All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 10 Lesson 6 Equivalent Fractions will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 10 Lesson 6 Equivalent Fractions
Fractions that name the same part of the whole are equivalent fractions. Equivalent fractions are equal and have the same size.
Math in My World
Example 1
Noah has one half of a fruit pizza. How could Noah cut the pizza into smaller equal-sized pieces and still have half of the whole pizza?
1. Use \(\frac{1}{4}\)-fraction tiles to equal the length of the \(\frac{1}{2}\)-fraction tile model.
How many \(\frac{1}{4}\)-tiles are there? ______________
So, \(\frac{1}{2}\) = \(\frac{2}{4}\). They are ____________ fractions. They represent the same part of one whole.
Answer:
\(\frac{1}{4}\)-fraction tiles to equal the length of the \(\frac{1}{2}\)-fraction tile model.
There are 2 \(\frac{1}{4}\)-fraction tiles that is equal to the length of \(\frac{1}{2}\)-fraction tile model.
2. Noah could cut half of the pizza into even smaller equal-sized pieces.
Use \(\frac{1}{8}\)-fraction tiles to equal the length of the \(\frac{1}{2}\)-fraction tile model.
How many \(\frac{1}{8}\)-tiles are there?
So, \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\). They are ____________ fractions.
Half of the fruit pizza is the same as \(\frac{2}{4}\) or \(\frac{4}{8}\) of the pizza.
Answer:
\(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\).
There are 4 fractions.
Example 2
Kwan’s bookshelf has 3 shelves. Only one of the shelves has books. Kwan says \(\frac{1}{3}\) of the shelves have books. His mom says \(\frac{2}{6}\) of the shelves have books. Are they both correct?
Use fraction tiles and number lines to find if the fractions are equivalent.
One Way:
Use fraction tiles.
One-third of one whole is equivalent to \(\frac{2}{6}\).
Another Way:
Use number lines.
One-third of one whole shares the same point on the number line as \(\frac{2}{6}\).
They are both correct. \(\frac{1}{3}\) = \(\frac{2}{6}\) so, they are ______________ fractions.
Answer:
Kwan’s bookshelf has 3 shelves. Only one of the shelves has books. Kwan says \(\frac{1}{3}\) of the shelves have books. His mom says \(\frac{2}{6}\) of the shelves have books.
\(\frac{2}{6}\) = \(\frac{1}{3}\)
So, yes they are both correct.
There are two fractions.
Talk Math
What pattern do you see in the equivalent fractions \(\frac{1}{2}\), \(\frac{2}{4}\), \(\frac{4}{8}\)?
Answer:
\(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\)
Guided Practice
Question 1.
Complete the number sentence with an equivalent fraction.
Answer:
\(\frac{1}{2}\) = \(\frac{2}{4}\)
The equivalent fraction of \(\frac{1}{2}\) is \(\frac{2}{4}\)
Independent Practice
Complete each number sentence to show equivalent fractions.
Question 2.
Answer:
\(\frac{1}{2}\) = \(\frac{3}{6}\)
The equivalent fraction of \(\frac{1}{2}\) is \(\frac{3}{6}\)
Question 3.
Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)
The equivalent fraction of \(\frac{6}{8}\) is \(\frac{3}{4}\)
Question 4.
Answer:
\(\frac{2}{4}\) = \(\frac{4}{8}\)
The equivalent fraction of \(\frac{2}{4}\) is \(\frac{4}{8}\)
Question 5.
Answer:
\(\frac{1}{3}\) = \(\frac{2}{6}\)
The equivalent fraction of \(\frac{1}{3}\) is \(\frac{2}{6}\)
Match each pair of equivalent fractions.
Answer:
Problem Solving
Question 10.
Raheem was at bat 8 times during a baseball game. He struck out 2 times. Circle the equivalent fractions that represent the number of times Raheem hit the ball.
\(\frac{2}{8}\) \(\frac{6}{8}\) \(\frac{1}{4}\) \(\frac{3}{4}\)
Answer:
Given,
Raheem was at bat 8 times during a baseball game. He struck out 2 times.
