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Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.1 Ratios to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.1 Ratios

Exercises Divide

Question 1.
\(\frac{10}{6}\) = \(\frac{60}{36}\) ______
Answer:
True,

Explanation:
\(\frac{10}{6}\) = \(\frac{60}{36}\), When we multiply both the numerator and denominator with 6,
we get equal ratio. \(\frac{10×6}{6×6}\) = \(\frac{60}{36}\).

Question 2.
\(\frac{4}{6}\) = \(\frac{16}{24}\) ______
Answer:
True,

Explanation:
\(\frac{4}{6}\) = \(\frac{16}{24}\),
When we multiply both the numerator and denominator with 4, we get equal ratio. \(\frac{4×4}{6×4}\) = \(\frac{16}{24}\).

Question 3.
\(\frac{13}{26}\) = \(\frac{39}{78}\) ______
Answer:
True,

Explanation:
\(\frac{13}{26}\) = \(\frac{39}{78}\), When we multiply both the numerator and denominator with 3, we get equal ratio. \(\frac{13×3}{26×3}\) = \(\frac{39}{78}\).

Question 4.
\(\frac{11}{5}\) = \(\frac{132}{60}\) _____
Answer:
True,

Explanation:
\(\frac{11}{5}\) = \(\frac{132}{60}\), When we multiply both the numerator and denominator with 12, we get equal ratio. \(\frac{11×12}{5×12}\) = \(\frac{132}{60}\).

Question 5.
\(\frac{18}{28}\) = \(\frac{27}{42}\) _____
Answer:
True,

Explanation:
\(\frac{18}{28}\) = \(\frac{27}{42}\), When we divide both the numerator and denominator with 2 , we get equal ratio. \(\frac{18}{28}\) ÷ \(\frac{2}{2}\) = \(\frac{9}{14}\).
When we multiply both the numerator and denominator with 3, we get equal ratio. \(\frac{9}{14}\) x \(\frac{3}{3}\) = \(\frac{27}{42}\).

Question 6.
\(\frac{6}{19}\) = \(\frac{15}{57}\) _____
Answer:
False,

Explanation:
\(\frac{6}{19}\) denominator is a prime number not divisible with any other then 19.
\(\frac{6}{19}\) = \(\frac{15}{57}\), can not be equated.

Question 7.
\(\frac{27}{52}\) = \(\frac{58}{104}\) _____
Answer:
False,

Explanation:
\(\frac{27}{52}\) the numerator and denominator are not divisible with same number.
\(\frac{27}{52}\) = \(\frac{58}{104}\) can not be equated.

Question 8.
\(\frac{18}{15}\) = \(\frac{12}{10}\) _____
Answer:
True,

Explanation:
\(\frac{18}{15}\) = \(\frac{12}{10}\) When we divide both the numerator and denominator with 3, we get equal ratio. \(\frac{18}{15}\) ÷ \(\frac{3}{3}\) = \(\frac{6}{5}\). When we multiply both the numerator and denominator with 2, we get equal ratio \(\frac{6}{5}\) x \(\frac{2}{2}\) = \(\frac{12}{10}\),
State the ratio as a fraction 3 : 2.

Question 9.
Paul is making a plaster mixture for his sculpture class. If he mixes 5 ounces of plaster with 4 ounces of water, what is the ratio of plaster to water?
Answer:
\(\frac{5 plaster}{4 water}\),

Explanation:
Paul has 5 ounces of plaster and 4 ounces of water,
to make a mixture for his sculpture class.
He needs the ratio of plaster to water is \(\frac{5 plaster}{4 water}\) or 5:4.

Question 10.
Erika’s mom separates the laundry into sets. If she puts two sheets and three pillow cases into each set, what is the ratio of pillowcases to sheets?
Answer:
\(\frac{3 pillow cases}{2 sheets}\),

Explanation:
If Erika’s mom puts two sheets and three pillow cases into each set,
The ratio of pillowcases to sheets is \(\frac{3 pillow cases}{2 sheets}\) or 3:2.

Question 11.
Floyd is setting tables for a sports banquet. For each place setting, he puts two forks to the left of the plate and a knife and a spoon to the right of the plate. What is the ratio of forks to knives?
Answer:
\(\frac{2 forks}{1 knife}\),

Explanation:
Floyd puts two forks to the left of the plate and a knife and a spoon to the right of the plate.
The ratio of forks to knives is \(\frac{2 forks}{1 knife}\) or 2:1.

Question 12.
Jean is making pizza. She adds 4 slices of pepperoni and 3 olives to each slice of pizza. What is the ratio of pepperoni to olives?
________________
What is the ratio of olives to pepperoni?
________________
Answer:
The ratio of pepperoni to olives is \(\frac{4 pepperoni}{3olives}\),
The ratio of olives to pepperoni is \(\frac{3 olives}{4peperoni}\),

Explanation:
Jean adds 4 slices of pepperoni and 3 olives to each slice of pizza. The ratio of pepperoni to olives is \(\frac{4 pepperoni}{3 olives}\) or 4:3. The ratio of olives to pepperoni is \(\frac{3olives}{4peperoni}\) 3:4.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.2 Proportions and Cross-Multiplying to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.2 Proportions and Cross-Multiplying

Exercises Solve
Indicate (True or False) whether the ratios are equal.

