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Math Unit 10

 

Study Guide

Unit 10: Fractions

 

Chapter 1- Examples of test questions:

  • Numerator – the top number that give the number of equal parts represented by the fraction
    • What is the numerator of ¾?
  • Denominator – the bottom number that gives equal parts the whole is divided into
    • What is the denominator of 5/6?
  • 5/6 = ___ sixths
  • Making a whole
    • ¾ and ___ make a whole
    • 4/9 and ___ make a whole
    • How many fourths are there in a whole?
    • How many twelfths in a whole?
    • 1 = ?/7
    •  
  • Shading of figures
    • Shade 7/8 of a figure with 8 pieces
    • If a figure has pieces shaded – What fraction of the figure is / is not shaded?
  • Comparing fractions
    • Which is greater: 3/7 or 6/7?
    • >, < between to fractions: 6/12 ____ 6/8
    • Arrange in order – begin with greatest / least.
      • 2/4, 2/7, 1/7, 2/9
  • Write a fraction that is greater than 1/5.

 

Chapter 2- Examples of test questions:

  • Write a fraction for a figure
    • A figure as a whole is written as 1
    • A figure in two pieces would be 2/2
    • A figure in six pieces would be 6/6
  • Write a fraction for shaded figures
    • Two figures that are the same size, and have the same ratio shaded – however, the number of pieces differ
      •  One figure has four pieces with two shaded and another has two pieces with one shaded: 2/4 = ½
      • One figure has ten pieces with eight shaded and another has five pieces with four shaded: 8/10 = 4/5
  • Equivalent
    • ½, 2/4, 3/6, and 4/8 are all equivalent fractions; they all name the same part of the whole
    • Change a fraction into an equivalent fraction by multiplying or dividing both the numerator and denominator by the same number
    • ¾ = ?/12
    • ¾ = 9/?
    • 6/12 = 3/?
    • Write an equivalent fraction for 3/8
  • Write the missing numerator and denominator: ?/7 = 6/14 = 9/?
  • A fraction can be simplified when its numerator and denominator can be divided by the same number: express 8/16 in its simplest form
  • Which fractions are in their simplest forms?
    • 6/12       4/8        2/3       7/9
    • order the fractions in order starting with the greatest / least
  • Which is the greater fraction?
    • ¾ or 7/12
  • 2/4 of the meal was salad.  2/3 of the meal was soup.  Was there more salad or soup?
    • 4 and 3 both go into 12, so it may help multiply the numerator/denominator in each fraction so the denominator is 12. (2/4 x 3/3 = 6/12)
  • Mom at 2/3 of the salad.  Dad ate 6/18 of the salad.  Sue ate 7/9 of the salad.  Who ate the most/least?
    • Make the common denominator 18 to compare the fractions.

 

Chapter 3- Examples of test questions:

  • To add like fractions, we add the numerator and the denominator stays the same (3/5 + 1/5 = 4/5).
  • Various ways to add fractions.
    • 4/9  + 2/9 = ___.  Give your answer in its simplest form.
    • Circle divided.  If there are 10 pieces: 4 pieces are pink, 2 pieces are red, and 1 piece is blue, write an addition sentence with fractions.  What fraction is colored?  What fraction is not colored?
    • Pictures of beakers shaded.  What fraction of the beaker is/is not filled?  Give the answer in its simplest form.
    • More than one beaker is shaded.  Write a fraction addition sentence.  Express your answer as a fraction in its simplest form.
    • Unit bar
      • Shaded unit bar.  Write in a missing fraction to make the sentence complete.
        • 4/7 + _____ = 1
      • Number sentence given.  Shade the unit bar to show the addition sentence.
        • 5/8 + 3/8 = ___ (shade in five pieces, but leave three of the eight blank and fill in the blank as 8/8)
    • ?/12 + ?/12 = 9/12 = ¾ (fill in the blanks so the numerators need to add up to 9)
    • Add 8/18, 4/18, and 2/18.  Show your work in the form of an addition sentence.  Give your answer in its simplest form.
  • Eric ate ¾ cup of nuts yesterday and another ¼ cup today.  How much did he eat in all?
  • A 1 liter bottle contains 2/4 liters of a liquid.  Another ¼ is added.  How much liquid is there now?  Can the bottle hold any more liquid?
  • Mrs. Tokkesdal walked the trail in her neighborhood three times.  The trail was 4/19 km long.  What was the total she walked?  Express your answer as a fraction in its simple form.

