Fraction and Decimal Equivalence in Math

 
 
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[
OBJECTIVE
]
 
The student will be able to express a fraction
with a denominator of 10 as an equivalent
fraction with a denominator of 100 and use
this technique to add two fractions with
respective denominators 10 and 100. The
student will be able to use decimal notation
for fractions with denominators of 10 and 100.
[
MY
 
SKILLS
]
 
Basic understanding of a fraction
Understanding of place value
[
ESSENTIAL
 
QUESTIONS
]
 
1.
What are equivalent fractions?
2.
How do you change a fraction to a decimal
when the denominator is 10 or 100?
3.
How do you change a decimal in the tenths
or hundredths place to a fraction?
[
LESSON
]
 
 
For her class, Tina records the distance a
ball rolls off a ramp. The first time she
rolls the ball, it travels       of a meter. The
second time, she raises the ramp and the
ball rolls       of a meter. What is the total
distance the ball rolled in the two trials?
Express your answer as a decimal.
S
 
Study the Problem
Underline the question.
This problem is asking me to find
the entire distance the ball rolled in both
trials given in decimal form.
[Cooperative Pairs]
 
 
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A
 
 
P
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B
Equivalent Fractions
 
10 sections
 
100 sections
 
How many sections are in each grid?
 
Tenths
 
Hundredths
 
When each picture is completely
shaded, it represents one whole.
Equivalent Fractions
 
Represent the fraction    by creating 3
groups of 10.
 
How many vertical strips are covered
by the centimeter cubes?
 
3
Equivalent Fractions
Now, slide the three strips of ten over
to the hundredths chart.
Equivalent Fractions
 
Did the number of centimeter cubes change
when we slid them to the next chart?
 
NO
 
There are 30 squares covered in
the hundredths chart
Equivalent Fractions
What fraction can we write to represent the
hundredths chart?
Equivalent Fractions
What can we conclude about the two
fractions we created?
 
They are 
EQUIVALENT FRACTIONS
!
Equivalent Fractions
Fraction
TENTHS
 
How many bars do we need to shade in the
tenths grid?
Equivalent Fractions
TENTHS
HUNDREDTHS
 
How many squares do we need to shade in
the hundredths grid?
Equivalent Fractions
HUNDREDTHS
EQUIVALENT
FRACTIONS
 
Write the equivalent fractions
Equivalent Fractions
Fraction
TENTHS
 
How many bars do we need to shade in the
tenths grid?
Equivalent Fractions
TENTHS
HUNDREDTHS
 
How many squares do we need to shade in
the hundredths grid?
Equivalent Fractions
HUNDREDTHS
EQUIVALENT
FRACTIONS
 
Write the equivalent fractions
Equivalent Fractions
Fraction
First
Fraction
 
How many bars do we need to shade
in the tenths grid?
Equivalent Fractions
Fraction
Second
Fraction
 
How many squares do we need to shade
in the hundredths grid?
Equivalent Fractions
First
Fraction
Second
Fraction
 
Remember, we can’t add fractions unless we
have a common denominator.
Equivalent Fractions
TENTHS
HUNDREDTHS
 
 
How did this example use a pictorial model to show
equivalent fractions?
 
Four tenths is the same as forty hundredths.
Equivalent Fractions
First
Fraction
Second
Fraction
Shade in the equivalent fractions on the
hundredths grids below.
Equivalent Fractions
First
Fraction
Second
Fraction
Equivalent Fractions
First
Fraction
Second
Fraction
SUM
 
Shade both fractions on the SUM grid.
Equivalent Fractions
Equivalent Fractions
Fraction
First
Fraction
 
How many bars do we need to shade
in the tenths grid?
Equivalent Fractions
Fraction
Second
Fraction
 
How many squares do we need to shade
in the hundredths grid?
Equivalent Fractions
First
Fraction
Second
Fraction
Remember, we can’t add fractions unless we
have a common denominator.
Equivalent Fractions
TENTHS
HUNDREDTHS
 
 
How have we used a pictorial model
to show equivalent fractions?
 
