Solutions: Section 7.6

Page 164

Q1. Are $\frac{1}{2}$ and $\frac{3}{6}$ equal? Answer: Yes.

Q2. Are $\frac{2}{3}$ and $\frac{4}{6}$ equivalent? Answer: Yes, they represent the same length.

Q3. How many $\frac{1}{6}$ make a $\frac{1}{2}$? Answer: 3 pieces ($\frac{3}{6} = \frac{1}{2}$).

Page 165

Q2. Two equivalent fractions for $\frac{2}{6}$: Answer: $\frac{1}{3}$ (simplest) and $\frac{3}{9}$ (multiplying by 1.5 numerator/denominator, or rather $\frac{1}{3} \times \frac{3}{3} = \frac{3}{9}$). Another is $\frac{4}{12}$.

Q3. $\frac{4}{6} = \dots$ Answer: $\frac{2}{3}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15}$.

Page 166 (Rotis)

Q1. 3 rotis shared by 4 children.

• Fraction: $\frac{3}{4}$
• Division Fact: $3 \div 4 = \frac{3}{4}$
• Addition Fact: $\frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4}$ (Wait, text says $1 = \frac{1}{4}+\dots$ for 1 roti. For 3 rotis, it is adding shares). Actually, each child gets $\frac{3}{4}$.

Q2. 2 Rotis shared by 4 children. Answer: Each gets $\frac{2}{4} = \frac{1}{2}$ roti.

Q3. Anil (2 cakes, 5 children). Answer: $\frac{2}{5}$ cake.

Page 168

Q1. Missing numbers:

• a. $\frac{5}{4} = \frac{10}{8}$ (Ans: 10)
• b. $\frac{4}{3} = \frac{16}{12}$ (Wait, $4 \times 4 = 16$. The text says “12 kgs… in __ bags”. Ah, potatoes. 4kg in 3 bags = $\frac{4}{3}$ kg/bag. 12 kg in $x$ bags. To have same weight/bag: $\frac{12}{x} = \frac{4}{3}$. $4 \times 3 = 12$, so $3 \times 3 = 9$. Ans: 9 bags).

Page 172: Equivalent Fractions

Q. Find equivalent pairs:

• a. $\frac{7}{2} = \frac{35}{10}$, $\frac{3}{5} = \frac{6}{10}$ (Common denom 10)
• b. $\frac{8}{3} = \frac{16}{6}$, $\frac{5}{6}$ stays $\frac{5}{6}$ (Common denom 6)
• c. $\frac{3}{4} = \frac{15}{20}$, $\frac{3}{5} = \frac{12}{20}$ (Common denom 20)

Page 173: Lowest Terms

Q. Express in lowest terms:

• a. $\frac{17}{51} = \frac{1}{3}$ (Divide by 17)
• b. $\frac{64}{144}$ -> $\frac{32}{72}$ -> $\frac{16}{36}$ -> $\frac{8}{18}$ -> $\frac{4}{9}$.
• c. $\frac{126}{147}$ -> Divide by 7 -> $\frac{18}{21}$ -> Divide by 3 -> $\frac{6}{7}$.
• d. $\frac{525}{112}$ -> Divide by 7 -> $\frac{75}{16}$.