recent survey asked girls and boys how they spend their free time. Three out of six girls said they spend their free time playing sports. One-half of the boys said they spend their free time playing sports. The results of the survey can be written using fractions. A fraction is a number written as __________ numerator . denominator A fraction represents part of a whole number. The denominator of a fraction cannot be 0. The line between the numerator and denominator can be read “out of ”. In the survey above, _36 of the girls and _ 12 of the boys said they spend their free time playing sports. There are times when information needs to be compared to make it easier to understand. Equivalent fractions allow you to determine whether two fractions are equal. Equivalent fractions are two fractions that name the same amount. To compare the fraction of girls that play sports to the fraction of boys that play sports, you can use models. Draw two equal-sized rectangles. Each rectangle represents one whole unit.
Divide each rectangle into equal-sized sections using the denominator to determine the number of sections. _ 3 6
_ 1 2
Use the value of the numerator to determine the number of sections to color in for each rectangle. _36 _1 2
The same amount of each rectangle is colored. This means that _36 is equivalent to _ 12 . According to the survey, the same portion of girls play sports in their free time as boys.
74
Lesson 3.2 ~ Equivalent Fractions
EXAMPLE 1
Use multiplication to find the missing number in the equivalent fractions. a. _ 1 = __ ☐ b. _ 3 = __ 6 2 8 8 ☐
Solutions
a. The denominator of 2 was multiplied by 4 to make a denominator of 8. Since the denominator was multiplied by 4, the numerator must also be multiplied by 4. The missing number is 4.
_ 1 = 2
__ 1
= __ 4 2 8
b. The numerator of 3 was multiplied by 2 to make a numerator of 6.
×2
Since the numerator was multiplied by 2, you must multiply the denominator by 2. The missing number is 16.
EXPLORE!
_ 3 = 8
__ 6 ☐
_ 3 = 8
__ 6 16
×2
CREATING EQUIVALENT FRACTIONS
Step 1: Choose a fraction from the purple box. Create a model of this fraction using fraction tiles. Draw or trace the fraction on paper. Write the fraction below the drawing.
×4 ×4
__ ☐ 8
_ 3 6
_ 4 8
3 __ 12
6 __ 10
6 __ 12
9 __ 12
_ 4 6
__ 2 10
10 __ 4 __ 2 __ 12 12 12
3 _ 6
6 _ 8
8 __ 10
5 2 __ _ 10 6
__ 4 10
_ 2 8
8 __ 12
Step 2: Use the fraction tiles to make an equivalent fraction with a smaller denominator. Record this on your paper to show that the two fractions are equivalent. _ 3 6 1 _ 2 Step 3: Repeat Steps 1-2 for four additional fractions from the purple box.
Step 4: Compare each of your fractions from the purple box to the equivalent fractions you formed. Were the original numerator and denominator multiplied or divided by a number to get the new fraction? Step 5: Try to find equivalent fractions with smaller numerators and denominators for the fractions below without using a model. 10 __ 6 __ 15 __ 30 12 20
Lesson 3.2 ~ Equivalent Fractions
75
EXAMPLE 2
Use division to find the missing number in the equivalent fractions. 8 = __ 12 = __ a. __ ☐ b. __ 1 16 8 36 ☐
Solutions
8 = a. The denominator of 16 was divided __ 16 by 2 to make a denominator of 8.
÷2
÷2 The denominator was divided by 2. 8 = __ The numerator must also be divided by 2. 16 The missing number is 4.
__ ☐ 8
_ 4 8
÷ 12
12 = b. The numerator of 12 was divided __ 36 by 12 to make a numerator of 1.
__ 1 ☐
12 = The numerator was divided by 12. __ 36 The denominator must also be divided by 12. ÷ 12 The missing number is 3.
_ 1 3
EXERCISES 1. Use models to determine if _ 13 is equivalent to _ 26 .
a. Copy the two rectangles below. _ 13
_ 26 b. Divide the first rectangle into three equal-sized sections. Divide the second rectangle into six equal-sized sections. c. Color in the number of sections given by the numerator of each fraction. d. Compare the two models. Are the fractions equivalent? Explain your answer. Use models to show whether or not each pair of fractions is equivalent. 2. _ 12 and _ 24 3. _ 25 and _ 36 4. _ 14 and
_ 3 8
5. Serj decided to use rectangular fraction tiles to show whether or not _ 58 is equivalent to _ 34 . Look at Serj’s model below. Are the fractions equivalent? How do you know?
76
Lesson 3.2 ~ Equivalent Fractions
6. Use rectangular tiles to show whether or not _46 is equivalent to _ 23 . Use multiplication to find the missing number for each equivalent fraction. 7. __ 1 = __ ☐ 8. __ 5 = __ ☐ 9. _ 35 = __ 18 2 8 30 6 ☐
10. _ 23 =
__ 14 11. __ 1 = 10 ☐
__ ☐ 30
12. _ 67 =
__ 60 ☐
Use division to find the missing number for each equivalent fraction.
Write two fractions that are equivalent to each fraction.
19. _ 13 20. __ 6 21. __ 4 12 10 22.
_ 2 23. _ 6 24. __ 10 8 9 25
25. Jedediah told his mom that _ 39 of his chores were completed. His mother
asked, “Are you telling me that _13 of your chores are done?” How should he answer this question? Explain your reasoning.