By shading the same area in the tenths and
hundredths grids.
Equivalent Fractions
First
Fraction
Second
Fraction
Shade in the equivalent fractions on the
hundredths grids below.
Equivalent Fractions
First
Fraction
Second
Fraction
Equivalent Fractions
First
Fraction
Second
Fraction
SUM
 
Shade both fractions on the SUM grid.
Equivalent Fractions
Tenths as Fractions and Decimals
 
Another way to represent a fraction is as a
 
DECIMAL
 
Where have you seen
decimals before?
Tenths as Fractions and Decimals
 
What place values do you see to the right of
the decimal point in our Place Value Chart?
 
In Part I of our lesson, we used tenths
and hundredths to add fractions on our
grids!
 
Tenths as Fractions and Decimals
Fraction
TENTHS
 
Shade the fraction in the TENTHS grid.
Tenths as Fractions and Decimals
TENTHS
Written
Words
 
Write the fraction in words.
 
Three
tenths
Tenths as Fractions and Decimals
Written
Words
Place Value Chart
 
How many tenths do we have?
 
Three
tenths
 
3
 
0
 
What would the decimal be if we had
four tenths?
 
4
 
6
 
What would the decimal be if we had
six tenths?
Hundredths as Fractions and Decimals
Fraction
HUNDREDTHS
 
Shade the fraction in the
HUNDREDTHS grid.
Hundredths as Fractions and Decimals
HUNDREDTHS
Written
Words
 
Write the fraction in words.
 
Thirty-two
hundredths
Hundredths as Fractions and Decimals
Written
Words
Place Value Chart
 
How many hundredths do we have?
Thirty-two
hundredths
 
Thirty-two hundredths
Hundredths as Fractions and Decimals
 
Let’s break thirty-two hundredths down into
tenths and hundredths.
 
3 Tenths
 
2 Hundredths
Hundredths as Fractions and Decimals
Written
Words
Place Value Chart
 
How many tenths do we have?
Three
tenths
 
3
 
0
 
How many hundredths do we have?
 
2
Fraction and Decimal Equivalence
Fraction
TENTHS
 
Identify what information is given and use
this information to complete the chart.
 
Given
Fraction and Decimal Equivalence
TENTHS
Written
Words
 
Write the fraction in words.
 
Eight
tenths
Fraction and Decimal Equivalence
Written
Words
Place Value Chart
 
Write the fraction as a decimal.
Eight
tenths
 
8
 
0
SOLVE
 
For her class, Tina records the distance a
ball rolls off a ramp. The first time she
rolls the ball, it travels       of a meter. The
second time, she raises the ramp and the
ball rolls       of a meter. What is the total
distance the ball rolled in the two trials?
Express your answer as a decimal.
S
 
Study the Problem
Underline the question.
This problem is asking me to find
the entire distance the ball rolled in both
trials given in decimal form.
 
 
For her class, Tina records the distance a ball
rolls off a ramp. The first time she rolls the
ball, it travels       of a meter. The second
time, she raises the ramp and the ball rolls
of a meter. What is the total distance the ball
rolled in the two trials? Express your answer
as a decimal.
 
O
 
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
First trial =       of a meter
Second trial =         of a meter
 
L
 
Line Up a Plan
 
Choose an operation or operations.
 
Addition
 
Write in words what your plan of action will
be.
 
 
Add the distance of the second trial to the
distance of the first trial. Then, change the
final fraction to a decimal.
 
V
 
Verify Your Plan with Action
Estimate your answer.
Approximately 0.8 of a meter
Carry out your plan.
 
 
 
 
 
The total distance the ball traveled was
or 0.82 of a meter.
 
 
 
E
 
Examine Your Results
Does your answer make sense?
(compare your answer to question.)
Yes, because I’m looking for the distance
traveled.
Is your answer reasonable?
(compare your answer to the estimate.)
Yes, because 0.8 is close to 0.82.
 
Is your answer accurate?
(check your work.)
Yes.
Write your answer in a complete sentence.
 
