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

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$$\frac{1}{4}$$
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.
Amount of apples left = $$\frac{5}{2}$$ or 2$$\frac{1}{2}$$
So, of the apples are left.

Explanation:
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 + $$\frac{1}{4}$$ + $$\frac{1}{4}$$ + _____________.
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?
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.

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.

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.

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.

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.

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.

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.

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$$\frac{1}{4}$$ = ____________ + _____________ + _____________ + _______________
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$$\frac{1}{2}$$ = _____________ + _____________ + _____________ + _____________ + _____________ + _____________
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$$\frac{2}{3}$$ = ____________ + _____________ + _____________ + _______________
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$$\frac{3}{8}$$ = ____________ + ____________ + ____________ + ____________ + ____________ + ____________ + ____________
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.
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.
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.
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.
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?