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# for Fractions and Decimals

## Use equivalent fractions as a strategy to add and subtract fractions.

### 5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

• Worksheet #1 (Online Sample)
• Worksheet #2
• Worksheet #3
• Worksheet #4
• Lesson: Adding Mixed Numbers with Unequal Denominators
• Worksheet #5
• Worksheet #6
• Lesson: Subtracting Fractions with Unequal Denominators
• Worksheet #7
• Worksheet #8
• Worksheet #9
• Worksheet #10
• Lesson: Subtracting Mixed Numbers with Unequal Denominators
• Worksheet #11
• Worksheet #12

### 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

• Lesson: Solving Problems - Adding Fractions and Mixed Numbers
• Worksheet #1
• Worksheet #2

## Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

### 5.NF.3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

• Lesson: Quotients of Whole Numbers that Equal Fractions
• Worksheet #1
• Worksheet #2

### 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

• Lesson: Multiplying Fractions Times Whole Numbers
• Worksheet #1
• Worksheet #2
• Worksheet #3

### a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

• Lesson: Multiplying Fractions Times Whole Numbers and Fractions
• Worksheet #6

### b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.)

• Lesson: Areas of Rectangles with Fractional Side Lengths
• Worksheet #7

### a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

• Lesson: Comparing Sizes of Products and Approximating Products
• Worksheet #1

### Note: The first half of part b above requires explanations of the results when multiplying by fractions less than 1 and greater than 1, and this is done in the preceding lesson on Comparing Sizes of Products and Approximating Products. The equivalence a/b = (n x a)/(n x b) is explained with a visual model in the following lesson.

• Lesson: Obtaining and Recognizing Equal Fractions
• Worksheet #2
• Worksheet #3

### 5.NF.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

• Lesson: Solving Problems Involving Multiplication of Fractions and Mixed Numbers
• Worksheet #1
• Worksheet #2

### b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

• Lesson: Division of Whole Numbers by Unit Fractions
• Worksheet #2

### c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

• Lesson: Word Problems - Division of Unit Fractions and Whole Numbers
• Worksheet #3

## Understand the place value system.

### 5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10

• Lesson: Dividing Whole Numbers and Decimals by Powers of 10
• Worksheet #2

### 5.NBT.3. Read, write, and compare decimals to thousandths.

• Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
• Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• Lesson: Reading and Writing Decimals
• Worksheet #1
• Worksheet #2
• Worksheet #3
• Worksheet #4
• Lesson: Reading and Writing Mixed Decimals
• Worksheet #5

### 5.NBT.4. Use place value understanding to round decimals to any place.

• Lesson: Rounding Decimals and Mixed Decimals
• Worksheet #1
• Worksheet #2

## Perform operations with multi-digit whole numbers and with decimals to hundredths.

### 5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

• Lesson: Addition of Decimals with Different Numbers of Decimal Places
• Worksheet #3
• Worksheet #4
• Lesson: Addition of Mixed Decimals
• Worksheet #5
• Worksheet #6
• Worksheet #7

### Note: Worksheet #3 has a sheet of Blank Decimal Squares attached for illustrating a few of the sums. Worksheet #7 has word problems involving addition of decimals and mixed decimals.

• Lesson: Subtraction of Decimals with Same Number of Decimal Places
• Worksheet #8
• Worksheet #9
• Worksheet #10
• Lesson: Subtraction of Decimals with Different Numbers of Decimal Places
• Worksheet #11
• Worksheet #12
• Lesson: Subtraction of Mixed Decimals
• Worksheet #13
• Worksheet #14
• Worksheet #15

### Note: Worksheets #8 and #11 each have a sheet of Blank Decimal Squares attached for illustrating differences involving decimals and mixed decimals. On worksheets #10 and #13, each exercise for computing a difference also asks for a corresponding approximation that involves rounding to the nearest tenth or nearest whole number. Worksheet #15 has word problems involving differences of decimals and mixed decimals.

• Lesson: Multiplication by Decimals
• Worksheet #19
• Worksheet #20
• Worksheet #21
• Lesson: Multiplication with Mixed Decimals
• Worksheet #22
• Worksheet #23
• Worksheet #24

### Note: Worksheet #18 has a sheet of Blank Decimal Squares attached for illustrating a few products involving decimals. On worksheet #22, there are exercises for approximating products by rounding mixed decimals to the nearest whole number. Worksheet #24 has word problems involving products of decimals and mixed decimals.

• Lesson: Division of Decimals by Whole Numbers
• Worksheet #25
• Worksheet #26
• Lesson: Division of Decimals by Decimals
• Worksheet #27
• Worksheet #28
• Worksheet #29
• Lesson: Division by Mixed Decimals
• Worksheet #30
• Worksheet #31
• Worksheet #32