Question

lesson review
in this lesson, you learned to

• compare fractions with like denominators,
• compare fractions with like numerators,

and

• compare fractions with unlike numerators

or denominators.

1. which statement shows how to compare $\frac{4}{6}$ and $\frac{3}{6}$?

a. $\frac{2}{3} > \frac{4}{6}$
b. $\frac{4}{6} > \frac{3}{6}$
c. $\frac{2}{3} < \frac{6}{6}$
d. $\frac{2}{3} = \frac{3}{6}$

1. which comparison is true?

a. $\frac{3}{8} = \frac{3}{6}$
b. $\frac{4}{8} > \frac{4}{6}$
c. $\frac{3}{8} < \frac{3}{6}$
d. $\frac{5}{6} > \frac{5}{7}$

1. which statement shows how to compare $\frac{2}{5}$ and $\frac{3}{10}$?

a. $\frac{6}{5} > \frac{6}{10}$
b. $\frac{2}{5} < \frac{3}{10}$
c. $\frac{6}{10} < \frac{6}{10}$
d. $\frac{4}{10} > \frac{3}{10}$

1. amir wants to find which nail is longer to use as he builds a chair. he wrote the lengths of the nails in a table below.

nail 1: $\frac{1}{2}$ inch
nail 2: $\frac{3}{4}$ inch
nail 3: $\frac{5}{8}$ inch
which comparison of nail lengths is correct?
a. $\frac{1}{2} = \frac{3}{4}$
b. $\frac{1}{2} < \frac{5}{8}$
c. $\frac{3}{4} < \frac{6}{8}$
d. $\frac{5}{8} < \frac{1}{2}$

1. choose two fractions with unlike numerators and denominators. change one or both of the fractions so that it is easy to compare the fractions. use > or < to compare the fractions. explain your reasoning.

to make it easy to compare fractions, either the numerator or the denominator

Explanation:

Step1: Compare like denominators

For $\frac{4}{6}$ and $\frac{3}{6}$, same denominator: $4>3$, so $\frac{4}{6}>\frac{3}{6}$.

Step2: Compare like numerators

For $\frac{3}{8}$ and $\frac{3}{6}$, same numerator: $8>6$, so $\frac{3}{8}<\frac{3}{6}$.

Step3: Standardize to common denominator

For $\frac{2}{5}$ and $\frac{3}{10}$, convert $\frac{2}{5}=\frac{4}{10}$. $4>3$, so $\frac{4}{10}>\frac{3}{10}$.

Step4: Test each nail length option

• A: $\frac{1}{2}=\frac{2}{4}

eq\frac{3}{4}$

• B: $\frac{1}{2}=\frac{4}{8}$, $4<5$, so $\frac{4}{8}<\frac{5}{8}$
• C: $\frac{3}{4}=\frac{6}{8}

less\frac{6}{8}$

• D: $\frac{5}{8}>\frac{4}{8}=\frac{1}{2}$

Step5: Pick & standardize two fractions

Choose $\frac{1}{3}$ and $\frac{2}{5}$. Convert to common denominator: $\frac{1}{3}=\frac{5}{15}$, $\frac{2}{5}=\frac{6}{15}$. $5<6$, so $\frac{5}{15}<\frac{6}{15}$.

Answer:

1. B. $\frac{4}{6}>\frac{3}{6}$
2. C. $\frac{3}{8}<\frac{3}{6}$
3. D. $\frac{4}{10}>\frac{3}{10}$
4. B. $\frac{1}{2}<\frac{5}{8}$
5. Example: Choose $\frac{1}{3}$ and $\frac{2}{5}$. Rewrite $\frac{1}{3}$ as $\frac{5}{15}$ and $\frac{2}{5}$ as $\frac{6}{15}$. Since $5<6$, $\frac{1}{3}<\frac{2}{5}$.