All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 8 Lesson 3 Simplest Form will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 8 Lesson 3 Simplest Form
Example 1
Angie has a vertical jump height of 12 inches, and Holly has a vertical jump height of 22 inches. So, Angie’s vertical jump is \(\frac{12}{22}\) of the vertical jump of Holly. Write the fraction in simplest form.
1. List the factors. Circle the GCF
12: 1, 2, 3, 4, 6, 12
22: 1, 2, 11, 22
The GCF of 12 and 22 is 2
2. Divide both the numerator and the denominator by the GCF. This results in an equivalent fraction.
= \(\frac{6}{11}\)
The GCF of 6 and 11 is 1.2
So, Angie’s vertical jump is 
of Holly’s vertical jump.
So, Angie’s vertical jump is 
of Holly’s vertical jump.
So, Angie’s vertical jump is \(\frac{6}{11}\) of Holly’s vertical jump.
Check Use models.
Example 2
Write \(\frac{18}{30}\) in simplest form.
Divide the numerator and denominator by the same common factor. Continue dividing until the fraction is in simplest form.
Divide 18 and 30 by the common factor 2.
Divide the numerator and denominator by the common factor 3.
Since 3 and 5 have no common factors other than 1, stop dividing.
So, \(\frac{18}{30}\) written in simplest form is 
So, \(\frac{18}{30}\) written in simplest form is \(\frac{3}{5}\).
Guided Practice
Write each fraction in simplest form. If the fraction is already in simplest form, write simplified
Talk Math
Explain how to find the simplest form of any fraction.
Question 1.
\(\frac{4}{6}\)
In simplest form, \(\frac{4}{6}\) = 
Answer:
Explanation:
The GCF of 4 and 6 is 2
Divide the numerator and denominator by the common factor 2
In simplest form, \(\frac{4}{6}\) =\(\frac{2}{3}\)
Question 2.
\(\frac{2}{12}\)
In simplest form, \(\frac{2}{12}\) = 
Answer:
Explanation:
The GCF of 2 and 12 is 2
Divide the numerator and denominator by the common factor 2
In simplest form, \(\frac{2}{12}\) =\(\frac{1}{6}\)
Independent Practice
Write each fraction in simplest form. If the fraction is already in simplest form, write simplified.
Question 3.
\(\frac{6}{8}\) _____
Answer:
\(\frac{3}{4}\)
Explanation:
The GCF of 6 and 8 is 2
Divide the numerator and denominator by the common factor 2
In simplest form \(\frac{6}{8}\) = \(\frac{3}{4}\)
Question 4.
\(\frac{6}{10}\) _____
Answer:
\(\frac{3}{5}\)
Explanation:
The GCF of 6 and 10 is 2
Divide the numerator and denominator by the common factor 2
In simplest form \(\frac{6}{10}\) = \(\frac{3}{5}\)
Question 5.
\(\frac{3}{18}\) _____
Answer:
\(\frac{1}{6}\)
Explanation:
The GCF of 3 and 18 is 3
Divide the numerator and denominator by the common factor 3
In simplest form \(\frac{3}{18}\) = \(\frac{1}{6}\)
Question 6.
\(\frac{2}{5}\) _____
Answer:
Simplified
Explanation:
The GCF of 2 and 5 is 1
So \(\frac{2}{5}\) is simplified.
Question 7.
\(\frac{4}{16}\) _____
Answer:
\(\frac{1}{4}\)
Explanation:
The GCF of 4 and 16 is 4
Divide the numerator and denominator by the common factor 4
In simplest form \(\frac{4}{16}\) = \(\frac{1}{4}\)
Question 8.
\(\frac{12}{24}\) _____
Answer:
\(\frac{1}{2}\)
Explanation:
The GCF of12 and 24 is 12
Divide the numerator and denominator by the common factor 12
In simplest form \(\frac{12}{24}\) = \(\frac{1}{2}\)
Question 9.
\(\frac{6}{25}\) _____
Answer:
Simplified
Explanation:
The GCF of 6 and 25 is 1
So \(\frac{6}{25}\) is simplified.
Question 10.
\(\frac{21}{30}\) _____
Answer:
\(\frac{7}{10}\)
Explanation:
The GCF of 21 and 30 is 3
Divide the numerator and denominator by the common factor 3
In simplest form \(\frac{21}{30}\) = \(\frac{7}{10}\)
Question 11.
\(\frac{4}{11}\) _____
Answer:
Simplified
Explanation:
The GCF of 4 and 11 is 1.2
So \(\frac{4}{11}\) is simplified.
Algebra Find each unknown.
Question 12.
\(\frac{8}{28}\) = \(\frac{m}{7}\)
m = ____
Answer:
m = 2
Divide the numbers
\(\frac{8}{28}\) = \(\frac{m}{7}\)
\(\frac{2}{7}\) = \(\frac{m}{7}\)
Multiply all terms by the same value to eliminate fraction denominators
7 × \(\frac{2}{7}\) = 7 ×\(\frac{m}{7}\)
Cancel multiplied terms that are in the denominator
2 = m
Move the variable to the left
m = 2
Question 13.
\(\frac{12}{40}\) = \(\frac{b}{10}\)
b = ____
Answer:
b = 3
Cancel terms that are in both the numerator and denominator
\(\frac{12}{40}\) = \(\frac{b}{10}\)
\(\frac{3}{10}\) = \(\frac{b}{10}\)
Multiply all terms by the same value to eliminate fraction denominators
10 × \(\frac{3}{10}\) = 10 × \(\frac{b}{10}\)
Cancel multiplied terms that are in the denominator
3 = b
Move the variable to the left
b = 3
Question 14.
