All the solutions provided in **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 8 Lesson 9 Mixed Numbers **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 8 Lesson 9 Mixed Numbers

A mixed number has a whole number part and a fraction part. It represents an amount greater than one whole.

There is more than 1 sandwich.

There are 1\(\frac{1}{2}\) sandwiches.

1 + \(\frac{1}{2}\) = 1\(\frac{1}{2}\)

The line is more than 2 inches long.

The line is 2\(\frac{1}{2}\) inches long.

1 + 1 + \(\frac{1}{4}\) = 2\(\frac{1}{4}\)

Answer:

Total length of sandwiches = 2\(\frac{1}{4}\) inches.

Explanation:

A mixed number has a whole number part and a fraction part.

There is more than 1 sandwich.

There are 1\(\frac{1}{2}\) sandwiches.

=> 1 + \(\frac{1}{2}\) = 1\(\frac{1}{2}\)

The Length of sandwich is more than 2 inches long.

The line is 2\(\frac{1}{2}\) inches long.

=> 1 + 1 + \(\frac{1}{4}\) = 2\(\frac{1}{4}\)

**Math in My World
**

**Example 1**

Caden had 3 apples. He cut off half of an apple to eat. What mixed number represents the amount of apples left?

Count the wholes. Then count the parts.

There are 2 whole apples and \(\frac{1}{2}\) of an apple left.

1 + 1 + \(\frac{1}{2}\) = 2\(\frac{1}{2}\)

So, of the apples are left.

Answer:

Amount of apples left = \(\frac{5}{2}\) or 2\(\frac{1}{2}\)

So, of the apples are left.

Explanation:

Number of apples Caden had = 3.

He cut off half of an apple to eat.

=>Amount of apples he cuts = \(\frac{1}{2}\)

Amount of apples left = Number of apples Caden had – Amount of apples he cuts

= 3 – \(\frac{1}{2}\)

= [(3 × 2) – 1] ÷ 2

= (6 – 1) ÷ 2

= \(\frac{5}{2}\) or 2\(\frac{1}{2}\)

OR

Amount of apples left = 1 + 1 + \(\frac{1}{2}\)

= 2 + \(\frac{1}{2}\)

= 2\(\frac{1}{2}\)

You can decompose a mixed number into a sum of whole numbers and unit fractions. Recall that a unit fraction is a fraction with a numerator of 1.

**Example 2
**Write the length of this leaf as a mixed number. Write an equation to show the mixed number.

1. Count the parts

The leaf is of an inch longer than 3 inches.

2. Count of parts.

The leaf is \(\frac{3}{4}\) of an inch longer than 3 inches.

3. Write the mixed number.

The leaf is 3\(\frac{3}{4}\) inches long.

4. Write the equation.

Three \(\frac{1}{4}\) – tiles can be used to model \(\frac{3}{4}\).

So, 3\(\frac{3}{4}\) = 1 + ____________ + 1 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + _____________.

Answer:

Mixed fraction of length of leaf = 3\(\frac{3}{4}\) = 1 + 1 + 1 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

Explanation:

Length of the leaf = 3\(\frac{3}{4}\)

Equation:

Mixed fraction:

Length of the leaf = 1 + 1 + 1 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

= 2 + 1 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

= 3 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

= 3\(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

= 3\(\frac{1}{2}\) + \(\frac{1}{4}\)

= 3\(\frac{3}{4}\) inches

**Talk Math
**How are fractions and mixed numbers alike? How are they different?

Answer:

Fractions and mixed numbers are alike as represent amounts that are greater than 1 and are different because a fraction is represented with its quotient and the remainder is a mixed fraction.

Explanation:

Improper fractions and mixed numbers are alike because both represent amounts that are greater than 1.

Improper fractions and mixed numbers are different because a fraction is represented with its quotient and remainder is a mixed fraction.

Guided Practice**
**Question 1.

Write a mixed number for the shaded model.

Answer:

Mixed fraction of shaded parts in the model = 2\(\frac{5}{6}\)

Explanation:

Total number of parts in a model = 6.

Number of shaded parts in the model = 1 + 1 + \(\frac{5}{6}\).

= 1 + 1 + \(\frac{5}{6}\)

= 2 + \(\frac{5}{6}\)

= 2\(\frac{5}{6}\)

**Independent Practice
**

**Write a mixed number for each shaded model.**

Question 2.

Answer:

Mixed fraction of shaded parts in the model = 1\(\frac{2}{5}\)

Explanation:

Total number of parts = 5.

Number of shaded parts in the model = 1 + \(\frac{2}{5}\)

= 1\(\frac{2}{5}\)

Question 3.

Answer:

Mixed fraction of shaded parts in the model = 2\(\frac{5}{6}\)

Explanation:

Total number of parts = 6.

Number of shaded parts in the model = 1 + 1 + \(\frac{5}{6}\)

= 2 + \(\frac{5}{6}\)

= 2\(\frac{5}{6}\)

Question 4.

Answer:

Mixed fraction of shaded parts in the model = 2\(\frac{4}{8}\)

Explanation:

Total number of parts = 8.

Number of shaded parts in the model = 1 + 1 + \(\frac{4}{8}\)

= 2 + \(\frac{4}{8}\)

= 2\(\frac{4}{8}\)

Question 5.

Answer:

Mixed fraction of shaded parts in the model = 2\(\frac{11}{12}\)

Explanation:

Total number of parts = 12.

