Lesson 6.1 Equivalent Fractions Chapter 6 Study Guide - Fractions - Equivalent Fractions fractions that name the same amount o Write one fraction that is equivalent to 1/2! Draw a model to represent 1/2. It is divided into two equal parts with one part shaded.! Divide the rectangle from above in half. Now the rectangle is divided into four equal parts with 2 parts shaded.! Answer: 1/2 = 2/4 Lesson 6.2 Generate Equivalent Fractions - Models: o Shade to model 1/3 using third size parts. o Shade to model 1/3 using sixth-size parts. o You need TWO sixth-size parts to make ONE third size part. - Multiplying:
o You can multiply both the numerator and the denominator by the same whole number to find equivalent fractions. Lesson 6.3 Simplest Forms - Simplest Form- a fraction is in it s simplest form when it is represented using as few equal parts as possible. o Dividing:! Divide both the numerator and the denominator by the exact same whole number.! Example: Tell whether 2/8 is in simplest form. 2 divided by 2 = 1 8 divided by 2 = 4 2/8 can be reduced to 1/4, so 2/8 is NOT in its simplest form. o Factors:! Look for common factors in the numerator and denominator. A fraction in its simplest form will only have a common factor of 1. If they have a common factor greater than 1, the fraction is not in it s simplest form! Example: Tell whether 7/8 is in simplest form. List the factors of the numerator: 7: 1,7 List the factors of the denominator: 8: 1, 2, 4, 8 The only common factor is 1, so YES 7/8 is in simplest form. Lesson 6.4 Common Denominators o Common Denominators - a common multiple of the denominators of two or more fractions. o Multiples:! List the multiples of both denominators.! Circle the common multiples.! A common multiple can be used as a common denominator.! Example: Rewrite the fractions with common denominators. 2/4 and 5/8! List the multiples of each denominator. 4: 4, 8, 12, 16, 20 8: 8, 16, 24, 32, 40! Circle the multiples. 8 is a common multiple.
! Rewrite 2/4 so it has a denominator of 8. To do this, you need to multiply the numerator AND denominator by 2 (numerator: 2 x 2 = 4; denominator: 4 x 2 = 8). This makes 2/4 = 4/8.! 5/8 already has a denominator of 8, so it stays the same.! 4/8 and 5/8 o Multiplying! Multiply each fraction by the denominator of the other fraction.! Example: Write 4/5 and 1/2 as a pair of fractions with common denominators. Multiply both the numerator and the denominator of 4/5 by 2. o 4 x 2 = 8 o 5 x 2 = 10 o 4/5 = 8/10 Multiply both the numerator and the denominator of ½ by 5 o 1 x 5 = 5 o 2 x 5 = 10 o 1/2 = 5/10 You can write 4/5 and ½ as 8/10 and 5/10 Lesson 6.5 Problem Solving and Finding Equivalent Fractions - Find equivalent fractions to answer word problems. - Models: o Example: Jackie is making a beaded bracelet. The bracelet will have no more than 12 beads. 1/3 of the beads will be green. What other fractions could represent the part of the beads that are green? o I can draw a model of 1/3. Then I can half each model to find equivalent fractions. o Equivalent fractions of 1/3 are 2/6 and 4/12. - Tables: o Example: Kyle s mom bought bunches of balloons for a party. Each bunch has 4 balloons and ¼ of the balloons are blue. If Kyle s mom buys 5 bunches of balloons, how many balloons did she buy? How many are blue? o I can make a table:
Number of Bunches 1 2 3 4 5 Total number of blue 1 2 3 4 5 balloons Total number of balloons 4 8 12 16 20 o Think : the total of blue balloons is the numerator and the total number of all balloons is the denominator. o Kyle s mom bought 20 balloons and 5 of them are blue. Lesson 6.6 Compare Fractions using Benchmarks o Models:! Shade a model to show each fraction.! Example: Shade the models to compare 3/4 and 7/8.! 7/8 is greater than 3/4 o Benchmark Fractions- a known size that helps you understand a different size.! Use a benchmark fraction to compare two fractions.! Example: Compare 1/4 and 5/6 using 1/2 as a benchmark. 0 ½ 1 ¼ 2/4 ¾ 0 ½ 1 1/6 2/6 3/6 4/6 5/6! 1/4 is less than 5/6
- Cross Multiply: o Multiply the denominator of one fraction by the numerator of the other fraction. o Repeat with the other denominator o Whichever product is larger is the larger fraction. o Example: Lesson 6.7 Compare Fractions - Common Denominators: o Find common denominators. o Example: Compare 3/8 and 1/4! Think: 8 is a multiple of both 4 and 8. I can use 8 as a common denominator.! 1/4 = 1 x 2 = 2 = 2/8 4 x 2 = 8! 2/8 is less than 3/8 - Common Numerators: o Find common numerators o Example: Compare 3/8 and 1/4! Think: 3 is a multiple of both 1 and 3. I can use 3 as a common numerator.! 1/4 = 1 x 3 = 3 = 3/12 4 x 3 = 12! 3/8 is greater than 3/12 Lesson 6.8 Comparing and Ordering Fractions: - The fraction with the greatest distance from 0 has the greatest value. - Common Denominators: o Step 1: Identify a common denominator for all fractions.
o Step 2: Use the common denominator to write equivalent fractions. o Step 3: Compare the numerators o Step 4: Order the fractions in order from least to greatest, using the original fractions. o Example: Write 3/8, 1/4, and 1/2 in order from least to greatest.! Step 1: Multiples of 8: 8, 16, 24, Multiples of 4: 4, 8, 12, 16 Multiples of 2: 2, 4, 6, 8! Step 2: 3/8 stays the same 1/4 = 1x2 = 2/8 4x2 1/2 = 1x4 = 4/8 2x4! Step 3: 2 <3<4! Step 4: 2/8 < 3/8 < 4/8! SO: 1/4 < 3/8 < 1/2 - Using a number line: o Step 1: Compare each fraction to 1/2! List all fractions that are less than 1/2! List all fractions that are more than 1/2! Identify the smallest fraction and place on the number line. o Step 2: Compare the remaining fractions then place them on the number line. o Example: Write 7/10, 1/3, 7/12, and 8/10 in order from least to greatest. 0 1/3 1/2 7/12 7/10 8/10! Step 1: Fractions less than 1/2 : 1/3 Fractions greater than 1/2: 7/10, 7/12, 8/10 Place 1/3 on the number line! Step 2: 7/10 > 7/12 7/10 < 8/10 place 7/10, 7/12, and 8/10 on the number line! 1/3, 7/12, 7/10, 8/10