Addition with Unlike Denominators

Transcription

1 Lesson. Addition with Unlike Denominators Karen is stringing a necklace with beads. She puts green beads on _ of the string and purple beads on 0of the string. How much of the string does Karen cover with beads? You can use fraction strips to help you add fractions with unlike denominators. Trade fraction strips of fractions with unlike denominators for equivalent strips of fractions with like denominators. Use fraction strips to find the sum. Write your answer in simplest form. _ 0 Step Use a _ strip and three 0strips to model fractions with unlike denominators. Step Trade the _ strip for five 0 strips. Step Step Add the fractions with like denominators Write the answer in simplest form. 0 5 _ 5 So, Karen covers _ of the string with beads. 5 sum Use fraction strips to find the sum. Write your answer in simplest form R50

2 Lesson. Subtraction with Unlike Denominators You can use fraction strips to help you subtract fractions with unlike denominators. Trade fraction strips of fractions with unlike denominators for equivalent strips of fractions with like denominators. Use fraction strips to find the difference. Write your answer in simplest form. _ 0 Step Use a _ fraction strip to model the first fraction. Step Trade the _ strip for five 0 strips. Step _ Subtract by taking away So, _ Written in simplest form, 0 5 _ 5. Use fraction strips to find the difference. Write your answer in simplest form R5

3 Lesson. Estimate Fraction Sums and Differences You can round fractions to 0, to _, or to to estimate sums and differences. Estimate the sum. Step Find _ on the number line. Is it closest to 0, _, or? The fraction _ is closest to _. Step Find _ on the number line. Is it closest to 0, _, or? The fraction _ is closest to 0. Step To estimate the sum, add the two rounded numbers. So, is about _ _ 0 5 _ Estimate the sum or difference R5

4 Lesson. Common Denominators and Equivalent Fractions You can find a common denominator of two fractions. A common denominator of two fractions is a common multiple of their denominators. Find a common denominator of _ and 7 0. Rewrite the pair of fractions using a common denominator. Step Identify the denominators. The denominators are and 0. Step List the multiples of the greater denominator, 0. Multiples of 0: 0, 0, 0, 0, 50, 0,... Step Check if any of the multiples of the greater denominator are evenly divisible by the other denominator. Both 0 and 0 are evenly divisible by. Common denominators of _ and 7 0are 0 and 0. Step Rewrite the fractions with a denominator of 0. Multiply the numerator and the denominator of each fraction by the same number so that the denominator results in 0. _ Use a common denominator to write an equivalent fraction for each fraction.. 5,., 5 common denominator: common denominator:., common denominator:., 0 common denominator: R5

5 Lesson.5 Add and Subtract Fractions To add or subtract fractions with unlike denominators, you need to rename them as fractions with like denominators. You can do this by making a list of equivalent fractions. Add. 5 Step Write equivalent fractions for 5 5., 0, 5, 0 Step Write equivalent fractions for _. _,, Step Rewrite the problem using the equivalent fractions. Then add. 5 _ becomes 0 5. Subtract. 0 _ Step Write equivalent fractions for 0. Step Write equivalent fractions for _. Step _, _, _, _, 5 0 Rewrite the problem using the equivalent fractions. Then subtract. 0, 0, 7, _ becomes Written in simplest form, _. Stop when you find two fractions with the same denominator. Find the sum or difference. Write your answer in simplest form R5

6 Lesson. Add and Subtract Mixed Numbers When you add or subtract mixed numbers, you may need to rename the fractions as fractions with a common denominator. Find the sum. Write the answer in simplest form. 5 Step Model 5 _ and _. Step A common denominator for _ so rename 5 _ as 5 and _ and _ is, as. Step Step Add the fractions. 5 Add the whole numbers So, 5 5. Add the sums. Write the answer in simplest form , or find the sum or difference. Write your answer in simplest form R55

7 Lesson.7 Subtraction with Renaming You can use a common denominator to find the difference of two mixed numbers. Estimate. Step Estimate by using 0, _, and as benchmarks. 5 So, the difference should be close to. Step Step Step Identify a common denominator. A common denominator of and is. Write equivalent fractions using the common denominator. _ Rename if needed. Then subtract. Since, rename as. Subtract. 5 5 So, 5 5. Since the difference of 5 is close to, the answer is reasonable. Estimate. Then find the difference and write it in simplest form.. Estimate:. Estimate: Estimate:. Estimate: 7 5. Estimate: 5. Estimate: 7 5 R5

8 Lesson. Algebra Patterns with Fractions You can find an unknown term in a sequence by finding a rule for the sequence. Find the unknown term in the sequence. _, 7 5 0,, _, _ 5 Step Find equivalent fractions with a common denominator for all of the terms. The denominators are 5 and 0. A common denominator is 0. _ and _ Step Step Step Write the terms in the sequence using the common denominator., 7 0 0,, _, 0 Write a rule that describes the pattern. The sequence increases. To find the difference between terms, subtract at least two pairs of consecutive terms So, a rule is to add 0. Use the rule to find the unknown term. Add to the third term to find the unknown term Write a rule for the sequence. Then, find the unknown term..,, _, 5,., 7,, _, Rule: Rule: R57

9 Lesson. Problem Solving Practice Addition and Subtraction Makayla walks for exercise. She wants to walk a total of miles. On Monday, she walked 5_ miles. On Tuesday, she walked _ miles. How many more miles does Makayla need to walk to reach her goal? Read the Problem What do I need to find? I need to find the distance that Makayla needs to walk.. Solve the Problem Start with the equation. 5 5 x Subtraction is the inverse operation of addition. What information do I need to use? I need to use wants to walk and How will I use the information? First Then the distance she I can write an equation I can work backward to solve the problem. the distance she has already walked. 5 5 x. Ben has 5 _ cups of sugar. He uses _ cup of sugar to make cookies. Then he uses _ cups of sugar to make fresh lemonade. How many cups of sugar does Ben have left?... Use subtraction to work backward and rewrite the equation. 5 5 x Subtract to find the value of x _ _ Estimate to show that your answer is reasonable. 5 5_ 7 5_ So, Makayla has to walk more miles to reach her goal.. Cheryl has 5 ft of ribbon. She cuts a _ -ft strip to make a hair bow. Then she cuts a 5_ -ft strip for a border on a scrapbook page. Is there enough ribbon for Cheryl to cut two _ -ft pieces to put on a picture frame? Explain. R5

10 Lesson.0 Algebra Use Properties of Addition You can use the properties of addition to help you add fractions with unlike denominators. Use the Commutative Property and the Associative Property. Add _ _ 5 5 _ 7 5 _ 5 + _ _ _ Use the Commutative Property to order fractions with like denominators. Use the Associative Property to group fractions with like denominators. Use mental math to add the fractions with like denominators. Write equivalent fractions with like denominators. Then add. Rename and simplify. Use the properties and mental math to solve. Write your answer in simplest form.. _ R5