fractiondecimalconceptsstudent slides.notebook
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March 06, 2015
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4th Grade
FractionDecimal Concepts
www.njctl.org
20130122
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Table of Contents
Number Line Location
Convert Decimals to FractionsConvert Fractions to Decimals
Click on the topic to go to that section
Fraction ReviewMixed Numbers
Compare and Order FractionsEquivalent Fractions
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Fraction Review
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Fractions can be used to name a part of a whole object.
You ate of the pie.
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Fractions can also be used to name a part of a collection of objects.
of the balls are needed for practice.
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Naming fractions
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top number = numeratorbottom number = denominator
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Mixed Numbers
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Take out the following number of pattern blocks
hexagon1
trapezoid9
rhomb
us
8triangle11
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If a hexagon is worth 1, what are 3 trapezoids worth?
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If a hexagon is worth 1, what are 4 rhombi worth?
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1 If a hexagon is worth 1, what are 5 triangles worth?
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2 If a hexagon is worth 1, what are 11 triangles worth?
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3 If a hexagon is worth 1, what are 9 trapezoids worth?
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4 If the triangle is , what shape is ONE?
A hexagon
B rhombusC trapezoid
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5 If the triangle is , what is a trapezoid worth?
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6 If the triangle is , what is the hexagon worth?
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Fractions that are greater than one are often called improper fractions, even though there is nothing improper about them.
Improper Fraction Mixed Number
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A mixed number is a number that has a whole part and a fractional part.
For example: 6 is the whole part is the fractional part
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To convert an improper fraction to a mixed number.First divide 31 by 6
56 31 30 1
QuotientDivisor
Remainder
Then write in the form:
quotient remainderdivisor
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To convert an improper fraction to a mixed number.First divide 30 by 4
74 30 28 2
QuotientDivisor
Remainder
Then write in the form:
quotient remainderdivisor
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Match the Mixed Numbers and Improper Fractions.
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Compare and Order Fractions
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The first step when comparing fractions is to look at the numerators and denominators.
numeratorsdenominators
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When the denominators are the same:
the unit fractions are the same sizeonly need to compare the number of pieces (numerators) need to be compared
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Order the following fractions least to greatest.
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7 Which of the following is ordered least to greatest?
A B C
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When the numerators are the same:
there are the same number of piecescompare the size of the denominator
The smaller the denominator, the larger the size of
each piece.
The larger the denominator, the smaller the size of each piece.
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Order the following fractions least to greatest.
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8 Which of the following is ordered least to greatest?
A B C
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If numerators and denominators are not the same, we need to use other methods to compare fractions.
Use benchmarks to see if the fraction is close to 0, 1/2, or 1 and then order them.
0 12 1
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Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.
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9 Which of the following is ordered least to greatest?
A B C
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10 Which of the following is ordered least to greatest?
A B C
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If the previous strategies don't work to compare fractions, we need to find
equivalent fractions in order to compare them.
Equivalent Fractions
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A fraction stick is a model for the whole, or ONE.
Use it to find equivalent fractions.
Find equivalent fractions for
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A fraction stick is a model for the whole, or ONE.
Use it to compare fractions.
Which number is larger? or
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Splitting Fractions Sticks to Make Equivalent Fractions
What fraction of the whole is shaded?
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If a horizontal line is drawn to divide each part of the rectangle into 2 parts, what fraction of the whole is shaded?
Has the shaded amount of the rectangle changed?
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11 What fraction of the whole is shaded?
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12 Use these two horizontal lines to divide the whole.
What fraction of the whole is shaded now?
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110
110
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110
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110
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What do you notice about the denominators in each set of equivalent fractions?
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What patterns have you noticed in the previous examples about making equivalent fractions?
What important idea do we know about multiplying by 1?
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Multiplication Rule
To find an equivalent fraction, multiply both the numerator and the denominator of the fraction by the same number.
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25
= ??
Use the multiplication table to make equivalent fractions.
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What important idea to we know about dividing by 1?
How can we use division to find equivalent fractions?