Question 1.
\(\frac{4}{9}\) = \(\frac{36}{81}\) ______
Answer:
True,

Explanation:
\(\frac{4}{9}\) = \(\frac{36}{81}\), When we multiply numerator and denominator with 9, we get equal ratios.
\(\frac{4×9}{9×9}\) = \(\frac{36}{81}\).

Question 2.
\(\frac{5}{7}\) = \(\frac{35}{42}\) ______
Answer:
False,

Explanation:
\(\frac{5}{7}\) = \(\frac{35}{42}\), When we multiply numerator and denominator with 7, we get \(\frac{35}{49}\) ratios. \(\frac{35}{49}\)  is not equal to  \(\frac{35}{42}\). Hence, \(\frac{5}{7}\) = \(\frac{35}{42}\) is false.

Question 3.
\(\frac{4}{3}\) = \(\frac{12}{9}\) ______
Answer:
True,

Explanation:
\(\frac{4}{3}\) = \(\frac{3}{9}\), When we multiply numerator and denominator with 3, we get equal ratios.
\(\frac{4×3}{3×3}\) = \(\frac{12}{9}\).

Question 4.
\(\frac{9}{8}\) = \(\frac{16}{18}\) _____
Answer:
False,

Explanation:
\(\frac{9}{8}\) = \(\frac{16}{18}\), When we multiply numerator and denominator with 2, we get \(\frac{18}{16}\) ratios. \(\frac{18}{16}\) is not equal to \(\frac{16}{18}\). Hence, \(\frac{9}{8}\) = \(\frac{16}{18}\) is false.

Question 5.
\(\frac{5}{12}\) = \(\frac{125}{300}\) _____
Answer:
True,

Explanation:
\(\frac{5}{12}\) = \(\frac{125}{300}\), When we multiply numerator and denominator with 25, we get equal ratios.
\(\frac{5×25}{12×25}\) = \(\frac{125}{300}\).

Question 6.
\(\frac{6}{5}\) = \(\frac{36}{32}\) _____
Answer:
False,

Explanation:
\(\frac{6}{5}\) = \(\frac{36}{32}\), When we multiply numerator and denominator with 6, we get \(\frac{36}{30}\) ratios. \(\frac{36}{30}\) is not equal to \(\frac{36}{32}\). Hence, \(\frac{6}{5}\) = \(\frac{36}{32}\) is false.

Question 7.
\(\frac{7}{11}\) = \(\frac{84}{132}\) _____
Answer:
True,

Explanation:
\(\frac{7}{11}\) = \(\frac{84}{132}\), When we multiply numerator and denominator with 12, we get equal ratios.
\(\frac{7×12}{11×12}\) = \(\frac{84}{132}\).

Question 8.
\(\frac{5}{8}\) = \(\frac{25}{40}\) _____
Answer:
True,

Explanation:
\(\frac{5}{8}\) = \(\frac{25}{40}\), When we multiply numerator and denominator with 5, we get equal ratios.
\(\frac{5×5}{8×5}\) = \(\frac{25}{40}\).

Solve for the unknown variable.

Question 9.
\(\frac{10}{6}\) = \(\frac{n}{36}\) _____
Answer:
n = 60,

Explanation:
\(\frac{10}{6}\) = \(\frac{n}{36}\) = \(\frac{10X36}{nX6}\) = \(\frac{360}{6n}\),
n = \(\frac{360}{6}\), n = 60.

Question 10.
\(\frac{4}{x}\) = \(\frac{16}{24}\) _____
Answer:
x = 6,

Explanation:
\(\frac{4}{x}\) = \(\frac{16}{24}\) = \(\frac{4X24}{xX16}\) = \(\frac{96}{16x}\),
x = \(\frac{96}{16}\), x = 6.

Question 11.
\(\frac{13}{26}\) = \(\frac{y}{78}\) _____
Answer:
y = 39,

Explanation:
\(\frac{13}{26}\) = \(\frac{y}{78}\) = \(\frac{13X78}{yX26}\) = \(\frac{1014}{26y}\),
y = \(\frac{1014}{26}\), y = 39.

Question 12.
\(\frac{11}{m}\) = \(\frac{132}{60}\) _____
Answer:
m = 5,

Explanation:
\(\frac{11}{m}\) = \(\frac{132}{60}\) = \(\frac{11X60}{mX132}\) = \(\frac{660}{132m}\),
m = \(\frac{660}{132}\), m = 5.

Question 13.
\(\frac{18}{28}\) = \(\frac{n}{42}\) _____
Answer:
n = 27,

Explanation:
\(\frac{18}{28}\) = \(\frac{n}{42}\) = \(\frac{18X42}{nX28}\) = \(\frac{756}{28n}\),
n = \(\frac{756}{28}\), n = 27.

