All the solutions provided in **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 8 Lesson 10 Mixed Numbers and Improper Fractions **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 8 Lesson 10 Mixed Numbers and Improper Fractions

An improper fraction has a numerator that is greater than or equal to its denominator. Mixed numbers can be written as improper fractions.

**Math in My World
**

**Example 1**

Nyoko is selling pies at a bake sale. Each pie has 5 slices. There are 7 slices left. What fraction of the pies is left?

One Way

Count the wholes and the parts.

Another Way

Count the parts.

So, , of the pies is left.

Answer:

Fraction of the pies is left = \(\frac{7}{5}\) or 1\(\frac{2}{5}\)

Explanation:

Number of slices each pie has = 5.

Number of slices left = 7.

Fraction of the pies is left = Number of slices left ÷ Number of slices each pie has

= 7 ÷ 5 or \(\frac{7}{5}\) or 1\(\frac{2}{5}\)

You can change a mixed number to an improper fraction. You can also change an improper fraction to a mixed number.

**Example 2
**Write 1\(\frac{3}{8}\) as an improper fraction.

The model shows 1\(\frac{3}{8}\).

Answer:

Improper fraction of 1\(\frac{3}{8}[/latex = [latex]\frac{11}{8}\)

Explanation:

Mixed fraction:

1\(\frac{3}{8}[/latex = [(1 × 8) + 3] ÷ 8

= (8 + 3) ÷ 8

= 11 ÷ 8 or [latex]\frac{11}{8}\)

**Example 3
**Write \(\frac{9}{4}\) as a mixed number.

The model shows 9 divided into groups of 4.

There are 2 wholes and 1 out of 4 left over.

So, \(\frac{9}{4}\) = .

Answer:

So, \(\frac{9}{4}\) =

Explanation:

\(\frac{9}{4}\)

There are 2 wholes and 1 out of 4 left over.

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

**Talk Math
**Why does the improper fraction and mixed number for Exercise 1 have the same denominator?

Answer:

The improper fraction and mixed number for Exercise 1 have the same denominator because number of the whole parts are same.

Explanation:

Improper Fraction = A fraction whose numerator is larger than the denominator.

Mixed Number = An integer combined with a proper fraction showing how many wholes and how many parts are in the number.

**Guided Practice
**Question 1.

Write a mixed number and an improper fraction for the shaded model.

Answer:

Improper fraction = \(\frac{9}{4}\)

Mixed fraction of \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

Explanation:

Number of shaded parts = 9.

Number of parts = 5.

Improper fraction = Number of shaded parts ÷ Number of parts

= 9 ÷ 5 or \(\frac{9}{5}\)

Mixed fraction = \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

### McGraw Hill My Math Grade 4 Chapter 8 Lesson 10 My Homework Answer Key

**Practice
**

**Write a mixed number and an improper fraction for each shaded model.**

Question 1.

Answer:

Improper fraction = \(\frac{7}{4}\)

Mixed fraction of \(\frac{7}{4}\) = 1\(\frac{3}{4}\)

Explanation:

Number of shaded parts = 7.

Number of parts = 4.

Improper fraction = Number of shaded parts ÷ Number of parts

= 7 ÷ 4 or \(\frac{7}{4}\)

Mixed fraction = \(\frac{7}{4}\) = 1\(\frac{3}{4}\)

Question 2.

Answer:

Improper fraction = \(\frac{8}{3}\)

Mixed fraction of \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

Explanation:

Number of shaded parts = 8.

Number of parts = 3.

Improper fraction = Number of shaded parts ÷ Number of parts

= 8 ÷ 3 or \(\frac{7}{3}\)

Mixed fraction = \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

**Write a mixed number and an improper fraction for each model.
**Question 3.

Answer:

Improper fraction = \(\frac{13}{4}\)

Mixed fraction of \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Explanation:

Number of shaded parts = 13.

Number of parts = 4.

Improper fraction = Number of shaded parts ÷ Number of parts

= 13 ÷ 4 or \(\frac{13}{4}\)

Mixed fraction = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 4.

Answer:

Improper fraction = \(\frac{17}{12}\)

Mixed fraction of \(\frac{17}{12}\) = 1\(\frac{5}{12}\)

Explanation:

Number of shaded parts = 17.

Number of parts = 12.

Improper fraction = Number of shaded parts ÷ Number of parts

= 17 ÷ 12 or \(\frac{17}{12}\)

Mixed fraction = \(\frac{17}{12}\)= 1\(\frac{5}{12}\)

Question 5.

Draw a model to write 2\(\frac{3}{5}\) as an improper fraction.

Answer:

Explanation:

2\(\frac{3}{5}\) = [(2 × 5) + 3] ÷ 5

= (10 + 3) ÷ 5

= 13 ÷ 5 or \(\frac{13}{5}\)

Question 6.

Draw a model to write \(\frac{30}{4}\) as a mixed number.

Answer:

Mixed number of \(\frac{30}{4}\) = 7\(\frac{2}{4}\)

Explanation:

\(\frac{30}{4}\) = 7 × 4 = 28 + 2 = 30.

= 7\(\frac{2}{4}\)

**Problem Solving
**Question 7.

**Mathematical PRACTICE**Use Number Sense Ana walked \(\frac{13}{3}\) miles. Write \(\frac{13}{3}\) as a mixed number.

Answer:

Mixed number of \(\frac{13}{3}\) = 4\(\frac{1}{3}\)

Explanation:

Number of miles of Ana walked = \(\frac{13}{3}\)

Mixed number:

\(\frac{13}{3}\) = 4\(\frac{1}{3}\)

Question 8.

There are 5\(\frac{4}{5}\) cups of milk left in a carton. Write 5\(\frac{4}{5}\) as an improper fraction.

Answer:

Improper fraction of 5\(\frac{4}{5}\) = \(\frac{29}{5}\)

Explanation:

Number of cups of milk left in a carton = 5\(\frac{4}{5}\)

Improper fraction:

5\(\frac{4}{5}\) = [(5 × 5) + 4] ÷ 5

= (25 + 4) ÷ 5

= 29 ÷ 5 or \(\frac{29}{5}\)

**Vocabulary Check
**Question 9.

Is \(\frac{10}{3}\) an improper fraction? Explain.

Answer:

\(\frac{10}{3}\) is an improper fraction because the numerator is greater than the denominator.

Explanation:

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

\(\frac{10}{3}\)

**Test Practice
**Question 10.

Amelia needs 3\(\frac{2}{3}\) cups of sugar to make cupcakes. Which improper fraction names this amount?

(A) \(\frac{5}{3}\) cups

(B) \(\frac{8}{3}\) cups

(C) \(\frac{11}{3}\) cups

(D) \(\frac{18}{3}\) cups

Answer:

Improper fraction names this amount = \(\frac{2}{3}\) cups.

(C) \(\frac{11}{3}\) cups

Explanation:

Number of cups of sugar Amelia needs to make cupcakes = 3\(\frac{2}{3}\).

Improper fraction:

3\(\frac{2}{3}\) = [(3 × 3) + 2] ÷ 3

= (9 + 2) ÷ 3

= 11 ÷ 3 or \(\frac{2}{3}\) cups.