All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 8 Lesson 7 Use Models to Write Fractions as Decimals will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 8 Lesson 7 Use Models to Write Fractions as Decimals
You can use models to write fractions as equivalent decimals.
Draw It
Use a model to write \(\frac{1}{2}\) as a decimal.
1. Write \(\frac{1}{2}\) as an equivalent fraction with a denominator of 10.
2. Shade a model of 
using the grid.
Shade 
using the grid.
How many tenths are shaded? five
The model shows five tenths or 0.5
So, \(\frac{1}{2}\) = \(\frac{5}{10}\)
Helpful Hint
Multiplying \(\frac{1}{2}\) by \(\frac{5}{5}\) is the same as multiplying \(\frac{1}{2}\) by 1. The result is an equivalent fraction.
Try It
Use a model to write \(\frac{3}{4}\) as a decimal.
1. Write \(\frac{3}{4}\) as a fraction with a denominator of 100.
\(\frac{3}{4}\) = \(\frac{75}{100}\)
2. Shade a model of using the 10-by-10 grid.
Shade a model of \(\frac{75}{100}\) using the 10-by-10 grid.
How many squares out of the loo are shaded? 75
The model shows seventy five hundredths or 0.75
So, \(\frac{3}{4}\) = \(\frac{75}{100}\)
Talk About It
Question 1.
Mathematical PRACTICE 4 Model Math In the first activity, how would it change if \(\frac{1}{2}\) was written as a fraction with a denominator of 100? Would the result be the same? Explain.
Answer:
The result will be same
If \(\frac{1}{2}\) was written as a fraction with a denominator of 100 the result will be \(\frac{50}{100}\) that is 0.50 which is same as 0.5
Explanation:
Find equivalent fractions with a denominator of 100.
Since 2 × 50 = 100, multiply 1 × 50 to obtain 50.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{1}{2}\) = \(\frac{50}{100}\) means fifty hundredths, or 0.50.
Question 2.
Do \(\frac{3}{5}\) and 0.6 represent equivalent numbers? Explain.
Answer:
Yes
Explanation:
\(\frac{3}{5}\) is equal to 0.6. We’ve just expressed this as a decimal.
0.6 is the same thing as \(\frac{6}{10}\), which could be rewritten as \(\frac{3}{5}\) or vice versa.
Practice It
Mathematical PRACTICE 5 Use Math Tools Shade each model. Then write each fraction as a decimal.
Question 3.
\(\frac{1}{4}\) = _____
Answer: 0.25
Explanation:
Find equivalent fractions with a denominator of 100.
Since 4× 25 = 100, multiply 1 × 25 to obtain 25.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{1}{4}\) = \(\frac{25}{100}\) means twenty five hundredths, or 0.25.
Read the decimal as twenty five hundredths
Question 4.
\(\frac{3}{20}\) = _____
Answer: 0.15
Explanation:
Find equivalent fractions with a denominator of 100.
Since 20× 5= 100, multiply 3 × 5 to obtain 15.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{3}{20}\) = \(\frac{15}{100}\) means fifteen hundredths, or 0.15.
Read the decimal as fifteen hundredths
Question 5.
\(\frac{2}{5}\) = _____
Answer: 0.4
Explanation:
Find equivalent fractions with a denominator of 10.
Since 5 × 2= 10, multiply 2 × 2 to obtain 4.
Write the fraction with a denominator of 10 as a decimal.
So, \(\frac{2}{5}\) = \(\frac{4}{10}\) means four tenths, or 0.4.
Read the decimal as four tenths
Question 6.
\(\frac{3}{5}\) = _____
Answer: 0.6
Explanation:
Find equivalent fractions with a denominator of 10.
Since 5 × 2= 10, multiply 3 × 2 to obtain 6.
Write the fraction with a denominator of 10 as a decimal.
So, \(\frac{3}{5}\) = \(\frac{6}{10}\) means six tenths, or 0.6.
Read the decimal as six tenths
Question 7.
\(\frac{7}{10}\) = _____
Answer: 0.7
Explanation:
Since it is the fraction with denominator 10 we can make it to decimal.
\(\frac{7}{10}\) = seven tenths or 0.7
Question 8.
\(\frac{8}{25}\) = _____
Answer: 0.32
Explanation:
Find equivalent fractions with a denominator of 100.
Since 25× 4 = 100, multiply 8 × 4 to obtain 32.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{8}{25}\) = \(\frac{32}{100}\) means thirty two hundredths, or 0.32.
Read the decimal as thirty two hundredths
Apply It
Question 9.
Juanita practiced shooting 25 free throws at basketball practice. She made \(\frac{17}{25}\) of the attempts. Write the fraction of attempts made as a decimal. Use models to help you solve.
Answer: The fraction of attempts made is 0.68
Explanation:
Find equivalent fractions with a denominator of 100.
Since 25× 4 = 100, multiply 17 × 4 to obtain 68.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{17}{25}\) = \(\frac{68}{100}\) means sixty eight hundredths, or 0.68.
Read the decimal as sixty eight hundredths
Question 10.
Travis spent 20 minutes getting ready for school in the morning. He spent \(\frac{9}{20}\) of the time eating breakfast. Write this fraction of time as a decimal. Use models to help you solve.
