Add and Subtract Parts of a Whole
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1 Lesson 7. Add and Subtract Parts of a Whole Justin has _ pound of cheddar cheese and 2_ pound of brick cheese. How much cheese does he have in all? Step Use fraction strips to model the problem. Use three _ -strips to represent _ pound of cheddar cheese. Step 2 Join two more _ -strips to represent the amount of brick cheese. Step Count the number of _ -strips. There are five _ -strips. Write the amount as a fraction. Justin has Step Use the model to write an equation. _ pound of cheese. _ 2 Suppose Justin eats _ pound of cheese. How much cheese is left? Step Use five _ -strips to represent the _ pound of cheese. Step 2 Remove one _ -strip to show the amount eaten. Step Count the number of _ -strips left. There are four _ fraction strips. There is pound left. Step Write an equation for the model. 2 Use the model to write an equation
2 Lesson 7.2 Write Fractions as Sums A unit fraction tells the part of the whole that piece represents. A unit fraction always has a numerator of. Bryan has pound of clay for making clay figures. He wants to use pound of clay for each figure. How many clay figures can he make? Use fraction strips to write as a sum of unit fractions. Step Represent with fraction strips. Step 2 Each is a unit fraction. Write a addend for each -strip you used to show. Step Count the number of addends. The number of addends represents the number of clay figures Bryan can make. So, Bryan can make clay figures. Write the fraction as the sum of unit fractions
3 Lesson 7. Add Fractions Using Models Fractions with like denominators have the same denominator. You can add fractions with like denominators using a number line. Model. Step Draw a number line labeled with sixths. Model the fraction _ by starting at 0 and shading sixths Step 2 Add the fraction _ by shading more sixth. Step How many sixths are there in all? sixths Write the number of sixths as a fraction. sixths Model Find the sum. Use a model to help
4 Lesson 7. Subtract Fractions Using Models You can subtract fractions with like denominators using fraction strips. Model _ 2 2_. Step Shade the eighths you start with. Shade eighths. Step 2 Subtract 2_. Think: How many eighths are taken away? Cross out 2 of the shaded eighths. Step Count the shaded eighths that remain. There are eighths remaining. Step Write the number of eighths that remain as a fraction. eighths _. Model 2 2. _ Subtract. Use fraction strips to help. _ 2. 2 _
5 Lesson 7. Add and Subtract Fractions You can find and record the sums and the differences of fractions. Add. 2 Step Model it. Step 2 Think: How many sixths are there in all? There are sixths. sixths _ Step Record it. Write the sum as an addition equation. 2 _ Subtract. 2 2 Step Model it. Step 2 Think: There are tenths. I take away 2 tenths. How many tenths are left? There are tenths left. tenths Step Record it. Write the difference as a subtraction equation. 2 2 Find the sum or difference.. 7 eighth-size parts 2 eighth-size parts 7_ 2 _ _ 2 _ 2_ _ 7-
6 Lesson 7. Rename Fractions and Mixed Numbers A mixed number is made up of a whole number and a fraction. You can use multiplication and addition to rename a mixed number as a fraction greater than. Rename 2 _ as a fraction. First, multiply the denominator, or the number of parts in the whole, by the whole number. 2 2 Then, add the numerator to your product. 2 7 So, = 7 total number of parts number of parts in the whole You can use division to write a fraction greater than as a mixed number. Rename as a mixed number. To rename as a mixed number, divide the numerator by the denominator. Use the quotient and remainder to write a mixed number. q So,. Write the mixed number as a fraction Write the fraction as a mixed number
7 Lesson 7.7 Add and Subtract Mixed Numbers Find the sum. _ 2_ Add the whole number and fraction parts. Add the whole numbers: 2 Add the fractions: 2_ Write the sum as a mixed number, so the fractional part is less than. _ 2 _ 2_ Find the difference. _ 2 _ Subtract the fraction and the whole number parts. Subtract the fractions: _ 2 Subtract the whole numbers: 2 _ 2 Find the sum or difference
8 Lesson 7. Subtraction with Renaming Fraction strips can help you subtract mixed numbers or subtract a mixed number from a whole number. Find the difference. _ 2 22_ Step Model the number you are subtracting from, _. Step 2 Because you cannot subtract 2_ from _ without renaming, change one of the strips to three _ strips. Then subtract by crossing out two wholes and two _ strips. Find the difference. 2 2 _ So, _ _ 2 _. Step Model the number you are subtracting from, 2. Step 2 Because you cannot subtract _ from without renaming, change one of the strips to four _ strips. Then subtract by crossing out one whole and one _ strip. So, 2 2. Find the difference = =
9 Lesson 7.9 Algebra Fractions and Properties of Addition Properties of addition can help you group and order addends so you can use mental math to find sums. The Commutative Property of Addition states that when the order of two addends is changed, the sum is the same. The Associative Property of Addition states that when the grouping of addends is changed, the sum is the same. ( ) ( ) Use the properties and mental math to add _ 7. Step Look for fractions that combine to make. 7 _ Step 2 Use the Commutative Property to order the addends so that the fractions with a sum of are together. 7 7 Step Use the Associative Property to group the addends that you can add mentally. ( ) 7 _ Step Add the grouped numbers and then add the other mixed number. Step Write the sum. (7) 7 _ 2 7 _ Use the properties and mental math to find the sum.. ( 2 ) 2. ( 7 ). 7 ( ). (2 2 2) ( ). 9 2 ( 7 ) 7-2
10 Lesson 7. Problem Solving Multistep Fraction Problems Jeff runs _ mile each day. He wants to know how many days he has to run before the total number of miles he runs is a whole number. Read the Problem What do I need to find? I need to find how many days Jeff needs to run _ mile until the total number of miles he runs is a whole Solve the Problem Describe how to act it out. Use a number line number. What information do I need to use? _ Jeff runs mile a day. He wants the distance run to be a whole number How will I use the information? I can use a number line and patterns the problem. to. act out Day : _ mile _ Day 2: _ mile whole mile and _ mile more _ 9_ Day : 9 _ mile whole mile and _ mile more Day : 2 mile 2 whole miles and 2 _ mile more _ Day : mile whole miles So, Jeff will run miles in days. 2. Lena runs 2_ mile each day. She wants to know how many days she has to run before she has run a whole number of miles. 2. Mack is repackaging _ -pound bags of birdseed into -pound bags of birdseed. What is the least number of _ -pound bags of birdseed he needs in order to fill -pound bags without leftovers? 7-2
_ _ _ _ _ _. Add and Subtract Parts of a Whole R54. Name. Justin has 3_. How much cheese does he have in all?
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