 

Chapter 4- Examples of test questions:

  • To subtract like fractions, we subtract the numerators.  The denominator stays the same (4/5 – 1/5 = 3/5)
  • Subtract fractions in various ways.
    • Unit bar shaded and students label the various parts in fractions.  Count the parts and label how many pieces total (If nine pieces: 9/9).  Count the shaded (3/9) and parts not shaded (6/9) and label them.  Write a subtraction sentence using the fractions (9/9 – 3/9 = 6/9).
      • Be careful because some questions only mark part of the unit bar for the problem.  For instance, there could be 12 pieces, but they may only be working with 7 pieces for the total.
    • Subtract 6/8 from 8/8.
    • Find the difference between 5/9 and 8/9.  Give your answer in its simplest form.
    • 1 – 7/18 = ___ (Change 1 to 18/18.  18/18 – 7/18 = ___)
    • 1 – 8/18 – 7/18 = _____
    • 17/18 – 13/18 - ?/18 = 2/18 Write the missing numerator
  • The pie was cut into 6 equal pieces.  Sophia ate 1/6.  Samuel and Wyatt each ate 2/6 of the pie.  What fraction of the pie was left?
  • The French bread was cut into 12 equal pieces.  Madeline took 3 pieces and Jack took 5 pieces.  What fraction of the bread was left?
  • Emily divided the lemonade into 6 equal portions.  She gave 3/6 of it to Brenna.  What fraction of the lemonade was left?
  • A 1 liter bottle contains 6/7 liter of a liquid.  3/7 liter was poured into one container and 2/7 liter into another.  How much was poured?  How much was left in the bottle?

 

Chapter 5- Examples of test questions:

  • Up until now, students have only dealt with fractions as fractions of one whole.  Here, the concept of fraction of a set of more than one object is introduced.
  • To find 1/5 of a set of 20 objects, we can divide the set of 20 into 5 equal parts and determine how many objects there are in one part.
  • To find 3/5 of 20, we also divide the set of 20 into 5 equal parts.  Then we determine how many objects there are in three parts.
  • Various objects are drawn.  What fraction of the objects are ___?
    • Lets say there are 15 circles.  7 are dotted, 4 are shaded, 3 are striped, and 1 is blank.  What fraction of the circles are shaded?
    • Lets say there are 8 objects.  4 are rectangles and 4 are hexagons.  Use the figure to find ½ of 8.  ½ of 8 is ___.
    • ?/? of 12 is ___.  12 objects are in 4 equal groups.  One group of 3 is shaded. The answer would be ¼ of 12 is 3.
  • What is 1/3 of 9?
  • Davis had 9 m of electrical cord.  He needed 2/3 of it for the science experiment.  How many meters did he have left?
  • Preston-Nicolas had 8 markers.  He used ¾ of his markers to decorate his Sail America brochure.  How many markers did he use?

 

Chapter 6- Examples of test questions:

  • Read and write a sum of money as a fraction of another sum of money.  For example, 3 dimes out of a total of 10 dimes is 3/10 of a dollar.
  • Pictures of various coins.  How many coins are there?  What fraction of the coins are dimes?
  • What fraction of a dollar is:
    • $0.75? ___
    • 1 penny? ____
  • What is 20/100 of a dollar? ____
  • 10 pennies are ?/? of a dollar. (Write a fraction)
  • How much do a dime, three nickels and five pennies make? $_____
    • What fraction of a dollar is that?
  • Zoe has 6 dimes, 2 nickels, 8 quarters, and 9 pennies.
    • What fraction of her coins are nickels?
    • What fraction of a dollar are the 9 pennies?
    • How much does she have altogether?
    • She changed 5 pennies for a nickel.  What fraction of her coins are pennies now?
  • Shaylie has 80c.  What is 80c as a fraction of a dollar?
    • The 80c she has is made up of 4 dimes, 2 nickels, 1 quarter, and 5 pennies.  What fraction of the coins do the nickels make up?

 

Unit 10 Cumulative Test:

  • Review all of Units 1 - 10
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