The total distance the ball traveled in the two
trials was 0.82 meters.
[
ESSENTIAL
 
QUESTIONS
]
 
1.
What are equivalent fractions?
 
(Fractions that are equal; they have
different names but the same value.)
[
ESSENTIAL
 
QUESTIONS
]
 
 
2.
How do you change a fraction to a decimal
when the denominator is 10 or 100?
 
(If the denominator is 10, place the
numerator of the fraction directly to the
right of the decimal point. Follow the same
steps when the denominator is 100, unless
the numerator is less than 10, then you
must place a 0 in the tenths place and the
numerator in the hundredths place.)
[
ESSENTIAL
 
QUESTIONS
]
 
3.
How do you change a decimal in the
tenths or hundredths place to a fraction?
 
(If the digit is only in the tenths place,
make that digit the numerator and make
the denominator 10. If numerals are
both in the tenths and hundredths
place, take those digits and place them
in the numerator over a denominator of
100.)
 
Equivalent Fractions
Numerator
Denominator
Decimal
Tenths
Hundredths
 
 
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Discover how to express fractions with denominators of 10 as equivalent fractions with denominators of 100 in order to add them together. Learn to use decimal notation for fractions and explore essential questions on equivalent fractions, decimal conversion, and converting decimals to fractions. Engage in hands-on activities to reinforce the concepts.


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  1. Lesson 21 Fraction and Decimal Equivalence

  2. [OBJECTIVE] The student will be able to express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators 10 and 100. The student will be able to use decimal notation for fractions with denominators of 10 and 100.

  3. [MYSKILLS] Basic understanding of a fraction Understanding of place value

  4. [ESSENTIALQUESTIONS] 1. What are equivalent fractions? 2. How do you change a fraction to a decimal when the denominator is 10 or 100? 3. How do you change a decimal in the tenths or hundredths place to a fraction?

  5. [LESSON] For her class, Tina records the distance a ball rolls off a ramp. The first time she rolls the ball, it travels of a meter. The second time, she raises the ramp and the ball rolls of a meter. What is the total distance the ball rolled in the two trials? Express your answer as a decimal. S Study the Problem Underline the question. This problem is asking me to find the entire distance the ball rolled in both trials given in decimal form. 2 __ 10 62 ___ 100

  6. [Cooperative Pairs] Partner A Partner B

  7. Equivalent Fractions How many sections are in each grid? 10 sections Tenths 100 sections Hundredths When each picture is completely shaded, it represents one whole.

  8. Equivalent Fractions Represent the fraction by creating 3 groups of 10. by the centimeter cubes? 3 3 __ 10 How many vertical strips are covered 3 10

  9. Equivalent Fractions Now, slide the three strips of ten over to the hundredths chart.

  10. Equivalent Fractions There are 30 squares covered in the hundredths chart Did the number of centimeter cubes change when we slid them to the next chart? NO

  11. Equivalent Fractions What fraction can we write to represent the hundredths chart? 30 100

  12. Equivalent Fractions What can we conclude about the two fractions we created? They are EQUIVALENT FRACTIONS! 3 10 30 100 =

  13. Equivalent Fractions How many bars do we need to shade in the tenths grid? Fraction TENTHS 3 10

  14. Equivalent Fractions How many squares do we need to shade in the hundredths grid? TENTHS HUNDREDTHS

  15. Equivalent Fractions Write the equivalent fractions EQUIVALENT FRACTIONS HUNDREDTHS 3 30 100 = 10

  16. Equivalent Fractions How many bars do we need to shade in the tenths grid? Fraction TENTHS 7 10

  17. Equivalent Fractions How many squares do we need to shade in the hundredths grid? TENTHS HUNDREDTHS

  18. Equivalent Fractions Write the equivalent fractions EQUIVALENT FRACTIONS HUNDREDTHS 7 70 100 = 10

  19. Equivalent Fractions How many bars do we need to shade in the tenths grid? First Fraction Fraction 4 32 100 + 10

  20. Equivalent Fractions How many squares do we need to shade in the hundredths grid? Second Fraction Fraction 4 32 100 + 10

  21. Equivalent Fractions Remember, we can t add fractions unless we have a common denominator. First Fraction Second Fraction +

  22. Equivalent Fractions How did this example use a pictorial model to show equivalent fractions? Four tenths is the same as forty hundredths. TENTHS HUNDREDTHS

  23. Equivalent Fractions Shade in the equivalent fractions on the hundredths grids below. First Fraction Second Fraction +