Question 14.
\(\frac{x}{19}\) = \(\frac{15}{57}\) _____
Answer:
x = 5,

Explanation:
\(\frac{x}{19}\) = \(\frac{15}{57}\) = \(\frac{xX57}{19X15}\) = \(\frac{57x}{285}\),
x = \(\frac{285}{57}\), x = 5.

Question 15.
\(\frac{x}{52}\) = \(\frac{58}{104}\) _____
Answer:
x = 29,

Explanation:
\(\frac{x}{52}\) = \(\frac{58}{104}\) = \(\frac{x  X 104}{52 X 58}\) = \(\frac{104x}{3016}\),
x = \(\frac{3016}{104}\), x = 29.

Question 16.
\(\frac{18}{15}\) = \(\frac{n}{10}\) _____
Answer:
n = 12,

Explanation:
\(\frac{18}{15}\) = \(\frac{n}{10}\) = \(\frac{18X10}{nX15}\) = \(\frac{180}{15n}\),
n = \(\frac{180}{15}\), n = 12.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.3 Rates to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.3 Rates

Exercises Solve

Question 1.
George likes to sweeten his ice tea. When he is drinking a 20 – ounce ice tea, he adds two teaspoons of sugar. If he makes a gallon of ice tea, how many teaspoons of sugar should he add (there are 128 ounces in a gallon)?
Answer:
12.8 tea spoons of sugar,

Explanation:
1cup of ice tea has 20 – ounce, he adds two teaspoons of sugar.
1gallon of ice tea = 128 ounces, Number of teaspoons of sugar should he add
= \(\frac{128 X 2}{20}\) = 12.8, Therefore 12.8 tea spoons of sugar.

Question 2.
Peter wants to make scrambled eggs for the customers at the diner. His recipe calls for 12 eggs and is enough for 5 people. How many eggs will he need if he has to feed 75 customers?
Answer:
180 eggs,

Explanation:
His recipe calls for 12 eggs and is enough for 5 people.
Number of eggs he need to feed 75 customers = \(\frac{75 X 12}{5}\)
= \(\frac{900}{5}\) = 180 eggs.

Question 3.
A person needs to drink 3 quarts of water for every hour of running time. If a runner plans to complete a marathon in 5 hours, how many quarts of water should she drink during the race?
Answer:
15 quarts,

Explanation:
A person needs to drink 3 quarts of water for every hour of running time.
If a runner plans to complete a marathon in 5 hours, Total quarts of water should she drink during the race of 5 hours for 1 hour 3 quarters of water for 5 hours = \(\frac{5 X 3}{1}\) = 15 quarters.

Question 4.
Diane’s car uses 5 gallons of gasoline to travel 125 miles. How far will Diane be able to travel on 20 gallons of gasoline?
Answer:
500 miles,

Explanation:
Diane’s car uses 5 gallons of gasoline to travel 125 miles.
Total miles he travel for 20 gallons of gasoline = \(\frac{125 X 20}{5}\) =
\(\frac{2500}{20}\) = 500 miles.

Question 5.
When Frank goes on a 4-day vacation with his family, he packs 4 t-shirts and 3 pairs of shorts. If he is going on an extended vacation for 12 days, how many t-shirts and shorts will he need to pack?
Answer:
T-shirts 12; Shorts 9,

Explanation:
Frank packs 4 t-shirts and 3 pairs of shorts for vacation.
If he is going on an extended vacation for 12 days for days vacation he need 4 t-shirts and 3 pairs of shorts. For 12 days he need (4 t-shirts and 3 pairs of shorts) x 3
= 4 x 3 t-shirts and 3 x 3 shorts, Total t-shirts and shorts will he need to pack for 12 days, 12 t-shirts and 9 shorts.

Question 6.
There were 90 customers at the restaurant on Friday, 60 of whom ordered the vegetarian meal. If there are 195 customers on Sunday, how many vegetarian meals would you expect to sell?
Answer:
130 meals,

Explanation:
There were 90 customers at the restaurant on Friday, 60 of whom ordered the vegetarian meal. If there are 195 customers on Sunday, Total vegetarian meals would you expect to sell on Sunday 90 costumers = 60 meals, 195 customers = \(\frac{60 X 195}{90}\), x = \(\frac{11700}{90}\) = 130.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.4 Proportions and Percent to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.4 Proportions and Percent

Exercises Calculate Using Proportions

Question 1.
40% of 50 is _____
Answer:
20,

Explanation:
40% of 50 is \(\frac{40}{100}\) X 50, Let it be x = \(\frac{40 X 50}{100}\), x = \(\frac{2000}{100}\), x = 20.

Question 2.
72 is 18% of ___________
Answer:
400,

Explanation:
72 is 18% of 72 X \(\frac{18}{100}\), Let it be x =  \(\frac{72 X 100}{18}\), x = \(\frac{7200}{18}\), x = 400.

Question 3.
14 is ________% of 35
Answer:
40%,

Explanation:
14 is x% of 35, So 14 = \(\frac{x}{100}\) X 35, Let x = \(\frac{14 X 100}{350}\), x = \(\frac{1,400}{35}\), x = 40.

