4-1 Adding and Subtracting with like Denominators

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Name:_____________________Chapter 4 Test Date:_______

Chapter 4: Adding and Subtracting Fractions

Lesson 4.1 Adding and Subtracting Fractions

with Like Denominators

Warm-Up: Simply each fraction.

1. [pic]= 2. [pic] = 3. [pic]= 4. [pic]=

Steps to adding fractions with like denominators:

1. Add numerators.

2. Keep the same denominator.

3. Reduce if possible; divide the numerator and denominator by the GCF.

Write the answer in lowest terms.

1. [pic] 2. [pic] 3. [pic]

+ [pic] + [pic] - [pic]

_____ ______ ______

Steps to subtracting fractions with like denominators:

1. Subtract numerators

2. Keep the same denominator

3. Reduce if possible; divide the numerator and denominator by the GCF.

Write the answer in lowest terms.

1. [pic] 2. [pic]

- [pic] - 2

______ ______

More practice examples on workbook page 45 front.

Lesson 4.2 Adding and Subtracting Fractions

with Different Denominators

Warm-Up: Find the LCM for each set of numbers.

Hint: The LCM is ≥the largest number in the set.

1. 12 and 4 _______________ 2. 9 and 2 ___________________

3. 10 and 5 _______________ 4. 8 and 6 ___________________

5. 6 and 5 ________________ 6. 3, 4 and 6 _________________

Steps to Adding fractions with unlike denominators:

1. Find the least common denominator (LCD).

2. Write equivalent fractions.

3. Add numerators.

4. Reduce if possible; divide the numerator and denominator by the GCF.

Write the answer in lowest terms.

1. [pic] 2. [pic]

+ [pic] + [pic]

______ ______

Steps to Subtracting fractions with unlike denominators:

1. Find common denominators (LCD).

2. Write equivalent fractions.

3. Subtract numerators.

4. Reduce if possible; divide the numerator and denominator by the GCF.

Write the answer in lowest terms.

1. 2[pic] 2. [pic] 3. [pic]

-[pic] - [pic] - [pic]

______ ______ ______

More practice problems on workbook page 46 front.

Something to think about:

1. Describe the steps you would use to perform the addition and subtraction of fractions with like denominators? Unlike denominators? _____________

___________________________________________________________________________________________________________________________________________________________________________

2. What is your opinion of adding and subtracting fractions?____________

__________________________________________________________________________________________________________________

3. How would you generate a plan to add and subtract fractions if you were stuck on your homework assignment tonight rather than simply giving up. _________________________________________________________

__________________________________________________________________________________________________________________

Lesson 4.3 Look for a Pattern

Notes:

Lesson 4.4 Estimating Sums and Differences of Fractions and Mixed Numbers

Warm-Up: Estimate. (Quick and Easy)

1. 3.55 + 7.3 = __________ 2. 5 + 3.66 = __________

3. 0.8 – 0.25 = __________ 4. 3 – 2.45 = __________

Estimating- If the fraction is greater than or equal to[pic], round up to the next whole number, if not leave the whole number the same (leave it alone).

[pic]= [pic]= [pic]=

Create your own examples:

Estimating Sums and Differences-

Round numbers to the nearest whole number, then add or subtract.

Examples:

1. [pic] + [pic]= 2. [pic]- [pic]=

Lesson 4.5 Adding Mixed Numbers

Warm-Up: Write as mixed numbers.

1. [pic] = 2. [pic]= 3. [pic] = 4. [pic]=

1. If the denominators are the same:

1. Add the fractions.

2. Add the whole numbers.

3. Simplify. Reduce if possible; divide the numerator and denominator by the GCF. Write the answer in lowest terms.

Examples:

1. [pic]+ [pic]=

2. [pic]+ [pic]=

_________________________________________________________

2. If the denominators are different:

1. Find common denominators, whatever you do to the denominator, bottom, you do to the numerator, top.

2. Add.

3. Simplify. Reduce if possible; divide the numerator and denominator by the GCF. Write the answer in lowest terms.

Examples:

1. [pic] + [pic] =

2. 7 + [pic]=

Something to think about:

1. Suppose you had to list the steps necessary to add mixed numbers with like denominators? Unlike denominators? What would you do? _________________________________________________________

___________________________________________________________________________________________________________________________________________________________________________

2. Suppose you are stuck on your homework tonight, what do you do? Giving up is NOT an option. _________________________________________

___________________________________________________________________________________________________________________________________________________________________________

Lesson 4.6 Subtracting Mixed Numbers

Warm-Up: Simplify.

1. [pic] + [pic]= 2. [pic] - [pic]=

3. [pic] - [pic] = 4. [pic]+ [pic]=

Steps to Subtracting Mixed Numbers without Renaming (aka: borrowing)

1. Line up vertically.

2. Find common denominators (LCD). Make sure first numerator is larger than the second one; make equivalent fractions.

3. Subtract.

4. Simplify. Reduce if possible; divide the numerator and denominator by the GCF. Write the answer in lowest terms.

Example:

1. [pic] - [pic] =

Steps to Subtracting Mixed Numbers with Renaming

1. Line up Vertically.

2. Look for common denominators. Find the LCD if necessary. Write equivalent fractions.

(whatever you do to the top you do to the bottom).

3. Take one whole from the whole number.

*If the 1st numerator (top one) is less than the second (bottom one). If not borrow and rename from the first whole number. 4. Write the one as a fraction.

*The denominator (LCD) determines the amount borrowed and added to the numerator.

5. Add that numerator to the given numerator of the fractions already given.

6. Subtract.

7. Subtract numerators first, bring down the LCD, stays the same. 8. Subtract whole numbers.

9. Simplify. Reduce if possible; divide the numerator and denominator by the GCF. Write the answer in lowest terms.

10. Check your work. Then you are done and ready to move on to another one.

Examples:

1. [pic] 2. [pic] 3. [pic]

- [pic] - [pic] - [pic]

______ ______ ______

Something to think about:

1. How can you find the difference of two mixed numbers? Justify your answer. ___________________________________________________

__________________________________________________________________________________________________________________

2. Recommend a strategy to assist you with be successful when subtracting mixed numbers?_____________________________________________

_________________________________________________________

Lesson 4.7 Choose a Computation Method

Three strategies to use:

1. paper and pencil – 6th grade math homework

2. mental math-quick and easy

3. calculator-complex problems

Lesson 4.8 Exact or Estimate

Exact

Questions that indicate an exact answer is needed:

What is the total?

How many?

How much?

Do you always need an exact answer?

Estimate

Questions that indicate only an estimate is needed:

Will there be enough?

More or less than?

Examples on workbook page 52 front.

What should YOU do to prepare for the Chapter 4 Test???

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