The fraction is \(\frac{2}{8}\)
So, the equivalent fraction of \(\frac{2}{8}\) is \(\frac{1}{4}\)
Question 11.
Leah said that it rained 2 of the last 4 school days. Circle the equivalent fractions that represent the number of days it rained over the last 4 school days.
\(\frac{2}{4}\) \(\frac{1}{2}\) \(\frac{4}{2}\) \(\frac{3}{4}\)
Answer:
Leah said that it rained 2 of the last 4 school days.
The fraction is \(\frac{2}{4}\)
So, the equivalent fraction of \(\frac{2}{4}\) is \(\frac{1}{2}\)
Question 12.
Mathematical PRACTICE Reason Andrew had 8 math problems to do for homework. He completed half of them after school. Shade the bar below to show the fraction of problems he still has to do. Then write two equivalent fractions.
Answer:
Given,
Andrew had 8 math problems to do for homework. He completed half of them after school.
The fraction is \(\frac{4}{8}\) = \(\frac{1}{2}\)
HOT Problems
Question 13.
Mathematical PRACTICE Find the Error Circle the fraction that does not belong with the other 3. Explain.
Answer:
Question 14.
Building on the Essential Question How do you know if two fractions are equivalent?
Answer: Two fractions are said to be equivalent if their values are the same. We usually multiply the numerator and denominator of a fraction by the same number to get its equivalent fraction.
McGraw Hill My Math Grade 3 Chapter 10 Lesson 6 My Homework Answer Key
Practice
Complete each number sentence to show equivalent fractions.
Question 1.
Answer:
The equivalent fraction of 1/4 is 2/8.
In the first figure, 1 part is shaded among 4 and in the second figure 2 parts are shaded among 8.
Question 2.
Answer:
The equivalent fraction of 4/6 is 2/3
In the first figure, 4 part is shaded among 6 and in the second figure 2 parts are shaded among 3.
Question 3.
Answer:
The equivalent fraction of 1/2 is 3/6
In the first figure, 1 part is shaded among 2 and in the second figure 3 parts are shaded among 6.
Question 4.
Answer:
The equivalent fraction of 2/4 is 1/2.
In the first figure, 2 part is shaded among 4 and in the second figure 1 part are shaded among 2.
Problem Solving
Question 5.
Hiroshi made 6 puppets. Two of the puppets were dogs, two were cats, and two were birds. Circle the equivalent fractions that represent the part of the puppets that were cats.
\(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{2}{4}\) \(\frac{2}{6}\)
Answer:
Given,
Hiroshi made 6 puppets. Two of the puppets were dogs, two were cats, and two were birds.
2 out of 6 were cats.
So, the fraction is \(\frac{2}{6}\) and the equivalent fraction is \(\frac{1}{3}\)
Question 6.
Mathematical PRACTICE Use Number Sense A rosebush had 8 blossoms. Two of the blossoms withered and fell off. Circle the equivalent fractions which represent the part of the blossoms still on the bush.
\(\frac{2}{8}\) \(\frac{7}{8}\) \(\frac{3}{4}\) \(\frac{6}{8}\)
Answer:
Given,
A rosebush had 8 blossoms. Two of the blossoms withered and fell off.
The fraction is \(\frac{2}{8}\)
The equivalent fraction that the part of the blossoms still on the bush is \(\frac{2}{8}\)
Vocabulary Check
Question 7.
Write a definition for equivalent fractions. Then give an example.
Answer:
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, \(\frac{2}{4}\) and \(\frac{3}{6}\) are equivalent fractions, because they both are equal to the \(\frac{1}{2}\)
Test Practice
Question 8.
Which of the following are not equivalent fractions?
(A) \(\frac{2}{6}\) and \(\frac{1}{3}\)
(B) \(\frac{2}{3}\) and \(\frac{4}{6}\)
(C) \(\frac{1}{4}\) and \(\frac{2}{8}\)
(D) \(\frac{1}{2}\) and \(\frac{3}{8}\)
Answer:
(D) \(\frac{1}{2}\) and \(\frac{3}{8}\) are not equivalent fractions.