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Steps to simplifying fractions.1. Find the GCF of both numbers.2. Divide the numerator and denominator by that number.3. Answer will be the fraction in simplified form.
GCF = 2
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Try these.
GCF = 8
GCF = 12
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13 What is in simplified form?
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Converting Decimals to Fractions
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To convert a decimal to a fraction:
1. Put the digits in the numerator.2. The denominator represents the place value.3. Simplify fraction if you can.
Example:
0.9 =
0.25 =
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Match the following decimals with their fraction equivalents.
0.6 =
0.3 =
0.06 =
0.03 =
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Converting Fractions to Decimals
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Converting fractions to decimal form by changing the denominator.
Steps:1. Use mental math, the multiplication rule or the division rule to change each fraction to an equivalent fraction having a denominator of 10 or 100.2. Write the new fraction as a decimal.
Way 1
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Examples:
x 4
x 4
x 5
x 5
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6_
_
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Match each decimal to its equivalent fraction.
0.7
0.280.35
0.14
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Match each decimal to its equivalent fraction.
3.12
3.853.823.8
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Convert the following fractions to decimals.
When you can not make an equivalent fraction with a denominator of 10 or 100, then you must divide to find the decimal equivalent.
Way 2
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.3758 3.000 24 60 56 40 40 0
Steps:1. The numerator is the dividend and the denominator is the divisor.2. Put a decimal point in the dividend and add zeros as needed.3. Divide.
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16 3
Steps:1. The numerator is the dividend and the denominator is the divisor.2. Put a decimal point in the dividend and add zeros as needed.3. Divide.
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3 1
Notice what happens with this division.This is called a repeating decimal andit is written as 0.3 and is read as point three repeating.
_
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Use a calculator to convert these fractions to decimals to see the repeating pattern.
fraction calculator display decimal
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5 12
4 11
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Number Line Location
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0.4 0.5
On the following number line, draw a line and move the decimals to their correct location.
0.420.45
0.48
Steps:1. Divide the number line into smaller parts using tick marks.2. Compare the decimals and place them correctly.
PullPull
for steps
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6.45 6.46
On the following number line, draw a line and move the decimals to their correct location.
6.4526.458
Steps:1. Divide the number line into smaller parts using tick marks.2. Compare the decimals and place them correctly.
PullPull
for steps
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Label the numbers on the number line.
Steps:1. Convert numbers to same form. 2. Divide the number line into smaller parts using tick marks.2. Compare the numbers and place them correctly.
PullPull
for steps
2 3
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Label the numbers on the number line.
Steps:1. Convert numbers to same form. 2. Divide the number line into smaller parts using tick marks.2. Compare the numbers and place them correctly.
PullPull
for steps
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Steps to create your own number line.
1. Convert numbers all to the same form.
2. Order the numbers to determine the range of numbers you need to include.
3. Draw a number line and divide it into equal size pieces.
4. Put a dot and label each number.
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Example:Plot and label the numbers in the box on a number line.
1. Convert numbers all to the same form.In this case, all to decimal will be the easiest.1.5, 0.75, 0.2, 1.2, 0.45
2. Order the numbers to determine the range of numbers you need to include.
0.2, 0.45, 0.75, 1.2, 1.5We need a number line from 0 to 2
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3. Draw a number line and divide it into equal size pieces.Label 0, 1 and 2Divide in between the whole numbers into tenths.
4. Put a dot and label each number.
.2 .45 .75 1.2 1.5
0 1 2
0 1 2
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Example:Plot and label the numbers in the box on a number line.
1. Convert numbers all to the same form.In this case, all to decimal will be the easiest.1.2, 0.6, 0.4, 1.8, 1
2. Order the numbers to determine the range of numbers you need to include.
0.4, 0.6, 1, 1.2, 1.8We need a number line from 0 to 2
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3. Draw a number line and divide it into equal size pieces.Label 0, 1 and 2Divide in between the whole numbers into twotenths.
4. Put a dot and label each number.
0 1 2
0 1 2.4 .6 1.2 1.8
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Plot and label the following sets of numbers on a number line. Make a separate number line for each set.
Set 1 Set 2 Set 3
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