Question 4.
12% of 85 is ___________
Answer:
10.2,

Explanation:
12% of 85 is \(\frac{12}{100}\) X 85, Let x \(\frac{12 X 85}{100}\) = x,
\(\frac{1,020}{100}\) = x, x = 10.2.

Question 5.
50 is 40% of _____
Answer:
125,

Explanation:
50% of 40 is \(\frac{50}{100}\) X 40 = x, \(\frac{50 X 100}{40}\) = x,
\(\frac{5,000}{40}\) = x, x = 125.

Question 6.
18 is ________% of 270
Answer:
6.7%,

Explanation:
18 is x% of 270, 18 = \(\frac{x}{100}\) X 270, x = \(\frac{18 X 100}{270}\), x = \(\frac{1,800}{270}\), x = 6.7%.

Question 7.
70% of 70 is __________
Answer:
49,

Explanation:
70% of 70 is \(\frac{70}{100}\) X 70, let it be x = \(\frac{70 X 70}{100}\), x = \(\frac{4,900}{100}\), x = 49.

Question 8.
66 is 30% of ____
Answer:
220,

Explanation:
66 is 30% of \(\frac{30}{100}\) X 66, Let it be x =  \(\frac{66 X 100}{30}\), x = \(\frac{6,600}{30}\), x = 220.

Question 9.
1.5 is ________% of 75
Answer:
2%,

Explanation:
1.5 is x% of 75, 1.5 = \(\frac{x}{100}\) X 75, Let it be x = \(\frac{1.5 X 100}{75}\), x = \(\frac{150}{75}\), x = 2.

Question 10.
140% of 95 is __________
Answer:
133,

Explanation:
140% of 95 is \(\frac{140}{100}\) X 95, Let it be x, \(\frac{140 X 95}{100}\) = x, x = \(\frac{13,300}{100}\), x = 133.

Question 11.
13 is 65% of ___________
Answer:
20,

Explanation:
13 is 65% of 13 X \(\frac{65}{100}\), Let it be x \(\frac{13 X 100}{65}\) , x = \(\frac{1300}{65}\), x = 20.

Question 12.
12 is ___ % of 32
Answer:
37.5%,

Explanation:
12 is x% of 32, 12 = \(\frac{x}{100}\) X 32, Let it be x = \(\frac{12 X 100}{32}\) = \(\frac{1200}{32}\), x = 37.5.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.5 Percent Change, Mark-up, and Discount to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.5 Percent Change, Mark-up, and Discount

Exercises Solve

Question 1.
What is the selling price for an item that costs $50 and has a mark-up of 40%?
Answer:
$70.00,

Explanation:
The cost of an item is $50,Mark up o f 40%, discounted amount of an item is $50  x 40%
= 50 x \(\frac{40}{100}\), 50 x 0.4 = 20 the selling price for an item = 50 + 20 = 70, So $70.00.

Question 2.
What is the mark-up amount for an item that costs $125 and has a mark-up of 35%?
Answer:
$43.75,

Explanation:
The cost of an item is $125 Mark up of 35% discount amount of an item = $125  x 35%
= 125 x \(\frac{35}{100}\) = 125 x 0.35, So  43.75.

Question 3.
What is the selling price for an item that costs $70 and has a discount of 40%?
Answer:
$42.00,

Explanation:
The cost of an item is $70, Percentage of discount is 40%, discounted amount of an item is $70 x 40% = 70 x \(\frac{40}{100}\) = 70 x 0.40 = 28.00 the selling price for an item = 70 – 28 = 42, So $42.00.

Question 4.
What is the discount amount for an item that costs $160 and has a discount of 45%?
Answer:
$72.00,

Explanation:
The amount for an item that costs $160, Percentage of discount is 45%,
discount amount of an item = $160 x 45% = 160 x \(\frac{45}{100}\),
= 160 x 0.45, So 72.00.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.6 Percents and Fractions to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.6 Percents and Fractions

Exercises Calculate Using Multiplication

Question 1.
18 is ____ % of 60
Answer:
30%,

Explanation:
18 is x% of 60 is 18 = \(\frac{x}{100}\) X 60, x = \(\frac{18 X 100}{60}\), x = \(\frac{1800}{60}\).
So x = 30.

Question 2.
20% of 85 is ___________
Answer:
17,

Explanation:
20% of 85 is x = \(\frac{20}{100}\) X 85, x = \(\frac{20 X 85}{100}\),
x = \(\frac{1700}{100}\), x = 17.

Question 3.
\(\frac{42}{70}\) = ____ %
Answer:
60%,

Explanation:
Let x = \(\frac{42}{70}\), 70 x = 42, x = \(\frac{42}{70}\), x = 0.6,
Multiply with 100 to convert into percentage
0.6 x 100% = 60%.

Question 4.
30% of 90 is ___________
Answer:
27,

Explanation:
30% of 90 is \(\frac{30}{100}\) X 90, Let x = \(\frac{30 X 90}{100}\),
x = \(\frac{2700}{100}\), x = 27.

