Equivalent Fractions

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Questions and Answers

Which of the following statements accurately describes equivalent fractions?

Fractions that have the same denominator but different numerators.
Fractions that represent different values but have the same denominators.
Fractions that have the same numerator but different denominators.
Fractions that represent the same value, even with different numerators and denominators. (correct)

The fractions $\frac{3}{4}$ and $\frac{9}{12}$ are equivalent.

True (A)

Which of the following fractions is equivalent to $\frac{1}{3}$?

$\frac{2}{6}$ (correct)
$\frac{3}{6}$
$\frac{2}{9}$
$\frac{4}{9}$

Consider two gardens: one divided into 3 sections and another into 4. If you want to divide both gardens into the same number of equal sections, what is the minimum number of sections each garden should have?

12 sections (B) Signup and view all the answers

Finding a common denominator between two fractions changes the value of the original fractions.

False (B) Signup and view all the answers

When comparing $\frac{2}{5}$ and $\frac{1}{4}$, what is the least common denominator that can be used?

20 Signup and view all the answers

Before you can accurately compare two fractions with unlike denominators, you need to rewrite them using a ________ denominator.

common Signup and view all the answers

Which set of fractions is equivalent to $\frac{1}{3}$ and $\frac{2}{5}$ using the least common denominator?

$\frac{5}{15}$ and $\frac{6}{15}$ (C) Signup and view all the answers

Match the fraction with its equivalent fraction:

$\frac{1}{2}$ = $\frac{5}{10}$ $\frac{1}{4}$ = $\frac{3}{12}$ $\frac{2}{3}$ = $\frac{8}{12}$ $\frac{3}{5}$ = $\frac{6}{10}$ Signup and view all the answers

Which of the following is NOT a method to determine if two fractions are equivalent?

Adding the numerators and denominators together. (C) Signup and view all the answers

Which of the following fractions is NOT equivalent to $\frac{4}{6}$?

$\frac{10}{12}$ (B) Signup and view all the answers

If $\frac{3}{5}$ is equivalent to $\frac{x}{15}$, what is the value of x?

9 Signup and view all the answers

Equivalent fractions always have the same numerator and denominator.

False (B) Signup and view all the answers

Consider the fractions $\frac{5}{6}$ and $\frac{7}{9}$. What is the least common denominator (LCD) that would allow you to easily compare these fractions?

18 (D) Signup and view all the answers

Sarah wants to compare $\frac{3}{5}$ of an hour to $\frac{5}{8}$ of an hour. To compare them, she needs to find a common denominator. Which of the following could she use as a common denominator?

40 (C) Signup and view all the answers

You have two ribbons. One is $\frac{2}{3}$ of a meter long, and the other is $\frac{3}{4}$ of a meter long. If you want to cut both ribbons into equal-length pieces, what is the shortest length each piece can be so that you use the entire length of both ribbons?

$\frac{1}{12}$ meter (B) Signup and view all the answers

If $\frac{2}{7}$ is equivalent to $\frac{x}{21}$, and $\frac{3}{5}$ is equivalent to $\frac{y}{25}$, what is the value of $x + y$?

21 (A) Signup and view all the answers

Which of the following pairs demonstrates the correct process of rewriting fractions with a common denominator to determine equivalence?

$\frac{3}{7} = \frac{6}{14}$ because multiplying both the numerator and denominator of $\frac{3}{7}$ by 2 results in $\frac{6}{14}$ (B) Signup and view all the answers

Explain, using an example, how multiplying both the numerator and denominator of a fraction by the same number results in an equivalent fraction.

Multiplying the numerator and denominator by the same number is the same as multiplying by 1, which doesn't change the value. For example, $\frac{1}{2} * \frac{2}{2} = \frac{2}{4}$, and $\frac{2}{4}$ is equivalent to $\frac{1}{2}$. Signup and view all the answers

What is the least common denominator (LCD) of $\frac{1}{3}$ and $\frac{1}{8}$? Show your work.

The least common denominator is 24. Explanation: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24. Multiples of 8: 8, 16, 24. Signup and view all the answers

Consider two gardens: one divided into 5 sections and the other into 7 sections. If you want to divide both gardens into more sections so that they have the same number of equal-sized sections, what is the minimum number of sections each garden should have?

Each garden should have 35 sections. It's because 35 is the least common multiple of 5 and 7. Signup and view all the answers

Is $\frac{3}{5}$ equivalent to $\frac{9}{15}$? Explain how you know.

Yes, $\frac{3}{5}$ and $\frac{9}{15}$ are equivalent. $\frac{3}{5}$ multiplied by $\frac{3}{3}$ equals $\frac{9}{15}$. Signup and view all the answers

In week 1, a plant grew $\frac{2}{5}$ inch, and in week 2, it grew $\frac{3}{7}$ inch. In which week did it grow more? Explain your answer.

Week 2. Convert $\frac{2}{5}$ and $\frac{3}{7}$ to have a common denominator of 35. The fractions become $\frac{14}{35}$ and $\frac{15}{35}$, so plant grew more in week 2. Signup and view all the answers

Flashcards

What are Equivalent Fractions?

Fractions that represent the same value, even though they may look different.

What is Modeling Equivalent Fractions?

A method to visually represent equivalent fractions using shapes or diagrams.