Maria ran $\frac{3}{4}$ of a mile and Kevin ran $\frac{4}{5}$ of a mile. Which statement correctly compares the distances they ran?

The distances cannot be compared.

If two fractions have the same positive numerator but different denominators, which statement is always true?

The fraction with the larger denominator is greater.

The fraction with the smaller denominator is greater.

The two fractions are always equal.

You must use cross-multiplication to know for sure.

A student incorrectly states that $\frac{5}{12}$ is greater than $\frac{2}{3}$ because 12 is a larger number than 3. What is the flaw in this reasoning?

A larger denominator means the whole is divided into smaller pieces.

The student should have only compared the numerators 5 and 2.

Fractions cannot be compared unless the numerators are the same.

Investigation 2: Investigating Fractions with Manipulatives Practice — Grade 6 math

Investigation 2: Investigating Fractions with Manipulatives — Practice Questions

1. Use the cross-multiplication method to compare the fractions $\frac{5}{8}$ and $\frac{4}{7}$. Fill in the blank with the correct symbol: $<$, $>$, or $=$. $\frac{5}{8}$ ___ $\frac{4}{7}$
2. Maria ran $\frac{3}{4}$ of a mile and Kevin ran $\frac{4}{5}$ of a mile. Which statement correctly compares the distances they ran?
- A. $\frac{3}{4} > \frac{4}{5}$
- B. $\frac{3}{4} < \frac{4}{5}$
- C. $\frac{3}{4} = \frac{4}{5}$
- D. The distances cannot be compared.
3. If two fractions have the same positive numerator but different denominators, which statement is always true?
- A. The fraction with the larger denominator is greater.
- B. The fraction with the smaller denominator is greater.
- C. The two fractions are always equal.
- D. You must use cross-multiplication to know for sure.
4. A recipe calls for $\frac{3}{4}$ cup of sugar. You only have a $\frac{1}{12}$-cup measuring scoop. You measure out 9 scoops. Compare the amounts using $<$, $>$, or $=$. $\frac{3}{4}$ ___ $\frac{9}{12}$
5. A student incorrectly states that $\frac{5}{12}$ is greater than $\frac{2}{3}$ because 12 is a larger number than 3. What is the flaw in this reasoning?
- A. The reasoning is correct.
- B. A larger denominator means the whole is divided into smaller pieces.
- C. The student should have only compared the numerators 5 and 2.
- D. Fractions cannot be compared unless the numerators are the same.
6. Convert the improper fraction $\frac{13}{5}$ to a mixed number. The result is ___.
7. A recipe requires $\frac{7}{3}$ cups of milk. Which of the following mixed numbers is equivalent to this amount?
- A. $2\frac{1}{3}$
- B. $1\frac{4}{3}$
- C. $3\frac{1}{3}$
- D. $2\frac{2}{3}$
8. When converting the improper fraction $\frac{19}{6}$ to a mixed number, what is the whole number part of the result?
- A. 1
- B. 3
- C. 6
- D. 19
9. A piece of wood is $\frac{35}{8}$ feet long. Write this length as a mixed number. Answer: ___
10. Which mixed number is equivalent to the improper fraction $\frac{17}{4}$?
- A. $4\frac{1}{4}$
- B. $3\frac{5}{4}$
- C. $4\frac{3}{4}$
- D. $1\frac{13}{4}$