Question 5.
\(\frac{16}{128}\) = ____ %
Answer:
12.5%,

Explanation:
\(\frac{16}{128}\) = x%, 128x = 16, x = \(\frac{16}{128}\),
x = 0.125, Multiply with 100 to convert into percentage 0.125 x 100% = 12.5%.

Question 6.
\(\frac{12}{48}\) = ____ %
Answer:
25%,

Explanation:
Let x = \(\frac{12}{48}\), 48x = 12, x = \(\frac{12}{48}\),
x = 0.25,
Multiply with 100 to convert into percentage 0.25 x 100% = 25%.

Question 7.
15% of 60 is __________
Answer:
9,

Explanation:
Let 15% of 60 is \(\frac{15}{100}\) X 60,
x = \(\frac{15 X 60}{100}\),
x = \(\frac{900}{100}\), x = 9.

Question 8.
\(\frac{24}{160}\) = ____ %
Answer:
15%,

Explanation:
Let x = \(\frac{24}{160}\), 160x = 24,
x = \(\frac{24}{160}\),
x = 0.15, Multiply with 100 to convert into percentage 0.15 x 100% = 15%.

Question 9.
35% of 220 is ____
Answer:
77,

Explanation:
Let x = 35% of 220 is \(\frac{35}{100}\) X 220,
\(\frac{35 X 220}{100}\) = x,
\(\frac{7700}{100}\) = x, x = 77.

Question 10.
1\(\frac{1}{5}\) = ____ %
Answer:
120%,

Explanation:
1\(\frac{1}{5}\) = x%, \(\frac{6}{5}\) = x%, 5x = 6,
x = \(\frac{6}{5}\), x = 1.2,
Multiply with 100 to convert into percentage
1.2 x 100% = 120%.

Question 11.
40% of 65 is ____
Answer:
26%,

Explanation:
40% of 65 is \(\frac{40}{100}\) X 65,
Let  x = \(\frac{40 X 65}{100}\) = x,
\(\frac{2600}{100}\) = x, x = 26.

Question 12.
\(\frac{75}{250}\) = ____ %
Answer:
30%,

Explanation:
\(\frac{75}{250}\) = x%, 200x = 75,
x = \(\frac{75}{250}\), x = 0.3,
Multiply with 100 to convert into percentage is 0.3 x 100 = 30%.

Question 13.
\(\frac{3}{50}\) = ____ %
Answer:
6%,

Explanation:
\(\frac{3}{50}\) = x%, 50x = 3, x = \(\frac{3}{50}\),
x = 0.06,
Multiply with 100 to convert into percentage 0.06 x 100% = 6%.

Question 14.
\(\frac{55}{1100}\) = ____ %
Answer:
5%,

Explanation:
\(\frac{55}{1100}\) = x%, 1100x = 55, x = \(\frac{55}{1100}\),
x = 0.05, Multiply with 100 to convert into percentage 0.05 x 100 = 5%.

Question 15.
65% of 40 is ____
Answer:
26,

Explanation:
65% of 40 is \(\frac{65}{100}\) X 40 = x,
\(\frac{65 X 40}{100}\) = x,
\(\frac{2600}{100}\) = x,
x = 26.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.7 Multiplying Percents and Fractions to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.7 Multiplying Percents and Fractions

Exercises Calculate

Question 1.
\(\frac{5}{12}\) × 60% = ____
Answer:
25%,

Explanation:
Let \(\frac{5}{12}\) X 60%,  x = \(\frac{5}{12}\) × \(\frac{60}{100}\) = \(\frac{5 X 60}{12 X 100}\) = \(\frac{300}{1200}\) = \(\frac{1}{4}\) = 0.25,
To convert to percentage multiply with 100,
So, 0.25 x 100% = 25%.

Question 2.
\(\frac{3}{5}\) × 82% = ____
Answer:
49.2%,

Explanation:
Let \(\frac{3}{5}\) X 82%, \(\frac{3}{5}\) X \(\frac{82}{100}\),
\(\frac{3 X 82}{5 X 100}\), \(\frac{246}{500}\) = 0.492,
To convert to percentage multiply with 100.
So, 0.492 x 100% = 49.2%.

Question 3.
\(\frac{6}{5}\) × 55% = ____
Answer:
66%,

Explanation:
Let \(\frac{6}{5}\) X 55%, \(\frac{6}{5}\) X \(\frac{55}{100}\)
= \(\frac{6 X 55}{5 X 100}\),
\(\frac{330}{500}\) = 0.66,
To convert to percentage multiply with 100%.
So, 0.66 x 100% = 66%.

Question 4.
\(\frac{8}{25}\) × 125% = ____
Answer:
40%,

Explanation:
\(\frac{8}{25}\) × 125%, \(\frac{8}{25}\) × \(\frac{125}{100}\) = \(\frac{8 X 125}{25 X 100}\), = \(\frac{1000}{2500}\) = 0.4,
To convert to percentage multiply with 100.
So 0.4 x 100% = 40%.