26. Mykesha gave away 24 of the 30 sticks of gum in her pack.
a. Write a fraction to represent the portion of gum she gave away. b. Write an equivalent fraction with a smaller numerator and denominator to represent the portion of gum she gave away.
REVIEW List the factors of each number. State whether the number is prime or composite.
27. 11 28. 24 29. 39 Find the GCF of each pair of numbers using any method.
30. 10 and 30
31. 20 and 24
32. 42 and 72 Lesson 3.2 ~ Equivalent Fractions
77
T ic -T ac -T oe ~ F r ac t ion G a m e Step 1: Draw a game board on a piece of poster board with a starting place and more than sixteen squares that lead to an ending place. Step 2: Write at least 8 different fractions in simplest form, one on each square, not including the starting point. You may use the same fraction up to two times. Step 3: Write 3 equivalent fractions on small cards for each simplified fraction you wrote on your game board. (There will be at least 24 cards.) Step 4: Write directions for your game. Examples: Do players go backward if they draw a card that has a fraction that is equivalent to one behind them but none in front of them? How do they get to the ending place? Are there places on the game board where they are stuck until they can answer a specific question with fractions? Step 5: Try the game with your family or friends to make sure it works. Step 6: Bring your game to class to play.
T ic -T ac -T oe ~ E qu i va l e n t F r ac t ion s Common fractions are fractions used in our world. For example, they are fractions used in cooking, sewing, woodworking, etc. Some examples of common fractions are:
1 2
_
1 _ 4
3 _ 4
1 _ 3
2 _ 3
1 _ 8
Write three equivalent fractions for each fraction above. Make a poster to display the sets of fractions. Use models to show each common fraction and its equivalent fractions.
Page 1 of 5. 74 Lesson 3.2 ~ Equivalent Fractions. EQUIVALENT FRACTIONS. LESSON 3.2. A recent survey asked girls and boys how they spend their free ...
Celia's cell phone company charges $0.39 per minute if she goes over her allotted minutes. for the month. Last month she went over by 15 minutes. How much ...
2014 Common Core, Inc. Some rights reserved. commoncore.org. This work is licensed under a. Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Application Problem (7 minutes). Hannah traces square-inch tiles to draw 3 larger
each category. (Post the shape names.) S: B and G might be squares. All of them are quadrilaterals. H and K might be rhombuses. It's. hard to know if their ...
S: The vase could hold some rice, but the cube stick can't really hold anything. T: Okay, so I can figure out the capacity of the vase, but is the cube stick meant to ...
Concept Development (30 minutes). Materials: (T) Completed page 1 sample of Problem Set (analyzing tool) (S) 4 circle templates, ruler,. crayons, Problem Set.
This is like the last one. There are lots of ways it could look. T: With your partner, decide how many chocolate and how many vanilla cookies Susie had. Make a. picture about your story in the 5-group way on your personal board and write the number s
Read the expression aloud with me. S: (Read.) T: What do you notice about this expression that would help us translate these words into symbols? Turn and talk.
As students see varied growth patterns. related to saving money, their number. sense is supported. To expedite ... Use your calculator to fill in the chart and find out. how much money he will have saved by the end of the year. T: Is this ... G5-M6-F
Sign in. Page. 1. /. 14. Loading⦠Page 1 of 14. Page 1 of 14. Page 2 of 14. Page 2 of 14. Page 3 of 14. Page 3 of 14. DF-38_The Enigma.pdf. DF-38_The ...
Choose the one you consider correct and record your choice in soft pencil on ... The company proposes a capital reconstruction scheme with the following terms.
199. Page 3 of 32. Mullen_More_Playful_Interfaces_329899_1_En_9_Chapter_OnlinePDF.pdf. Mullen_More_Playful_Interfaces_329899_1_En_9_Chapter_OnlinePDF.pdf. Open. Extract. Open with. Sign In. Main menu. Displaying Mullen_More_Playful_Interfaces_329899_
Write your name, Centre number and candidate number on the Answer Sheet in the spaces ... C Ordinary shareholders in a company are members with voting rights. .... $1800 favourable and the materials usage variance is $1000 adverse.
Services such as information retrieval, business planning, basic record keeping, management. assistance, and marketing assistance would greatly benefit the ...
Choose the one you consider correct and record your choice in soft pencil on the ... 7 A company is to purchase an unincorporated business by the issue of 120 ...
Which entry is shown in the income statement for the year ended 30 September 2014 for the ... A Debenture holders always hold security on the assets of the company. .... 25 A company has a policy of holding inventory equal to next month's ...
May 1, 2017 - 1200-08-32-.10 Infectious and Hazardous Waste. 1200-08-32-.03 ..... The process of treating water used for dialysis purposes in order to maintain a ..... There shall be evidence of monthly assessment for new and recurrent ...
12 In a set of limited company accounts, which item would be included in the statement of changes in equity .... 27 A company sells its products at $2.10 per unit.
May 1, 2017 - Techniques and systems for identifying, reporting, investigating and controlling infections ..... assessed through quality management activities; ...
... to represent the. University and Australia in a global business planning competition. Evan J. Douglas, Professor and Head. Brisbane Graduate School of Business. Queensland University of Technology. 2 George Street, Brisbane, Australia 4000. Tel:
