McGraw Hill Math

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 6 Lesson 6 Adding Mixed Numbers with Unlike Denominators are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 6 Lesson 6 Adding Mixed Numbers with Unlike Denominators

Solve

Find equivalent fractions and add. Change improper fractions to mixed numbers.

Question 1.
1\(\frac{1}{4}\) + \(\frac{1}{6}\) ________________
Answer:
1\(\frac{3}{12}\) + \(\frac{2}{12}\) = 1\(\frac{5}{12}\)

Question 2.
1\(\frac{2}{3}\) + \(\frac{1}{2}\) _______________
Answer:
\(\frac{10}{6}\)+\(\frac{4}{6}\)  = 2\(\frac{1}{3}\).

Explanation:
The equivalent fraction of \(\frac{5}{3}\) + \(\frac{1}{2}\) which is \(\frac{10}{6}\) and \(\frac{4}{6}\). So the addition of \(\frac{10}{6}\)+\(\frac{4}{6}\) is \(\frac{10+4}{6}\)
= \(\frac{14}{6}\)
= 2\(\frac{2}{6}\)
= 2\(\frac{1}{3}\).

Question 3.
2\(\frac{1}{4}\) + 3\(\frac{5}{8}\) _______________
Answer:
\(\frac{18}{8}\)+\(\frac{29}{8}\) = 5\(\frac{7}{8}\).

Explanation:
The equivalent fraction of \(\frac{9}{4}\) + \(\frac{29}{8}\) which is \(\frac{18}{8}\) and \(\frac{29}{8}\). So the addition of \(\frac{18}{8}\)+\(\frac{29}{8}\) is \(\frac{18+29}{8}\)
= \(\frac{47}{8}\)
= 5\(\frac{7}{8}\).

Question 4.
2\(\frac{1}{9}\) + \(\frac{5}{6}\) ________________
Answer:
\(\frac{114}{54}\)+\(\frac{45}{54}\) = 2\(\frac{1}{9}\).

Explanation:
The equivalent fraction of \(\frac{19}{9}\) + \(\frac{5}{6}\) which is \(\frac{114}{54}\) and \(\frac{45}{54}\). So the addition of \(\frac{114}{54}\)+\(\frac{45}{54}\) is \(\frac{114+45}{54}\)
= \(\frac{159}{54}\)
= 2\(\frac{6}{54}\) = 2\(\frac{1}{9}\).

Question 5.
4\(\frac{3}{8}\) + 2\(\frac{1}{6}\) ________________
Answer:
\(\frac{210}{48}\)+\(\frac{104}{48}\) = 6\(\frac{13}{16}\).

Explanation:
The equivalent fraction of \(\frac{35}{8}\) + \(\frac{13}{6}\) which is \(\frac{210}{48}\) and \(\frac{104}{48}\). So the addition of \(\frac{210}{48}\)+\(\frac{104}{48}\) is \(\frac{210+104}{8}\)
= \(\frac{314}{48}\) =6\(\frac{26}{48}\)
= 6\(\frac{13}{16}\).

Question 6.
1\(\frac{1}{5}\) + 1\(\frac{1}{2}\) ________________
Answer:

\(\frac{18}{8}\)+\(\frac{29}{8}\) = 5\(\frac{7}{8}\).

Explanation:
The equivalent fraction of \(\frac{9}{4}\) + \(\frac{29}{8}\) which is \(\frac{18}{8}\) and \(\frac{29}{8}\). So the addition of \(\frac{18}{8}\)+\(\frac{29}{8}\) is \(\frac{18+29}{8}\)
= \(\frac{47}{8}\)

Question 7.

Answer:
\(\frac{49}{14}\)+\(\frac{20}{14}\)= 1\(\frac{7}{16}\).

Explanation:
The equivalent fraction of \(\frac{7}{2}\) + \(\frac{10}{7}\) which is \(\frac{49}{14}\) and \(\frac{20}{14}\). So the addition of \(\frac{49}{14}\)+\(\frac{20}{14}\) is \(\frac{49+20}{48}\)
= \(\frac{69}{48}\) = 1\(\frac{21}{48}\)
= 1\(\frac{7}{16}\).

Question 8.

Answer:
\(\frac{35}{15}\)+\(\frac{24}{15}\) = 3\(\frac{14}{15}\).

Explanation:
The equivalent fraction of \(\frac{7}{3}\) + \(\frac{8}{5}\) which is \(\frac{35}{15}\) and \(\frac{24}{15}\). So the addition of \(\frac{35}{15}\)+\(\frac{24}{15}\) is \(\frac{35+24}{15}\)
= \(\frac{59}{15}\)
= 3\(\frac{14}{15}\).

Question 9.

Answer:
\(\frac{376}{56}\)+\(\frac{344}{56}\) = 12\(\frac{6}{7}\).

Explanation:
The equivalent fraction of \(\frac{47}{7}\) + \(\frac{43}{8}\) which is \(\frac{376}{56}\) and \(\frac{344}{56}\). So the addition of \(\frac{376}{56}\)+\(\frac{344}{56}\) is \(\frac{376+344}{56}\)
= \(\frac{720}{56}\) = \(\frac{90}{7}\)
= 12\(\frac{6}{7}\).

Question 10.

Answer:
\(\frac{150}{42}\)+\(\frac{175}{42}\) = 7\(\frac{31}{42}\).

Explanation:
The equivalent fraction of \(\frac{25}{7}\) + \(\frac{25}{6}\) which is \(\frac{150}{42}\) and \(\frac{175}{42}\). So the addition of \(\frac{150}{42}\)+\(\frac{175}{42}\) is \(\frac{150+175}{42}\)
= \(\frac{325}{42}\)
= 7\(\frac{31}{42}\).

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 6 Lesson 7 Subtracting Fractions with Unlike Denominators are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 6 Lesson 7 Subtracting Fractions with Unlike Denominators

Solve

Find equivalent fractions and subtract. Write the difference in simplest form.

Question 1.
\(\frac{2}{9}\) – \(\frac{1}{6}\) _____________
Answer:
\(\frac{4}{18}\) – \(\frac{3}{18}\) = \(\frac{1}{18}\)

Question 2.
\(\frac{1}{2}\) – \(\frac{1}{3}\) _______________
Answer:
\(\frac{3}{6}\)–\(\frac{2}{6}\) = \(\frac{1}{6}\).

Explanation:
The equivalent fraction of \(\frac{1}{2}\) – \(\frac{1}{3}\) which is \(\frac{3}{6}\) and \(\frac{2}{6}\). So the addition of \(\frac{3}{6}\)–\(\frac{2}{6}\) is \(\frac{3-2}{6}\)
= \(\frac{1}{6}\).

Question 3.
\(\frac{3}{8}\) – \(\frac{1}{3}\) _______________
Answer:
\(\frac{3}{6}\)–\(\frac{2}{6}\) = \(\frac{1}{6}\).

Explanation:
The equivalent fraction of \(\frac{1}{2}\) – \(\frac{1}{3}\) which is \(\frac{3}{6}\) and \(\frac{2}{6}\). So the addition of \(\frac{3}{6}\)–\(\frac{2}{6}\) is \(\frac{3-2}{6}\)
= \(\frac{1}{6}\).

Question 4.
\(\frac{3}{4}\) – \(\frac{1}{5}\) _______________
Answer:
\(\frac{15}{20}\)–\(\frac{4}{20}\) = \(\frac{11}{20}\).

Explanation:
The equivalent fraction of \(\frac{3}{4}\) – \(\frac{1}{5}\) which is \(\frac{15}{20}\) and \(\frac{4}{20}\). So the addition of \(\frac{15}{20}\)–\(\frac{4}{20}\) is \(\frac{15-4}{20}\)
= \(\frac{11}{20}\).

Question 5.

Answer:
\(\frac{7}{14}\)–\(\frac{6}{14}\) = \(\frac{1}{14}\).

Explanation:
The equivalent fraction of \(\frac{1}{2}\) – \(\frac{3}{7}\) which is \(\frac{7}{14}\) and \(\frac{6}{14}\). So the addition of \(\frac{7}{14}\)–\(\frac{6}{14}\) is \(\frac{7-6}{14}\)
= \(\frac{1}{14}\).

Question 6.

Answer:
\(\frac{8}{12}\)–\(\frac{3}{12}\) = \(\frac{5}{12}\).

Explanation:
The equivalent fraction of \(\frac{2}{3}\) – \(\frac{1}{4}\) which is \(\frac{8}{12}\) and \(\frac{3}{12}\). So the addition of \(\frac{8}{12}\)–\(\frac{3}{12}\) is \(\frac{8-3}{12}\)
= \(\frac{5}{12}\).

Question 7.

Answer:
\(\frac{11}{99}\)–\(\frac{9}{99}\) = \(\frac{2}{99}\).

Explanation:
The equivalent fraction of \(\frac{1}{9}\) – \(\frac{1}{11}\) which is \(\frac{11}{99}\) and \(\frac{9}{99}\). So the addition of \(\frac{11}{99}\)–\(\frac{9}{99}\) is \(\frac{11-9}{99}\)
= \(\frac{2}{99}\).

Question 8.

Answer:
\(\frac{7}{42}\)–\(\frac{6}{42}\) = \(\frac{1}{42}\).

Explanation:
The equivalent fraction of \(\frac{1}{6}\) – \(\frac{1}{7}\) which is \(\frac{7}{42}\) and \(\frac{6}{42}\). So the addition of \(\frac{7}{42}\)–\(\frac{6}{42}\) is \(\frac{7-6}{42}\)
= \(\frac{1}{42}\).

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 10.3 Changing Decimals to Fractions will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 10.3 Changing Decimals to Fractions

Exercises

Change Decimals To Fractions

Question 1.
.45
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.45 is in hundredths place so the fraction is 45/100

Question 2.
.470
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
.470 is in thousandths place so the fraction is 470/1000

Question 3.
1.4
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.

Question 4.
.68
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.68 is in hundredths place so the fraction is 68/100

Question 5.
.22
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.22 is in hundredths place so the fraction is 22/100

Question 6.
.25
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.25 is in hundredths place so the fraction is 25/100

Question 7.
3.75
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
3.75 is in hundredths place so the fraction is 375/100

Question 8.
.8125
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.8125 is in ten thousandths place so the fraction is 8125/10000

Question 9.
1.875
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
1.875 is in thousandths place so the fraction is 1875/1000

Question 10.
.11
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.11 is in hundredths place so the fraction is 11/100

Question 11.
.8
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.8 is in tenths place so the fraction is 8/100

Question 12.
.125
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.125 is in thousandths place so the fraction is 125/100

Question 13.
.65
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.65 is in hundredths place so the fraction is 65/100

Question 14.
.53
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.53 is in hundredths place so the fraction is 53/100

Question 15.
.44
_________
Answer:
To convert a decimal to a fraction, place the decimal number over its place value.
0.44 is in hundredths place so the fraction is 44/100

Question 16.
A recipe calls for 1.375 cups of flour to be mixed together with .125 cups of cornstarch. If Stefano has only an 1/8 cup measuring cup to measure the flour and cornstarch, how many measuring cups full of flour and how many measuring cups of cornstarch will he need to fill to complete the recipe?
_______ measuring cups of flour
______ measuring cups of cornstarch
Answer:
Given,
A recipe calls for 1.375 cups of flour to be mixed together with .125 cups of cornstarch.
If Stefano has only an 1/8 cup measuring cup to measure the flour and cornstarch
1/8 = 0.125
1.375/0.125 = 11
11 measuring cups of flour
11 measuring cups of cornstarch

Question 17.
Alphonse uses a pedometer to record how far he walks during his morning workout. After walking a while, he rests and notices that the pedometer shows he has walked .9 mile. If he walks 1\(\frac{4}{5}\) miles every day as part of his workout, how much farther does Alphonse need to walk to finish his workout? _______
Answer:
Given,
Alphonse uses a pedometer to record how far he walks during his morning workout. After walking a while, he rests and notices that the pedometer shows he has walked .9 mile.
1\(\frac{4}{5}\) = \(\frac{9}{5}\) = 1.8 mile
1.8 – 0.9 = 0.9 mile
Alphonse need to walk 0.9 mile to finish his workout.

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 6 Lesson 8 Subtracting Mixed Numbers with Unlike Denominators are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 6 Lesson 8 Subtracting Mixed Numbers with Unlike Denominators

Solve

Find equivalent fractions and subtract. Simplify improper fractions.

Question 1.
1\(\frac{1}{4}\) – \(\frac{1}{6}\) ______________
Answer:
1\(\frac{3}{12}\) – \(\frac{2}{12}\) = 1\(\frac{1}{12}\)

Question 2.
1\(\frac{2}{3}\) – \(\frac{1}{2}\) ______________
Answer:
1\(\frac{2}{3}\) – \(\frac{1}{2}\) = \(\frac{7}{6}\).

Explanation:
The difference between 1\(\frac{2}{3}\) – \(\frac{1}{2}\) is \(\frac{5}{3}\) – \(\frac{1}{2}\)
= \(\frac{10-3}{6}\)
= \(\frac{7}{6}\).

Question 3.
1\(\frac{7}{8}\) – 1\(\frac{3}{6}\) ______________
Answer:
1\(\frac{7}{8}\) – 1\(\frac{3}{6}\) = \(\frac{3}{8}\).

Explanation:
The difference between 1\(\frac{7}{8}\) – 1\(\frac{3}{6}\) is \(\frac{15}{8}\) – \(\frac{9}{6}\)
= \(\frac{90-72}{48}\)
= \(\frac{18}{48}\)
= \(\frac{3}{8}\).

Question 4.
Answer:

Question 5.
2\(\frac{1}{9}\) – \(\frac{5}{6}\) _______________
Answer:
2\(\frac{1}{9}\) – \(\frac{5}{6}\) = \(\frac{23}{18}\).

Explanation:
The difference between 2\(\frac{1}{9}\) – \(\frac{5}{6}\) is \(\frac{19}{9}\) – \(\frac{5}{6}\)
= \(\frac{114-45}{54}\)
= \(\frac{69}{54}\)
= \(\frac{23}{18}\).

Question 6.
3\(\frac{1}{2}\) – 2\(\frac{1}{5}\) _______________
Answer:
3\(\frac{1}{2}\) – 2\(\frac{1}{5}\) = \(\frac{24}{5}\).

Explanation:
The difference between 3\(\frac{1}{2}\) – 2\(\frac{1}{5}\) is \(\frac{7}{2}\) – \(\frac{11}{5}\)
= \(\frac{70-22}{10}\)
= \(\frac{48}{10}\)
= \(\frac{24}{5}\).

Question 7.

Answer:
3\(\frac{1}{2}\) – 1\(\frac{3}{7}\) = \(\frac{29}{14}\).

Explanation:
The difference between 3\(\frac{1}{2}\) – 1\(\frac{3}{7}\) is \(\frac{7}{2}\) – \(\frac{10}{7}\)
= \(\frac{49-20}{14}\)
= \(\frac{29}{14}\).

Question 8.

Answer:
2\(\frac{1}{3}\) – 1\(\frac{2}{5}\) = \(\frac{14}{15}\).

Explanation:
The difference between 2\(\frac{1}{3}\) – 1\(\frac{2}{5}\) is \(\frac{7}{3}\) – \(\frac{7}{5}\)
= \(\frac{35-21}{15}\)
= \(\frac{14}{15}\).

Question 9.

Answer:
5\(\frac{6}{7}\) – 4\(\frac{5}{6}\) = \(\frac{43}{42}\).

Explanation:
The difference between 5\(\frac{6}{7}\) – 4\(\frac{5}{6}\) is \(\frac{41}{7}\) – \(\frac{29}{6}\)
= \(\frac{246-203}{42}\)
= \(\frac{43}{42}\).

Question 10.

Answer:
6\(\frac{7}{8}\) – 1\(\frac{2}{3}\) = \(\frac{121}{24}\).

Explanation:
The difference between 6\(\frac{7}{8}\) – 1\(\frac{2}{3}\) is \(\frac{55}{8}\) – \(\frac{5}{3}\)
= \(\frac{165-40}{24}\)
= \(\frac{121}{24}\).

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 10.1 Decimal Place Value and Rounding will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 10.1 Decimal Place Value and Rounding

Round to the nearest whole number.

Question 1.
68.1
________
Answer:
To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If the digit is less than 5 then round to 0 and if the digit is greater than or equal to 5 then we have to round up to 1.
68.1 to the nearest whole number is 68.

Question 2.
17.7
________
Answer:
To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If the digit is less than 5 then round to 0 and if the digit is greater than or equal to 5 then we have to round up to 1.
17.7 to the nearest whole number is 18.

Question 3.
22.2
________
Answer:
To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If the digit is less than 5 then round to 0 and if the digit is greater than or equal to 5 then we have to round up to 1.
22.2 to the nearest whole number is 22.

Question 4.
47.5
________
Answer:
To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If the digit is less than 5 then round to 0 and if the digit is greater than or equal to 5 then we have to round up to 1.
47.5 to the nearest whole number is 48.

Question 5.
76.4
________
Answer:
To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If the digit is less than 5 then round to 0 and if the digit is greater than or equal to 5 then we have to round up to 1.
76.4 to the nearest whole number is 76.

Round to the nearest tenth.

Question 6.
18.47
________
Answer:
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth’s place.
18.47 to the nearest tenth is 18.5

Question 7.
21.23
________
Answer:
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth’s place.
21.23 to the nearest tenth is 21.2

Question 8.
44.44
________
Answer:
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth’s place.
44.44 to the nearest tenth is 44.4

Question 9.
11.14
________
Answer:
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth’s place.
11.14 to the nearest tenth is 11.1

Question 10.
59.49
________
Answer:
To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth’s place.
59.49 to the nearest tenth is 59.5

Round to the nearest hundredth.

Question 11.
429.345
________
Answer:
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. If that number is greater than 5, add 1 to the hundredth value. If it is less than 5, leave the hundredth place value as it is, and remove all the numbers present after the hundredth’s place.
429.345 to the nearest hundredth is 429.35

Question 12.
39.746
________
Answer:
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. If that number is greater than 5, add 1 to the hundredth value. If it is less than 5, leave the hundredth place value as it is, and remove all the numbers present after the hundredth’s place.
39.746 to the nearest hundredth is 39.75

Question 13.
313.313
________
Answer:
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. If that number is greater than 5, add 1 to the hundredth value. If it is less than 5, leave the hundredth place value as it is, and remove all the numbers present after the hundredth’s place.
313.313 to the nearest hundredth is 313.31

Question 14.
528.456
________
Answer:
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. If that number is greater than 5, add 1 to the hundredth value. If it is less than 5, leave the hundredth place value as it is, and remove all the numbers present after the hundredth’s place.
528.456 to the nearest hundredth is 528.46

Question 15.
832.832
________
Answer:
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. If that number is greater than 5, add 1 to the hundredth value. If it is less than 5, leave the hundredth place value as it is, and remove all the numbers present after the hundredth’s place.
832.832 to the nearest hundredth is 832.83

Round to the nearest thousandth.

Question 16.
32.3456
________
Answer:
The rounding of numbers to the nearest thousandth means rounding of any decimal number to its nearest thousandth value. If that number is greater than 5, add 1 to the thousandth value. If it is less than 5, leave the thousandth place value as it is, and remove all the numbers present after the thousandth’s place.
32.3456 to the nearest thousandth is 32.346

Question 17.
1.4141
________
Answer:
The rounding of numbers to the nearest thousandth means rounding of any decimal number to its nearest thousandth value. If that number is greater than 5, add 1 to the thousandth value. If it is less than 5, leave the thousandth place value as it is, and remove all the numbers present after the thousandth’s place.
1.1414 to the nearest thousandth is 1.141

Question 18.
12.1728
________
Answer:
The rounding of numbers to the nearest thousandth means rounding of any decimal number to its nearest thousandth value. If that number is greater than 5, add 1 to the thousandth value. If it is less than 5, leave the thousandth place value as it is, and remove all the numbers present after the thousandth’s place.
12.1728 to the nearest thousandth is 12.173

Question 19.
592.4219
________
Answer:
The rounding of numbers to the nearest thousandth means rounding of any decimal number to its nearest thousandth value. If that number is greater than 5, add 1 to the thousandth value. If it is less than 5, leave the thousandth place value as it is, and remove all the numbers present after the thousandth’s place.
592.4219 to the nearest thousandth is 592.220

Question 20.
837.8198
________
Answer:
The rounding of numbers to the nearest thousandth means rounding of any decimal number to its nearest thousandth value. If that number is greater than 5, add 1 to the thousandth value. If it is less than 5, leave the thousandth place value as it is, and remove all the numbers present after the thousandth’s place.
837.8198 to the nearest thousandth is 837.820

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 10.2 Changing Fractions to Decimals will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 10.2 Changing Fractions to Decimals

Exercises

Change Fractions To Decimals
Round to the nearest ten thousandth, If necessary.

Question 1.
\(\frac{1}{4}\)
_____________
Answer: 0.25
\(\frac{1}{4}\) in the decimal form can be written as 0.250

Question 2.
\(\frac{7}{8}\)
_____________
Answer: 0.875
\(\frac{7}{8}\) in the decimal form can be written as 0.875

Question 3.
\(\frac{1}{9}\)
_____________
Answer: 0.111
\(\frac{1}{9}\) in the decimal form can be written as 0.111

Question 4.
\(\frac{5}{7}\)
_____________
Answer: 0.714
\(\frac{5}{7}\) in the decimal form can be written as 0.714

Question 5.
\(\frac{5}{11}\)
_____________
Answer: 0.455
\(\frac{5}{11}\) in the decimal form can be written as 0.455

Question 6.
\(\frac{7}{19}\)
_____________
Answer: 0.368
\(\frac{7}{19}\) in the decimal form can be written as 0.368

Question 7.
\(\frac{15}{78}\)
_____________
Answer: 0.192
\(\frac{15}{78}\) in the decimal form can be written as 0.192

Question 8.
\(\frac{43}{44}\)
_____________
Answer: 0.977
\(\frac{43}{44}\) in the decimal form can be written as 0.977

Question 9.
\(\frac{3}{23}\)
_____________
Answer: 0.130
\(\frac{3}{23}\) in the decimal form can be written as 0.13

Question 10.
\(\frac{8}{15}\)
_____________
Answer: 0.533
\(\frac{8}{15}\) in the decimal form can be written as 0.533

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 10.4 Comparing and Ordering Decimals will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 10.4 Comparing and Ordering Decimals

Exercises Compare and Order

Put the numbers in order from least to greatest.

Question 1.
.33 .333 .3333
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
The decimals are given in hundredths, thousandths and ten thousandths
So, the order from least to greatest is 0.33, 0.333, 0.3333

Question 2.
.39 1.39 .388 .393
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
The decimals are given in hundredths, thousandths.
So, the order from least to greatest is 0.388, 0.39, 0.393, 1.39

Question 3.
4.44 4.441 .44 4.439
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
The decimals are given in hundredths, and thousandths.
So, the order from least to greatest is 0.44, 4.439, 4.44, 4.441

Question 4.
7.78 7.7778 7.778 7.7777
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
The decimals are given in hundredths, thousandths and ten thousandths
So, the order from least to greatest is 7.7777, 7.7778, 7.778, 7.78

Question 5.
4.4 44.5 .445 445
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
So, the order from least to greatest is 0.445445, 4.4, 44.5

Question 6.
22.2323 22.2332 22.3 22.23222
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
So, the order from least to greatest is 22.23222, 22.2323, 22.2332, 22.3

Question 7.
1.765 1.7655 1.766 1.76559
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
So, the order from least to greatest is 1.765, 1.7655, 1.76559, 1.766

Question 8.
.09 1.09 .08888 .090001
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
So, the order from least to greatest is 0.08888, 0.09, 0.090001, 1.09

Question 9.
9.98989 9.998989 9.999888 9.9999888
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. It is also called increasing order.
So, the order from least to greatest is 9.98989, 9.998989, 9.999888, 9.9999888

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 11.1 Adding Decimals will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 11.1 Adding Decimals

Exercises Add

Question 1.

Answer: 3.685

The sum of two decimal numbers 1.345 and 2.34 is 3.685

Question 2.

Answer: 11.105

The sum of two decimal numbers 7.772 and 3.333 is 11.105

Question 3.

Answer: 1.353

The sum of two decimal numbers 1.23 and 0.123 is 1.353

Question 4.

Answer: 137.78

The sum of two decimal numbers 12.35 and 125.43 is 137.78

Question 5.

Answer: 48.6666

The sum of two decimal numbers 4.4224 and 44.2442 is 48.6666

Question 6.

Answer: 53.4451

The sum of two decimal numbers 53.111 and 0.3341 is 53.4451

Question 7.

Answer: 2.761

The sum of two decimal numbers 0.251 and 2.51 is 2.761

Question 8.

Answer: 11.091

The sum of two decimal numbers 10.101 and 0.990 is 11.091

Question 9.

Answer: 22.211

The sum of two decimal numbers 11.1 and 11.111 is 22.211

Question 10.

Answer: 144.423

The sum of two decimal numbers 113.31 and 31.113 is 144.423

Question 11.

Answer: 345.345

The sum of two decimal numbers 345 and 0.345 is 345.345

Question 12.

Answer: 262.994

The sum of two decimal numbers 239.54 and 23.454 is 262.994

Question 13.

Answer: 578.0775

The sum of two decimal numbers is 525.525 and 52.5525 is 578.0775

Question 14.

Answer: 101.651

The sum of two decimal numbers is 101.55 and 0.101 is 101.651

Question 15.
Hailey is on the school track team. Her event is the triple jump. In her last meet the “hop” portion of her jump was 12.256 feet, the “skip” 11.114 feet, and the “jump” portion was 13.4455 feet. How far did she jump in total?
Answer:
Given,
Hailey is on the school track team. Her event is the triple jump.
In her last meet the “hop” portion of her jump was 12.256 feet, the “skip” 11.114 feet, and the “jump” portion was 13.4455 feet.
12.256 + 11.114 + 13.4455 = 36.8155 feet
Thus she jumps 36.8155 feet in total.

Question 16.
During a flight to the International Space Station, the space shuttle pilot had to conduct a mid-course correction by firing the shuttle’s rockets three times lasting 12.354 seconds, 11.4538 seconds, and 9.7392 seconds. What is the total time the rockets were fired?
Answer:
Given,
During a flight to the International Space Station, the space shuttle pilot had to conduct a mid-course correction by firing the shuttle’s rockets three times lasting 12.354 seconds, 11.4538 seconds, and 9.7392 seconds.
12.354 + 11.4538 + 9.7392 = 33.547 seconds

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 5 Lesson 2 Expressions with Parentheses are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 5 Lesson 2 Expressions with Parentheses

Solve.

Simplify and solve. Show your work.

Question 1.
(20 + 7) – 3
27 – 3 = 24
Answer:
(20 + 7) – 3 = 24.

Explanation:
Given that the expression is (20 + 7) – 3 which is
= (27) – 3
= 24.

Question 2.
8 + (5 × 8) × 6
Answer:
8 + (5 × 8) × 6 = 248.

Explanation:
Given that the expression is 8 + (5 × 8) × 6 which is
= 8 + (40) × 6
= 8 + 240
= 248.

Question 3.
(5 × 2) ÷ 2²
Answer:
(5 × 2) ÷ 2² = 2.5.

Explanation:
Given that the expression is (5 × 2) ÷ 2² = which is
= 10 ÷ 4
= 2.5.

Question 4.
(43 – 8) – (22 – 18)²
Answer:
(43 – 8) – (22 – 18)² = 19.

Explanation:
Given that the expression is (43 – 8) – (22 – 18)² which is
= (35) – (4)²
= 35 – 16
= 19.

Question 5.
3² × (2 × 5) + 7 – (2 × 3)
Answer:
3² × (2 × 5) + 7 – (2 × 3) = 91.

Explanation:
Given that the expression is 3² × (2 × 5) + 7 – (2 × 3) which is
= 3² × (10) + 7 – (6)
= 9 × (10) + 7 – 6
= 90 + 7 – 6
= 97 – 6
= 91.

Question 6.
4 + 2² × (5 × 2) ÷ 4
Answer:
4 + 2² × (5 × 2) ÷ 4 = 14.

Explanation:
Given that the expression is 4 + 2² × (5 × 2) ÷ 4 which is
= 4 + 2² × (10) ÷ 4
= 4 + 4× 10 ÷ 4
= 4 + 40 ÷ 4
= 4 + 10
= 14.

Question 7.
(40 ÷ 5) + (22 – 12)²
Answer:
(40 ÷ 5) + (22 – 12)² = 108.

Explanation:
Given that the expression is (40 ÷ 5) + (22 – 12)² which is
= (40 ÷ 5) + (22 – 12)²
= (8) + (10)²
= 8 + 100
= 108.

Question 8.
Use parentheses to show the operations used: 6 × 4 + 12 – 8 + 2² = 32
Answer:
(6 × 4) + (12 – 8) + 2² = 32.

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 5 Lesson 3 Expressions with Parentheses, Brackets, and Braces are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 5 Lesson 3 Expressions with Parentheses, Brackets, and Braces

Simplify each expression.

Question 1.
{[3(15 + 5) + 27] × 4}
Simplify inside the parentheses: {[3(20) + 27] × 4}
Simplify inside the brackets: ____________
Simplify inside the braces: ______________
{[3(15 + 5) + 27] × 4} = ________
Answer:
{[3(15 + 5) + 27] × 4} = 348.

Explanation:
Given the expression is {[3(15 + 5) + 27] × 4} which is
= {[3(20) + 27] × 4}
= {[60 + 27] × 4}
= 87 × 4
= 348.

Question 2.
3{[2(3 + 6) + 9] – 24}
Simplify inside the parentheses: __________
Simplify inside the brackets: _____________
Simplify inside the braces: _____________
3{[2(3 + 6) + 9] – 24} = _______
Answer:
3{[2(3 + 6) + 9] – 24} = 9.

Explanation:
Given the expression is 3{[2(3 + 6) + 9] – 24}
= 3{[2(9) + 9] – 24}
= 3{[18 + 9] – 24}
= 3{[27] – 24}
= 3{3}
= 9.

Question 3.
[(10 × 2 + 8) ÷ 14]²
Simplify inside the parentheses: ________________
Simplify inside the brackets: _______________
[(10 × 2 + 8) ÷ 14]² = _________
Answer:
[(10 × 2 + 8) ÷ 14]² = 4.

Explanation:
Given the expression is [(10 × 2 + 8) ÷ 14]² which is
= [(20 + 8) ÷ 14]²
= [(28) ÷ 14]²
= [2]²
= 4.