Question 5.
\(\frac{4}{15}\) × 75% = ____
Answer:
20%,

Explanation:
Let \(\frac{4}{15}\) X 75%, \(\frac{4}{15}\) × \(\frac{75}{100}\) = \(\frac{4 X 75}{15 X 100}\) = \(\frac{300}{1500}\) = 0.2,
To convert to percentage multiply with 100.
So 0.2 x 100 = 20%.

Question 6.
25% of \(\frac{4}{5}\) = ____
Answer:
\(\frac{1}{5}\),

Explanation:
Let x = 25% x \(\frac{4}{5}\) = \(\frac{25}{100}\) × \(\frac{4}{5}\) = \(\frac{25 X 4}{100 x 5}\) = \(\frac{100}{500}\) = \(\frac{1}{5}\).

Question 7.
20% of \(\frac{5}{6}\) = ____
Answer:
\(\frac{1}{6}\),

Explanation:
Let x = 20% x \(\frac{5}{6}\) = \(\frac{20}{100}\) X \(\frac{5}{6}\) = \(\frac{20 X 5}{100 X 6}\) = \(\frac{100}{600}\) =\(\frac{1}{6}\).

Question 8.
40% of \(\frac{15}{16}\) = ____
Answer:
\(\frac{3}{8}\),

Explanation:
40% x \(\frac{15}{16}\) = \(\frac{40}{100}\) × \(\frac{15}{16}\) = \(\frac{40 X 15}{100 X 16}\) = \(\frac{600}{1,600}\),
= \(\frac{6}{16}\) = \(\frac{3}{8}\).

Question 9.
75% of \(\frac{112}{150}\) = ____
Answer:
\(\frac{14}{25}\),

Explanation:
Let x = 75% X \(\frac{112}{150}\) = \(\frac{75}{100}\) X \(\frac{112}{150}\) = \(\frac{75 X 112}{100 X 150}\) = \(\frac{8,400}{15,000}\) = \(\frac{14}{25}\).

Question 10.
60% of \(\frac{40}{75}\) = ____
Answer:
\(\frac{8}{25}\),

Explanation:
Let x = 60% X \(\frac{40}{75}\) = \(\frac{60}{100}\) X \(\frac{40}{75}\) = \(\frac{60 X 40}{100 X 75}\) = \(\frac{2,400}{7,500}\)
= \(\frac{8}{25}\).

Question 11.
\(\frac{7}{12}\) × 72% = ____
Answer:
42%,

Explanation:
Let x = \(\frac{7}{12}\) X 72% = \(\frac{7}{12}\) X \(\frac{72}{100}\) = \(\frac{7 X 72}{12 X 100}\) = \(\frac{504}{1,200}\) = 0.42,
To convert to percentage multiply with 100.
So, 0.42 x 100 = 42%.

Question 12.
\(\frac{5}{4}\) × 42% = ____
Answer:
52.5%,

Explanation:
Let x = \(\frac{5}{4}\) X 42%, \(\frac{5}{4}\) X \(\frac{42}{100}\) = \(\frac{5 X 42}{4 X 100}\) = \(\frac{210}{400}\) = 0.525,
To convert to percentage multiply with 100.
So, 0.525 x 100% = 52.5%.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.8 Percents and Decimals to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 6.8 Percents and Decimals

Exercises Convert

Convert to a Percent.

Question 1.
.7612
Answer:
76.12% or \(\frac{5}{12}\),

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 0.7612 to percent we rewrite 0.7612 in terms of “per 100” or over 100.
Multiply 0.7612 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.7612 x \(\frac{4}{9}\) = \(\frac{76.12}{100}\) = 76.12%,
So, 0.7612 = 76.12%.

Question 2.
.01543
Answer:
1.543%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert .01543 to percent we rewrite .01543 in terms of “per 100” or over 100.
Multiply .01543 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
.01543 x \(\frac{100}{100}\),
= \(\frac{01.543}{100}\) = 1.543%,
So .01543 = 1.543%.

Question 3.
1.59
Answer:
159%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 1.59 to percent we rewrite 1.59 in terms of “per 100” or over 100.
Multiply 1.59 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
1.59 x \(\frac{100}{100}\),
= \(\frac{159}{100}\) = 159%.
So 1.59 = 159%.

Question 4.
.5721
Answer:
57.21%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 0.5721 to percent we rewrite 0.5721 in terms of “per 100” or over 100.
Multiply 0.5721 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.5721 x \(\frac{100}{100}\) = \(\frac{57.2}{100}\) = 57.21%,
So 0.5721 = 57.21%.

Question 5.
.0012
Answer:
0.12%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 0.0012 to percent we rewrite 0.0012 in terms of “per 100” or over 100.
Multiply 0.0012 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.0012 x \(\frac{100}{100}\),
= \(\frac{00.12}{100}\) = 0.12%, So, 0.0012 = 0.12%.

Question 6.
.000134
Answer:
0.0134%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert .000134 to percent we rewrite 0.000134 in terms of “per 100” or over 100.
Multiply 0.000134 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.000134 x \(\frac{100}{100}\),
= \(\frac{0.0134}{100}\) = 76.12%,
So, 0.0134 = 0.0134%.