Answer: 0.45
Explanation:
Find equivalent fractions with a denominator of 100.
Since 20× 5= 100, multiply 9 × 5 to obtain 45.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{9}{20}\) = \(\frac{45}{100}\) means forty five hundredths, or 0.45.
Read the decimal as forty five hundredths
Mathematical PRACTICE 2 Use Algebra For Exercises 11-13, refer to the equation \(\frac{2 \times p}{5 \times q}\) = \(\frac{40}{100}\)
Question 11.
What must be true about p and q if the equation shows equivalent fractions?
Answer:
p and q are both equal to 20.
Explanation:
\(\frac{40}{2}\) = p, so p = 20.
\(\frac{100}{5}\) = q, so q = 20
Question 12.
What property shows that \(\frac{2}{5}\) × 1 = \(\frac{40}{100}\).
Answer:
The property is to multiplying the same constant to both the numerator and denominator i.e. 20
Explanation:
Since we given that
\(\frac{2}{5}\) × 1 = \(\frac{40}{100}\)
There is a property of making equivalent fractions by multiplying the same constant to both numerator and denominator.
\(\frac{2}{5}\) × \(\frac{20}{20}\) = \(\frac{40}{100}\)
So, The property is to multiplying the same constant to both the numerator and denominator i.e. 20
Question 13.
Write the decimal equivalent for \(\frac{2}{5}\) and \(\frac{40}{100}\).
Answer:
The decimal equivalent for \(\frac{2}{5}\) and \(\frac{40}{100}\) 0.4
Explanation:
The decimal for \(\frac{2}{5}\) is 0.4
The decimal for \(\frac{40}{100}\) is 0.40 that is equal to 0.4
Write About It
Question 14.
How can I use models to write fractions as decimals?
Answer:
To convert a fraction to a decimal, we divide the numerator. by the denominator.
If we have a mixed number, the whole number stays to the left of the decimal.
Explanation:
Shading different areas could represent equivalent values for both 10ths and 5ths.
Any starting area’s will represent fractions easily and some decimals.
McGraw Hill My Math Grade 5 Chapter 4 Lesson 7 My Homework Answer Key
Practice
Shade each model. Then write each fraction as a decimal.
Question 1.
\(\frac{9}{10}\) = _____
Answer: 0.9
Explanation:
Since it is the fraction with denominator 10 we can make it to decimal.
\(\frac{9}{10}\) = nine tenths or 0.9
Question 2.
\(\frac{11}{20}\) = _____
Answer: 0.55
Explanation:
Find equivalent fractions with a denominator of 100.
Since 20× 5= 100, multiply 11 × 5 to obtain 55.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{11}{20}\) = \(\frac{55}{100}\) means fifty five hundredths, or 0.55.
Read the decimal as fifty five hundredths
Problem Solving
Question 3.
Terrell hit a total of 10 home runs during the baseball season. He hit \(\frac{4}{5}\) of the home runs during the first half of the season. Write the fraction of home runs hit during the first half of the season as a decimal. Draw models to help you solve.
Answer:
Fraction of home runs hit during the first half of the season as a decimal is 0.8
Explanation:
Find equivalent fractions with a denominator of 10.
Since 5 × 2= 10, multiply 4 × 2 to obtain 8.
Write the fraction with a denominator of 10 as a decimal.
So, \(\frac{4}{5}\) = \(\frac{8}{10}\) means eight tenths, or 0.8.
Read the decimal as eight tenths
Question 4.
Mathematical PRACTICE 5 Use Math Tools Bradley and his family drove to visit a museum. They drove \(\frac{9}{25}\) of the way and stopped to get gasoline. Write the fraction of the distance traveled as a decimal. Draw models to help you solve.
Answer:
Distance traveled is 0.36
Explanation:
Find equivalent fractions with a denominator of 100.
Since 25× 4= 100, multiply 9× 4 to obtain 36.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{9}{25}\) = \(\frac{36}{100}\) means thirty six hundredths, or 0.36.
Read the decimal as thirty six hundredths
Question 5.
Lilly let her friend borrow \(\frac{1}{10}\) of the money in her purse to buy a snack. Write the fraction as a decimal. Draw models to help you solve.
Answer: 0.1
Explanation:
Since it is the fraction with denominator 10 we can make it to decimal.
\(\frac{1}{10}\) = one tenths or 0.1
Question 6.
Jackson was playing chess. Out of all the games he played, he won \(\frac{7}{25}\) of the time. Write this fraction as a decimal. Draw models to help you solve.
Answer: 0.28
Explanation:
Find equivalent fractions with a denominator of 100.
Since 25× 4= 100, multiply 7× 4 to obtain 28.
Write the fraction with a denominator of 100 as a decimal.
So, \(\frac{7}{25}\) = \(\frac{28}{100}\) means twenty eight hundredths, or 0.28.
Read the decimal as twenty eight hundredths
Question 7.
Write the decimal that represents the shaded portion of the model.
Answer:
The decimal that represents the shaded portion of the model is 0.45
Explanation:
The fraction is \(\frac{45}{100}\)
forty five hundredths.