Number of shaded parts in the model = 1 + 1 + \(\frac{11}{12}\)

= 2 + \(\frac{11}{12}\)

= 2\(\frac{11}{12}\)

Question 6.

Answer:

Mixed fraction of shaded parts in the model = 1\(\frac{5}{8}\)

Explanation:

Total number of parts = 8.

Number of shaded parts in the model = 1 + \(\frac{5}{8}\)

= 1\(\frac{5}{8}\)

Question 7.

Answer:

Mixed fraction of shaded parts in the model = 2\(\frac{3}{4}\)

Explanation:

Total number of parts = 4.

Number of shaded parts in the model = 1 + 1 + \(\frac{3}{4}\)

= 2 + \(\frac{3}{4}\)

= 2\(\frac{3}{4}\)

**Algebra Write an equation that represents each mixed number as a sum of whole numbers and unit fractions.
**Question 8.

3\(\frac{1}{4}\) = ____________ + _____________ + _____________ + _______________

Answer:

Equation of 3\(\frac{1}{4}\) = 1 + 1 + 1 + \(\frac{1}{4}\)

Explanation:

Fraction given = 3\(\frac{1}{4}\):

= 3 wholes + \(\frac{1}{4}\)

= 1 + 1 + 1 + \(\frac{1}{4}\)

Question 9.

5\(\frac{1}{2}\) = _____________ + _____________ + _____________ + _____________ + _____________ + _____________

Answer:

Equation of 5\(\frac{1}{2}\) = 1 + 1 + 1 + 1 + 1 + \(\frac{1}{2}\)

Explanation:

Fraction given = 5\(\frac{1}{2}\):

= 5 wholes + \(\frac{1}{2}\)

= 1 + 1 + 1 + 1 + 1 + \(\frac{1}{2}\)

Question 10.

2\(\frac{2}{3}\) = ____________ + _____________ + _____________ + _______________

Answer:

Equation of 2\(\frac{2}{3}\) = 1 + 1 + \(\frac{2}{3}\)

Explanation:

Fraction given = 2\(\frac{2}{3}\):

= 2 wholes + \(\frac{2}{3}\)

= 1 + 1 + \(\frac{2}{3}\)

Question 11.

4\(\frac{3}{8}\) = ____________ + ____________ + ____________ + ____________ + ____________ + ____________ + ____________

Answer:

Equation of 4\(\frac{3}{8}\) = 1 + 1 + 1 + 1 + \(\frac{3}{8}\)

Explanation:

Fraction given = 4\(\frac{3}{8}\)

= 4 wholes + \(\frac{3}{8}\)

= 1 + 1 + 1 + 1 + \(\frac{3}{8}\)

**Problem Solving
**Question 12.

**Mathematical PRACTICE**Model Math Alex has one whole orange and one-fourth of a second orange. Write a mixed number that represents the amount of oranges he has.

Answer:

Mixed fraction that represents the amount of oranges he has = 1\(\frac{1}{4}\)

Explanation:

Alex has one whole orange and one-fourth of a second orange.

Mixed fraction that represents the amount of oranges he has = 1 whole + \(\frac{1}{4}\)

=> 1 + \(\frac{1}{4}\)

=> 1\(\frac{1}{4}\)

Question 13.

Brooke gave her dog two whole dog biscuits and a half of a third dog biscuit. Write a mixed number that represents the amount of dog biscuits she gave her dog.

Answer:

Mixed number that represents the amount of dog biscuits she gave her dog = 2\(\frac{2}{3}\)

Explanation:

Brooke gave her dog two whole dog biscuits and a half of a third dog biscuit.

Amount of dog biscuits she gave her dog = 2 wholes + half of a third

= 1 + 1 + \(\frac{2}{3}\)

= 2 + \(\frac{2}{3}\)

= 2\(\frac{2}{3}\)

Question 14.

There are three cans of Juice in the refrigerator and three-fourths of a fourth can. Write a mixed number that represents the amount of juice in the refrigerator.

Write an equation that represents this mixed number as a sum of whole numbers and unit fractions.

Answer:

Mixed number that represents the amount of juice in the refrigerator = 3\(\frac{3}{4}\)

Equation = 1 + 1 + 1 + \(\frac{3}{4}\) = 3\(\frac{3}{4}\)

Explanation:

There are three cans of Juice in the refrigerator and three-fourths of a fourth can.

Amount of juice in the refrigerator = 3 whole + three-fourths

= 1 + 1 + 1 + \(\frac{3}{4}\)

= 2 + 1 + \(\frac{3}{4}\)

= 3 + \(\frac{3}{4}\)

= 3\(\frac{3}{4}\)

**HOT Problem
**Question 15.

**Mathematical PRACTICE**Reason Write a mixed number that is greater than 3 and less than 4.

Answer:

Mixed number that is greater than 3 and less than 4 = 3\(\frac{1}{4}\)

Explanation:

Mixed number that is greater than 3 and less than 4:

=> 3 wholes + \(\frac{1}{4}\)

=> 3\(\frac{1}{4}\)

Question 16.

**Building on the Essential Question** How are mixed numbers used in the real world?

Answer:

Mixed numbers used in the real world is that serving a pizza.

Explanation:

Mixed numbers are used in the real world by expressing the parts of a whole as mixed fractions while serving a pizza or a pie at home.