Question 7.
10.45
Answer:
10.45%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 1.89 to percent we rewrite 1.89 in terms of “per 100” or over 100.
Multiply 1.89 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
10.45 x \(\frac{100}{100}\) = \(\frac{1,045}{100}\) = 10.45%,
So 10.45 = 10.45%.

Question 8.
1.89
Answer:
189%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 1.89 to percent we rewrite 1.89 in terms of “per 100” or over 100.
Multiply 1.89 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
1.89 x \(\frac{100}{100}\)
= \(\frac{189}{100}\) = 1.89,
So, 1.89 = 1.89%.

Question 9.
.569
Answer:
56.9%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 0.569 to percent we rewrite 0.569 in terms of “per 100” or over 100.
Multiply 0.569 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.569 x \(\frac{100}{100}\) = \(\frac{56.90}{100}\) = 56.90%,
So, 0.569 = 56.90%.

Question 10.
.9999
Answer:
99.99%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 0.9999 to percent we rewrite 0.9999 in terms of “per 100” or over 100.
Multiply 0.9999 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.9999 x \(\frac{100}{100}\) = \(\frac{99.99}{100}\) = 99.99,
So, 0.9999 = 99.99%.

Question 11.
0.0011
Answer:
0.11%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.To convert 0.0011 to percent we rewrite 0.0011 in terms of “per 100” or over 100.
Multiply 0.0011 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.0011 x \(\frac{100}{100}\),
= \(\frac{0.11}{100}\) = 0.11%,
So, 0.0011 = 0.11%.

Question 12.
3.1345
Answer:
313.45%,

Explanation:
To convert decimals to percentages, a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 3.1345 to percent we rewrite 3.1345 in terms of “per 100” or over 100.
Multiply 3.1345 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
3.1345  x \(\frac{100}{100}\) = \(\frac{313.45}{100}\) = 313.45%,
So, 3.1345 = 313.45%.

Question 13.
99.99
Answer:
99.99%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert 99.99 to percent we rewrite 99.99 in terms of “per 100” or over 100.
Multiply 99.99 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
99.99 x \(\frac{100}{100}\) = \(\frac{9,999}{100}\) = 99.99%,
So, 99.99 = 99.99%.

Question 14.
.175555578
Answer:
17.5555578%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert .175555578 to percent we rewrite .175555578 in terms of “per 100” or over 100.
Multiply .175555578 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
.175555578 X \(\frac{100}{100}\),
= \(\frac{17.5555578}{100}\) = 17.5555578%,
So 0.175555578 = 17.5555578%.

Question 15.
.187
Answer:
18.7%,

Explanation:
To convert decimals to percentages,
a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert .187 to percent we rewrite .187 in terms of “per 100” or over 100.
Multiply .187 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
.187 x \(\frac{100}{100}\) = \(\frac{18.7}{100}\) = 18.7%
So, 0.187 = 18.7%.

Question 16.
.87
Answer:
87%,

Explanation:
To convert decimals to percentages a decimal number to convert both the whole number and decimal part of the number to a percent value.
Multiply by 100 to convert a number from decimal to percent then add a percent sign %.
To convert .87 to percent we rewrite .87 in terms of “per 100” or over 100.
Multiply .87 by 100/100. Since 100/100 = 1,
we are only multiplying by 1 and not changing the value of our number.
0.87 X \(\frac{100}{100}\),
= \(\frac{87}{100}\) = 87%, So 0.87 = 18.7%.

All the solutions provided in McGraw Hill Math Grade 1 Answer Key PDF Chapter 7 Test as per the latest syllabus guidelines.

McGraw-Hill Math Grade 1 Chapter 7 Test Answer Key

Read the number sentences. Write the sums.

Question 1.
5 + 7 = ____________
7 + 5 = ____________
Answer:
5 + 7 = 12
7 + 5 = 12
Explanation:
If we change the pattern of addends the sum doesn’t change,
The sum remains the same.

Question 2.
12 + 6 = ____________
6 + 12 = ____________
Answer:
12 + 6 = 18
6 + 12 = 18
Explanation:
If we change the pattern of addends the sum doesn’t change,
The sum remains the same.

Question 3.
0 + 8 = ____________
Answer:
0 + 8 = 8
Explanation:
The sum of 0 and 8 is 8
If we add the zero to a number the number remains the same.

Question 4.
0 + 4 = ____________
Answer:
4
Explanation:
The sum of 0 and 4 is 4
If we add the zero to a number the number remains the same.

Question 5.
5 + 1 + 2 = ____________
Answer:
5 + 1 = 6
6 + 2 = 8
Explanation:
The sum of 5 and 1 is 6
and 6 and 2 is 8

Question 6.
3 + 6 + 4 = ____________
Answer:
6 + 4 = 10
10 + 6 = 16
Explanation:
First we have to form the ten, then we have to add the other number.

Read the problems. Write the missing number.

