flat, and you can draw them on a
piece of paper.
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When we work with 2-D shapes we are
usually considering perimeter and/or area.
2-D drawings are used for floor plans of
buildings, yards, parks, etc.
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3-D means “three-dimensional”; These shapes have
depth, and are difficult to draw on a piece of paper.
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A three dimensional shapes would include a box,
soup can, ball, most of the objects that we use in our
every day lives. When we work with 3-D shapes we
are usually considering surface area and/or
volume. We will discuss 3-D shapes more next
week.
Basic Shapes
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Quadrilateral - a shape with four sides, such
as a square, rectangle, parallelogram, or
trapezoid.
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Square - all sides are of an equal length
Basic Shapes
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Rectangle – two sides are the same length,
and the other two are the same length. We
usually call this width and length
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Parallelogram – usually described as a
“slanted” rectangle. Parallel means that two
(or more) lines will never cross. Squares and
rectangles are technically parallelograms.
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Trapezoid - a four sided shape with only one set of
parallel lines.
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Triangle – Three sided figure.
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*note: The small “ticks” or lines on the shapes indicate that those sides
are of equal length. For example, the sides with one “tick” are the same
length. The sides with two “ticks” are the same length.
Perimeter
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Imagine that you start at one corner of a
football field. If you walk around the outside
line, you will have found the perimeter of the
field.
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Perimeter – the distance around the outside
of an object. You can calculate the perimeter
of an shape by adding up the lengths of each
side of the object.
Ex4. What is the name of and
perimeter of the following shape?
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Trapezoid!
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Perimeter = 4 + 2 + 7 + 2 = 15 cm
*Always include the units of measurement
in your answer!
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Ex5. Marcel wants to put an ice rink in his back yard. He
determines that the length of the rink will be 25 ft and the
width will be 10 ft. What is the perimeter of his ice rink?
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*When solving measurement word problems,
always sketch it out!
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Perimeter = 25 + 10 + 25 + 10 = 70 ft