Fractions are parts of a whole' If an amount is divided into equal parts, or fair shares, we can und

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• Fractions are parts of a whole. If an amount is
  divided into equal parts, or fair shares, we can
  understand and name the fractions.
• There are three questions we need to answer to
  understand what any fraction really means.
• The first question is, What is the whole and how
  big is it? The context of the fraction answers
  this question.

Gr4-U8-L1
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• Fractions are parts of a whole. If an amount is
  divided into equal parts, or fair shares, we can
  understand and name the fractions.
• There are three questions we need to answer to
  understand what any fraction really means.
• The first question is, What is the whole and how
  big is it? The context of the fraction answers
  this question.

Gr4-U8-L1
3

• The second question is, Into how many equal
  parts has the whole been divided? The
  denominator of the fraction answers this
  question.
• The third question is, How many of the equal
  parts are we using? The numerator of the
  fraction answers this question.

Gr4-U8-L1
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• Equivalent fractions describe the same portion of
  a whole divided in different ways. In other
  words, different fractions that name the same
  portion of a whole are called equivalent
  fractions. For example, a half of a piece of
  paper can be represented as 1/2, 2/4, 3/6, 4/8,
  or 5/10 of the piece of paper, and so on.

Gr4-U8-L2
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• To find an equivalent fraction, you multiply the
  numerator and the denominator of your fraction by
  the same number. For example, 1/2 4/8 because
  both the numerator and the denominator are
  multiplied by 4.

Gr4-U8-L3
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• Any number multiplied by 1 equals itself. When
  we multiply the numerator and the denominator by
  the same number, it is like multiplying by 1, so
  the product is equal to the original fraction.

Gr4-U8-L3
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• We find a simpler equivalent fraction for a
  fraction by grouping many small parts into a few
  big parts. The simpler fraction has smaller
  numbers in the numerator and the denominator and
  is easier to understand. For example, 3/4 is
  easier to understand than 12/16.

Gr4-U8-L4
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• Any number divided by 1 equals itself. When we
  divide the numerator and the denominator by the
  same number, it is like dividing by 1, so the
  quotient is equal to the original fraction.

Gr4-U8-L5
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• To simplify a fraction you find an equivalent
  fraction with smaller numbers by dividing the
  numerator and the denominator of the fraction by
  the same number. For example, 8/12 2/3 because
  both the numerator and the denominator are
  divided by 4.

Gr4-U8-L5
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• Fractions can be ordered on a number line just as
  whole numbers can be ordered.
• Proper fractions are fractions in which the
  numerator is less than the denominator. For
  example, 1/2 is a proper fraction but 3/2 is not.
• Positive proper fractions are greater than 0 and
  less than 1, so they are found between 0 and 1 on
  the number line.

Gr4-U8-L6
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• Like fractions have the same denominator. For
  example, 3/4 and 2/4 are like fractions.
• When we compare like fractions, we just compare
  the numerators because the denominators are the
  same. For example, when we compare 3/4 and 2/4,
  we say that 3 is more than 2 because both
  fractions are fourths.

Gr4-U8-L6
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• Unlike fractions have different denominators.
  For example, 3/4 and 2/3 are unlike fractions.
• To find a common denominator for two unlike
  fractions, we can multiply the denominators. For
  example, 3/4 and 2/3 have a common denominator of
  12.

Gr4-U8-L7
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• To compare unlike fractions, we find equivalent
  fractions with a common denominator and then
  compare the numerators. For example, when we
  compare 3/4 and 2/3, we say 3/4 9/12 and 2/3
  8/12, and 9/12 gt 8/12, so 3/4 gt 2/3.

Gr4-U8-L7
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• A mixed number is a number that includes a whole
  number and a proper fraction. For example, 21/2
  represents 2 wholes and 1/2 of another whole
• An improper fraction is a fraction with a
  numerator equal to or greater than the
  denominator. For example, 5/2 is more than 1
  whole since 2/2 1.

Gr4-U8-L8
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• To change a mixed number to an improper fraction,
  you change each whole in the whole number to a
  fraction with the same denominator as the
  fractional part of the mixed number, and add all
  the fractions together. For example, 31/4 4/4
  4/4 4/4 1/4 13/4.

Gr4-U8-L9
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• To change an improper fraction to a mixed number,
  you make sets of the fractions each equal to 1
  whole, count the sets to find the number of
  wholes, and put that with the fraction that is
  left over. For example, 13/4 - 4/4 9/4, 9/4 -
  4/4 5/4, 5/4 - 4/4 1/4. 4/4 4/4 4/4
  1/4 31/4.