Question 7.
5 + = 9
9 – 5 = ____________
5 + ____________ = 9
Answer:
5 + 4 = 9
9 – 5 = 4
5 + 4 = 9
Explanation:
To find the missing number in addition we have to subtract

Question 8.
5 + 1 = 18
18 – 5 = ____________
5 + ____________ = 18
Answer:
5 + 13 = 18
18 – 5 = 13
5 + 13 = 18
Explanation:
To find the missing number in addition we have to subtract

Look at each addition sentence. Write another fact with the same sum.

Question 9.
9 + 2 = 11
____________ + ____________ = 11
Answer:
9 + 2 = 11
2 + 9 = 11
Explanation:
If we change the pattern of addends the sum doesn’t change,
The sum remains the same.

Question 10.
3 + 4 = 7
____________ + ____________ = 7
Answer:
3 + 4 = 7
4 + 3 = 7
Explanation:
If we change the pattern of addends the sum doesn’t change,
The sum remains the same.

Look at each set of numbers. Write = if they are equal. Write not = if they are not equal.

Question 11.
17 ____________ 17
Answer:
17 = 17
Explanation:
If the given numbers are equal they are represented with the symbol ‘=’

Question 12.
35 ____________ 30 + 5
Answer:
30 + 5 = 35
35 = 35
Explanation:
If the given numbers are equal they are represented with the symbol ‘=’

Question 13.
8 + 3 ____________ 12 + 5
Answer:
11 ≠ 17
Explanation:
If the given numbers are equal they are represented with the symbol ‘=’
If they are not equal we represent with ≠

Question 14.
9 – 3 ____________ 4 + 2
Answer:
9 – 3 = 6
4 + 2 = 6
6 = 6
Explanation:
If the given numbers are equal they are represented with the symbol ‘=’

Draw circles to make 10. Then write your answers.

Question 15.
8 + 5 = ?

10 + 3 = ____________
so 8 + 5 = _____________
Answer:

8 + 5 = 13
10 + 3 = 13
Explanation:
There are 8 green dots in ten frame
we have to add 5 more to get 13

Question 16.
9 + 6 = ?

10 + 5 = _____________
so 9 + 6 = _____________
Answer:

10 + 5 = 15
9 + 6 = 15
Explanation:
There are 9 red dots in ten frame.
so added 6 to get 15

Count on to add. Count back to subtract.

Question 17.
4 + 7 = ___________
Answer:

Explanation:
The sum of 4 and 7 is 11
4 + 7 = 11

Question 18.
18 – 12 = ___________
Answer:

Explanation:
The difference of 18 and 12 is 6
18 – 12 = 6

Look at the chart. Write an addition sentence. Then write a subtraction sentence.

Question 19.
__________ + ___________ = ___________
Answer:
2 + 4 = 6
4 + 2 = 6
Explanation:
If we change the pattern of addends the sum doesn’t change,
The sum remains the same.

Question 20.
__________ – ___________ = ___________
Answer:
6 – 2 = 4
6 – 4 = 2
Explanation:
The difference of 6 and 2 is 4, 6 and 4 is 2

Add or subtract to solve. Write the sum or difference. Use objects to help.

Question 21.
6 play. 2 sleep. How many are there?
6 + 2 = ___________
Answer:
6 + 2 = 8
Explanation:
Number of dogs that play = 6
Number of dogs that sleep = 2
so, there are 8 dogs in all.

Question 22.
Ben has 13 He gives 6 to Sara. How many does Ben have now?
13 – 6 ___________
Answer:
13 – 6 = 7
Explanation:
Number of coins that ben has= 13
Number of coins that he gave to Sara = 6
6 that Ben have now

All the solutions provided in McGraw Hill Math Grade 1 Answer Key PDF Chapter 7 Lesson 9 Equal as per the latest syllabus guidelines.

McGraw-Hill Math Grade 1 Answer Key Chapter 7 Lesson 9 Equal

Identify

Look at each number. Write an equal number.

Question 1.
6 = _________
Answer:
6
Explanation:
6 = 6
six is equals to six represented with the symbol ‘=’

Question 2.
23 = __________
Answer:
23
Explanation:
23 = 23
equals to is represented with the symbol ‘=’

Question 3.
103 = __________
Answer:
Explanation:
103 = 103
equals to is represented with the symbol ‘=’

Question 4.
82 = __________
Answer:
82
Explanation:
82 = 82
equals to is represented with the symbol ‘=’

Look at each set of numbers. Write = if they are equal. Write not = if they are not equal.

Question 5.
25 ___________ 32
Answer:
25 not equal 32
Explanation:
25 is not equal to 32

Question 6.
79 ___________ 79
Answer:
79 = 79
Explanation:
seventy nine equal to seventy nine
equals to is represented with the symbol ‘=’

Question 7.
4 + 3 ___________ 7
Answer:
4 + 3 = 7
7 = 7
Explanation:
7 is equal to 7
equals to is represented with the symbol ‘=’

Question 8.
2 + 6 ____________ 4 + 4
Answer:
2 + 6 = 8
4 + 4 = 8
Explanation:
8 is equal to 8
equals to is represented with the symbol ‘=’