\(\frac{9}{24}\) = \(\frac{3}{y}\)
y = ____
Answer:
y = 8
Cancel terms that are in both the numerator and denominator
\(\frac{9}{24}\) = \(\frac{3}{y}\)
\(\frac{3}{8}\) = \(\frac{3}{y}\)
Multiply all terms by the same value to eliminate fraction denominators
8y ×\(\frac{3}{8}\) = 8y ×\(\frac{3}{y}\)
Cancel multiplied terms that are in the denominator
y × 3 = 8 × 3
Re-order terms so that constants are on the left
3y = 8 × 3
Multiply the numbers
3y = 24
Divide both sides by the same factor
\(\frac{3y}{3}\) = \(\frac{24}{3}\)
Simplify, divide the numbers
y = 8
Problem Solving
Question 15.
Mathematical PRACTICE 1 Plan Your Solution The table shows the results of a survey about favorite movie theater snacks. Write a fraction in simplest form that compares the number of people who chose popcorn to the total number of people surveyed.
Answer:
\(\frac{2}{5}\)
Explanation:
Total number of people surveyed is 24 + 12 +11 +8 +5 =60
People who chooses popcorn is 24
The GCF of 24 and 60 is 12
Divide the numerator and denominator by the common factor 12
In simplest form \(\frac{24}{60}\) = \(\frac{2}{5}\)
Question 16.
Kara buys 24 bagels. Ten are whole wheat What fraction of the bagels are whole wheat? Write in simplest form.
Answer:
Since 10 is whole wheat, the fraction is \(\frac{10}{24}\)
simplest form is \(\frac{5}{12}\)
Explanation:
The GCF of 10 and 24 is 2
Divide the numerator and denominator by the common factor 2
In simplest form \(\frac{10}{24}\) = \(\frac{5}{12}\)
HOT Problems
Question 17.
Mathematical PRACTICE 3 Which One Doesn’t Belong? Circle the fraction that is not in simplest form. Explain.
Answer:
Explanation:
The GCF of 9 and 21 is 3
Divide the numerator and denominator by the common factor 3
In simplest form \(\frac{9}{21}\) = \(\frac{3}{7}\)
Question 18.
? Building on the Essential Question Why is it important to be able to write a fraction in simplest form?
Answer:
Simplifying a fraction can make it easier to understand its value.
To simplify a fraction, divide the numerator and the denominator by a common factor.
Sometimes you will also hear simplifying called reducing a fraction.
A fraction that has been simplified by the greatest common factor is in simplest form.
McGraw Hill My Math Grade 5 Chapter 4 Lesson 3 My Homework Answer Key
Write each fraction in simplest form. If the fraction ¡s already in simplest form, write simplified.
Question 1.
\(\frac{8}{9}\) _____
Answer:
Simplified
Explanation:
The GCF of 8 and 9 is 1
So \(\frac{8}{9}\) is simplified.
Question 2.
\(\frac{9}{18}\) _____
Answer:
\(\frac{1}{2}\)
Explanation:
The GCF of 9 and 18 is 9
Divide the numerator and denominator by the common factor 9
In simplest form \(\frac{9}{18}\) = \(\frac{1}{2}\)
Question 3.
\(\frac{26}{32}\) _____
Answer:
\(\frac{13}{16}\)
Explanation:
The GCF of 26 and 32 is 2
Divide the numerator and denominator by the common factor 2
In simplest form \(\frac{26}{32}\) = \(\frac{13}{16}\)
Problem Solving
Question 4.
Mathematical PRACTICE 3 Find the Error Nicholas wrote the steps below to simplify the fraction \(\frac{20}{30}\). Find his error and correct it.
Answer:
Divide the numerator and denominator by the common factor 10 should be done.
Explanation:
The GCF of 20 and 30 is 10
Divide the numerator and denominator by the common factor 10
In simplest form \(\frac{20}{30}\) = \(\frac{2}{3}\)
Question 5.
Mr. Rolloson’s class had a board game tournament. Out of the 24 games played, Timeka won 10 games. Write \(\frac{10}{24}\) in simplest form.
Answer:
\(\frac{5}{12}\)
Explanation:
The GCF of 10 and 24 is 2
Divide the numerator and denominator by the common factor 2
In simplest form \(\frac{10}{24}\) = \(\frac{5}{12}\)
Vocabulary Check
Question 6.
Fill in the blank with the correct term or number to complete the sentence.
A fraction is written in simplest form when the GCF of the numerator and the denominator is ____.
Answer:
1
Explanation:
A fraction is written in simplest form when the GCF of the numerator and the denominator is 1
Test Practice
Question 7.
Gil’s aunt cut his birthday cake into 32 equal pieces. Eighteen pieces were eaten at his birthday party. What fraction of the cake was left?
A. \(\frac{7}{16}\)
B. \(\frac{9}{16}\)
C. \(\frac{7}{12}\)
D. \(\frac{9}{14}\)
Answer:
B
Explanation:
The GCF of 18 and 32 is 2
Divide the numerator and denominator by the common factor 2
In simplest form \(\frac{18}{32}\) = \(\frac{9}{16}\)