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

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.
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$$\frac{3}{8}$$. 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, $$\frac{9}{4}$$ = .
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? 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. 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. 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. 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. 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. 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. 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.
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.
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.
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.
$$\frac{10}{3}$$ 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
Improper fraction names this amount = $$\frac{2}{3}$$ cups.
(C) $$\frac{11}{3}$$ cups
Number of cups of sugar Amelia needs to make cupcakes = 3$$\frac{2}{3}$$.
3$$\frac{2}{3}$$ = [(3 × 3) + 2] ÷ 3
= 11 ÷ 3 or $$\frac{2}{3}$$ cups.