Let's Be Rational Study Guide Name______

Let's Be Rational Study Guide Name______

1. Find each sum or difference. Show all your work.

a. / b. / c. / d.

2. For parts (a)–(b), tell which sum or difference is larger. Show your work.

a. or

b. or

3. Gregorio made money over his summer vacation by mowing lawns. One week he worked the following schedule:

Monday / hours
Wednesday / hours
Thursday / hours
Friday / hours

a. How many hours did Gregorio work for the week?

b. He needs to work 20 hours to earn the money for a trip. Will he have enough after working just this one week? Explain your thinking.

4. Jack and Helen are making cookies. The recipe says to combine cup of butter with cup chocolate chips and cup chopped nuts.

a. When these three ingredients are mixed together, how many cups of the mixture will Jake and Helen have? Show your work.

b. Jack and Helen decide to triple the recipe.

i. How many cups of butter will be needed?

ii. How many cups of chocolate chips will be needed?

iii. How many cups of chopped nuts will be needed?

c. When the ingredients for the tripled recipe are combined, how many cups of the mixture will Jack and Helen have?

5. Mr. Larson is planning the seating for a school recital. He needs to reserve of the seats for students and of the seats for parents.

a. After reserving seats for students and parents, what fraction of the seats in the auditorium are left?

b. Mr. Larson’s principal tells him that he also needs to reserve of the seats for teachers and school officials. The remainder can be used for open seating. What fraction of the seats are now left for open seating?

c. Later, Mr. Larson’s principal says he should reserve of the seats for students from other middle schools. Are there enough seats left? If not, explain why not; otherwise, state what fraction of the seats will be available for open seating.

6. Find the value of N that makes each number sentence correct.

a. / b. / c.
d. / e. / f.

7. Find each product. Show your work.

a. / b. / c.
d. / e. / f.

8. LiAnn works in the Olde Tyme Soda Shoppe. The shop sells chocolate shakes, double chocolate shakes, and triple chocolate shakes. A chocolate shake uses cup of chocolate syrup, a double chocolate shake uses cup of chocolate syrup, and a triple chocolate shake uses cup of chocolate syrup. How many shakes of each kind could she make with 3 cups of chocolate syrup?

9. Three groups of students are sharing leftover pizza (all the same size originally). In which group does each student get the most pizza? Explain your choice.

A. Six students equally share of a pizza.

B. Three students equally share of a pizza.

C. Four students equally share of a pizza.

10. Find the quotient.

d. ¸ 4 / e. ¸ 6 / f.
g. / h. / i.

Let's Be Rational Study Guide

Answer Section

SHORT ANSWER

1. ANS:

a. or ; .

b. ; or .

c. ; .

d. ; .

PTS: 1 DIF: L2 REF: Let's Be Rational | Check-Up 1

OBJ: Investigation 1: Extending Addition and Subtraction of Fractions

STA: 6OH N11 | 6OH N12 TOP: Problem 2.4 Algorithms for Addition and Subtraction

KEY: algorithm | adding fractions | subtracting fractions

2. ANS:

a. The sum of is larger than the sum of because is larger than and is larger than . Also, while .

b. The difference is larger than the difference because or and

PTS: 1 DIF: L2 REF: Bits and Pieces II | Extra Questions

OBJ: Investigation 1: Extending Addition and Subtraction of Fractions

NAT: CC 6.NS.C.6 | NAEP N1e | NAEP N2a | NAEP N2b STA: 6OH N13

TOP: Problem 1.1 Using Benchmarks KEY: benchmark | overestimate | underestimate

3. ANS:

b. No, he will be hours short of working the hours he needs.

PTS: 1 DIF: L2 REF: Bits and Pieces II | Extra Questions

OBJ: Investigation 1: Extending Addition and Subtraction of Fractions

STA: 6OH N11 | 6OH N12 TOP: Problem 2.2 Using Addition and Subtraction

KEY: adding fractions | number sentence

4. ANS:

a. cups

b. i. ii. iii.

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 2

OBJ: Investigation 1: Extending Addition and Subtraction of Fractions

STA: 6OH N11 | 6OH N12 TOP: Problem 2.2 Using Addition and Subtraction

KEY: adding fractions | number sentence

5. ANS:

c. Yes, there are enough seats, and are left for open seating.

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 2

OBJ: Investigation 1: Extending Addition and Subtraction of Fractions

STA: 6OH N11 | 6OH N12 TOP: Problem 2.1 Writing Addition and Subtraction Sentences

KEY: number sentence | adding fractions

6. ANS:

a. / b. / c.
d. / e. / f.
g. / h. / i.

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 2

OBJ: Investigation 1: Extending Addition and Subtraction of Fractions

STA: 6OH N11 | 6OH N12 TOP: Problem 2.2 Using Addition and Subtraction

KEY: adding fractions | subtracting fractions |

7. ANS:

a. / b. / c.
d. / e. / f.
g. / h. / i.

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 3

OBJ: Investigation 2: Building on Multiplication With Fractions

STA: 6OH N8 | 6OH N11 | 6OH N12 | 6OH N13

TOP: Problem 3.5 Writing a Multiplication Algorithm KEY: algorithm | multiplying fractions

8. ANS:

milkshake: 3 ÷ = 24 shakes

double milkshake: 3 ÷ = 12 double shakes

triple milkshake: 3 ÷ = 8 triple shakes

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 4

OBJ: Investigation 3: Dividing With Fractions

TOP: Problem 4.2 Dividing a Fraction by a Whole Number KEY: dividing fractions | reciprocal

9. ANS:

C; the four students who share of a pizza ( ÷ 4) will each get of the pizza. If you divide the amount of leftover pizza by the number of students in the other groups, you get: Group A: ÷ 6 = of the pizza for each student. Group B: ÷ 3 = of the pizza for each student.

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 4

OBJ: Investigation 3: Dividing With Fractions

TOP: Problem 4.2 Dividing a Fraction by a Whole Number

KEY: dividing fractions by a whole number | reciprocal

10. ANS:

a. 12 ÷ = 24 / b. 12 ¸ = 36 / c.
d. / e. / f.
g. / h. / i. = 2

PTS: 1 DIF: L2 REF: Bits and Pieces II | Additional Practice Investigation 4

OBJ: Investigation 3: Dividing With Fractions

TOP: Problem 4.3 Dividing a Fraction by a Fraction

KEY: dividing fractions by a whole number | dividing fractions | reciprocal