Gr4-U8-L10
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• To change an improper fraction to a mixed number,
  you divide the denominator into the numerator to
  find how many wholes there are and how many parts
  are left over. For example, 20/8 sixteen-inch
  pizzas 20 ? 8 2 R4, so 20/8 pizzas 24/8
  sixteen-inch pizzas.

Gr4-U8-L10
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• All whole numbers and mixed numbers can be
  written as improper fractions. All improper
  fractions can be written as either whole numbers
  or mixed numbers.

Gr4-U8-L10
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• We can estimate that fractions are close to 1/2
  by seeing if their denominators are about twice
  as much as their numerators. For example, in
  7/12 the 12 is almost twice as much as the 7, so
  7/12 of a sheet cake is about 1/2 of the cake.

Gr4-U8-L11
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• If a fraction is a very small part of a whole,
  the fraction is close to 0. For example, 1/12 is
  a very small part of 12/12, so 1/12 of a sheet
  cake is almost no cake at all.

Gr4-U8-L11
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• If the numerator is almost the same size as the
  denominator, the fraction is close to 1. For
  example, in 11/12, the 11 is almost as big as the
  12 and 11/12 of a sheet cake is almost the whole
  cake.
• Comparing a fraction to 0, 1/2, or 1 helps us
  estimate amounts or interpret data in a
  meaningful way.

Gr4-U8-L11
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• Adding like fractions is just like adding
  anything else. For example, 3 children 2
  children 5 children, so 3 eighths 2 eighths
  5 eighths.

Gr4-U8-L12
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• To add like fractions, we add the numerators and
  put the sum over the denominator. The
  denominator doesnt change, because the size of
  each piece doesnt change we just have more
  pieces. For example, 3/8 2/8 5/8 of a piece
  of paper. We still have eighths there are just
  more of them.

Gr4-U8-L12
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• To add unlike fractions, find equivalent
  fractions with a common denominator, add the
  numerators, and put the sum over the common
  denominator. For example, 2/5 1/2 4/10
  5/10 9/10 of a piece of paper.

Gr4-U8-L12
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• Amounts greater than 1 can be represented in many
  different ways. For example, 23/4 pies can be
  represented as 53/4 pies or 47/4 pies or 4 13/4
  pies.

Gr4-U8-L13
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• To add two like mixed numbers, you take three
  steps
• 1. Add the fractions and add the whole numbers.
• 2. If the sum of the fraction part of the mixed
  numbers is an improper fraction, change it to a
  whole or mixed number.
• 3. Add the wholes and simplify the answers if
  appropriate.

Gr4-U8-L14
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• To add two unlike mixed numbers, you take four
  steps
• 1. Change to equivalent like fractions.
• 2. Add the fractions and add the whole
  numbers.
• 3. If the sum of the fraction part of the
  mixed numbers is an improper fraction, change
  it to a whole or mixed number.
• 4. Add the wholes and simplify the answers if
  appropriate.

Gr4-U8-L14
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• To subtract like fractions, we subtract the
  numerators and put the difference over the
  denominator. The denominator doesnt change,
  because the size of each piece doesnt change we
  just have fewer pieces. For example, 5/8 - 2/8
  3/8 of a piece of paper. We still have eighths
  there are just fewer of them.

Gr4-U8-L15
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• Subtracting like fractions is just like
  subtracting anything else. For example, 5
  children - 2 children 3 children, so 5 eighths
  - 2 eighths 3 eighths of a piece of paper.

Gr4-U8-L15
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• To subtract unlike fractions, find equivalent
  fractions with a common denominator, subtract the
  numerators, and put the difference over the
  common denominator. For example, 5/6 - 1/2
  10/12 - 6/12 4/12, or 1/3, of an eight-inch pie.

Gr4-U8-L15
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• To subtract two like mixed numbers when the
  larger number also has the larger fraction, you
  take three steps
• 1. Subtract the Fractions.
• 2. Subtract the whole numbers.
• 3. Simplify the answer if appropriate.

Gr4-U8-L16
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• To subtract two unlike mixed numbers when the
  larger number also has the larger fraction, you
  take four steps
• 1. Change to equivalent like fractions.
• 2. Subtract the Fractions.
• 3. Subtract the whole numbers.
• 4. Simplify the answer if appropriate.

Gr4-U8-L16
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• To subtract two mixed numbers, you take five
  steps
• 1. Check the fractions and change to
  equivalent like fractions if necessary.
• 2. Compare the fractions and regroup 1 whole
  in the larger number.
• 3. Subtract the Fractions.
• 4. Subtract the whole numbers.
• 5. Simplify the answer if appropriate.

Gr4-U8-L17