  24. Equivalent Fractions First Fraction Second Fraction + +

  25. Equivalent Fractions Shade both fractions on the SUM grid. First Fraction Second Fraction SUM + = 72 100

  26. Equivalent Fractions 32 100 4 40 100 32 100 = + + 10 40 100 32 100 72 100 = +

  27. Equivalent Fractions How many bars do we need to shade in the tenths grid? First Fraction Fraction 5 11 100 + 10

  28. Equivalent Fractions How many squares do we need to shade in the hundredths grid? Second Fraction Fraction 5 11 100 + 10

  29. Equivalent Fractions Remember, we can t add fractions unless we have a common denominator. First Fraction Second Fraction +

  30. Equivalent Fractions How have we used a pictorial model to show equivalent fractions? hundredths grids. By shading the same area in the tenths and TENTHS HUNDREDTHS

  31. Equivalent Fractions Shade in the equivalent fractions on the hundredths grids below. First Fraction Second Fraction +

  32. Equivalent Fractions First Fraction Second Fraction + +

  33. Equivalent Fractions Shade both fractions on the SUM grid. First Fraction Second Fraction SUM + = 61 100

  34. Equivalent Fractions 11 100 5 50 100 11 100 = + + 10 50 100 11 100 61 100 = +

  35. Tenths as Fractions and Decimals Another way to represent a fraction is as a DECIMAL Where have you seen decimals before?

  36. Tenths as Fractions and Decimals What place values do you see to the right of the decimal point in our Place Value Chart? Hundredths Hundreds Tenths Ones Tens In Part I of our lesson, we used tenths and hundredths to add fractions on our grids!

  37. Tenths as Fractions and Decimals Shade the fraction in the TENTHS grid. Fraction TENTHS 3 10

  38. Tenths as Fractions and Decimals Write the fraction in words. Written Words TENTHS Three tenths

  39. Tenths as Fractions and Decimals How many tenths do we have? What would the decimal be if we had four tenths? six tenths? What would the decimal be if we had Written Words Place Value Chart Hundredths Tenths Ones Tens Three tenths 0 3 4 6

  40. Hundredths as Fractions and Decimals Shade the fraction in the HUNDREDTHS grid. Fraction HUNDREDTHS 32 100

  41. Hundredths as Fractions and Decimals Write the fraction in words. Written Words HUNDREDTHS Thirty-two hundredths

  42. Hundredths as Fractions and Decimals How many hundredths do we have? Thirty-two hundredths Written Words Place Value Chart Hundredths Tenths Ones Tens Thirty-two hundredths

  43. Hundredths as Fractions and Decimals Let s break thirty-two hundredths down into tenths and hundredths. = + 3 Tenths 2 Hundredths

  44. Hundredths as Fractions and Decimals How many tenths do we have? How many hundredths do we have? Written Words Place Value Chart Hundredths Tenths Ones Tens Three tenths 0 3 2

  45. Fraction and Decimal Equivalence Identify what information is given and use this information to complete the chart. Fraction TENTHS 8 10 Given

  46. Fraction and Decimal Equivalence Write the fraction in words. Written Words TENTHS Eight tenths

  47. Fraction and Decimal Equivalence Write the fraction as a decimal. Written Words Place Value Chart Hundredths Tenths Ones Tens Eight tenths 0 8

  48. SOLVE For her class, Tina records the distance a ball rolls off a ramp. The first time she rolls the ball, it travels of a meter. The second time, she raises the ramp and the ball rolls of a meter. What is the total distance the ball rolled in the two trials? Express your answer as a decimal. S Study the Problem Underline the question. This problem is asking me to find the entire distance the ball rolled in both trials given in decimal form. 2 __ 10 62 ___ 100

  49. For her class, Tina records the distance a ball rolls off a ramp. The first time she rolls the ball, it travels of a meter. The second time, she raises the ramp and the ball rolls of a meter. What is the total distance the ball rolled in the two trials? Express your answer as a decimal. 2 __ 10 62 ___ 100 O Organize the Facts Identify the facts. Eliminate the unnecessary facts. List the necessary facts. First trial = of a meter Second trial = of a meter 2 ___ 10 62 ___ 100

  50. L Line Up a Plan Choose an operation or operations. Addition Write in words what your plan of action will be. Add the distance of the second trial to the distance of the first trial. Then, change the final fraction to a decimal.

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