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McGraw-Hill Math Grade 7 Unit Test Lessons 13–15 Answer Key
Determine if the following proportions are equal. (Write Yes or No.)
Question 1.
\(\frac{5}{4}\) = \(\frac{24}{16}\)
Answer:
NO
Explanation:
LHS = \(\frac{5}{4}\) x \(\frac{4}{4}\)
= \(\frac{20}{16}\)
LHS is not equal to RHS
Question 2.
\(\frac{21}{12}\) = \(\frac{7}{36}\)
Answer:
NO
Explanation:
LHS = \(\frac{21}{12}\) x \(\frac{3}{3}\)
= \(\frac{7}{4}\)
LHS is not equal to RHS
Question 3.
\(\frac{12}{19}\) = \(\frac{36}{57}\)
Answer:
YES
Explanation:
LHS = \(\frac{12}{19}\) x \(\frac{3}{3}\)
= \(\frac{36}{57}\) = RHS
LHS = RHS
Question 4.
\(\frac{1}{4}\) = \(\frac{6}{24}\)
Answer:
YES
Explanation:
LHS = \(\frac{1}{4}\) x \(\frac{6}{6}\)
= \(\frac{6}{24}\) = RHS
LHS = RHS
Solve for x.
Question 5.
\(\frac{x}{10}\) = \(\frac{30}{20}\)
Answer:
x = 15
Explanation:
\(\frac{x}{10}\) = \(\frac{30}{20}\)
x = \(\frac{30}{20}\) x 10
x =\(\frac{30 X 10}{20}\)
x =15
Question 6.
\(\frac{25}{x}\) = \(\frac{40}{100}\)
Answer:
x = 62.5
Explanation:
\(\frac{25}{x}\) = \(\frac{40}{100}\)
x = \(\frac{25}{40}\) x 100
x = 0.625 x 100
x = 62.5
Question 7.
\(\frac{33}{96}\) = \(\frac{11}{x}\)
Answer:
x = 32
Explanation:
\(\frac{33}{96}\) = \(\frac{11}{x}\)
by cross multiplying
33 x = 96 x 11
x = \(\frac{96 X 11}{33}\)
x = 32
Question 8.
\(\frac{1}{10}\) = \(\frac{20}{x}\)
Answer:
x = 200
Explanation:
\(\frac{1}{10}\) = \(\frac{20}{x}\)
by cross multiplying
1 x = 20 x 10
x = \(\frac{20 X 10}{1}\)
x = 200
Solve.
Question 9.
Create a ratio to compare the length of the side of a barn (140 ft) to the width of the barn (64 ft).
Answer:
\(\frac{35}{16}\) or 35 : 16
Explanation:
\(\frac{Length}{width}\)
= \(\frac{140}{64}\)
by dividing both numerator and denominator by 4 for simplification
we get = \(\frac{35}{16}\)
Question 10.
Create a ratio to compare the amount of unsaturated fat in salad dressing (5 grams) to the amount of carbohydrates (9 grams).
Answer:
\(\frac{5}{9}\) or 5 : 9
Explanation:
The amount of unsaturated fat in salad dressing (5 grams),
The amount of carbohydrates (9 grams).
= \(\frac{unsaturated fat in salad dressing (5 grams)}{carbohydrates (9 grams)}\)
= \(\frac{5}{9}\)
Question 11.
Wallace rides his bicycle at an average speed of 18 miles per hour. How many miles does he travel in 3 \(\frac{1}{3}\) hours?
Answer:
60 miles
Explanation:
Distance = Speed x Time
Distance = 18 x 3\(\frac{1}{3}\)
D = 18 x 3.33
D = 60 miles
Question 12.
Jermaine can make 29 loaves of bread for every 3 batches he bakes. How many batches of bread does he need to bake in order to make 232 loaves?
Answer:
24 batches
Explanation:
\(\frac{29}{3}\) = \(\frac{232}{x}\)
= \(\frac{3}{29}\) X \(\frac{232}{x}\)
x = \(\frac{232 X 3}{29}\)
x =8 x 3
x = 24
Question 13.
Phyllis drinks \(\frac{3}{4}\) of a pint of water after each mile she walks. How many pints of water will she drink if she walks 5 \(\frac{3}{4}\) miles?
Answer:
4\(\frac{5}{16}\)
Explanation:
\(\frac{3}{4}\) = 1 pints of water she drinks
5\(\frac{3}{4}\) = let x pints of water
x \(\frac{3}{4}\) = 5\(\frac{3}{4}\)
x = \(\frac{3}{4}\) x \(\frac{23}{4}\)
x = \(\frac{3 X 23}{4 x 4}\)
x = \(\frac{69}{16}\)
x= 4\(\frac{5}{16}\)
Question 14.
Ginny needs to check the air in her tires every 750 miles. How many times will she need to check her tires if she is taking a trip that is 6,750 miles in length?
Answer:
9 times
Explanation:
Ginny needs to check the air in her tires every 750 miles.
Number of times she need to check her tires,
if she is taking a trip that is 6,750 miles in length.
= \(\frac{6,750}{750}\)
= 9 times (750 x 9 = 6,750)
Calculate.
Question 15.
30% of 1 \(\frac{2}{5}\)
Answer:
\(\frac{21}{50}\)
Explanation:
30% of 1 \(\frac{2}{5}\)
= 1 \(\frac{2}{5}\) x \(\frac{30}{100}\)
= \(\frac{7}{5}\) x \(\frac{3}{10}\)
= \(\frac{7 X 3}{5 X 10}\)
= \(\frac{21}{50}\)
Question 16.
40% of 440
Answer:
176
Explanation:
40% of 440
= 440 x \(\frac{40}{100}\)
= 4.4 x 40
= 176
Question 17.
\(\frac{1}{4}\) of 48%
Answer:
12%
Explanation:
\(\frac{1}{4}\) of 48%
= \(\frac{1}{4}\) x \(\frac{48}{100}\)
= 0.25 x 48%
= 12%
Question 18.
\(\frac{2}{5}\) of 70%
Answer:
28%
Explanation:
\(\frac{2}{5}\) of 70%
= 0.4 x 70%
= 28%
Question 19.
\(\frac{3}{8}\) of 340%
Answer:
127.5%
Explanation:
\(\frac{3}{8}\) of 340%
= 0.375 x 340%
= 127.5%
Question 20.
43% of 0.705
Answer:
0.30315
Explanation:
43% of 0.705
= \(\frac{43}{100}\) of 0.705
= 0.705 x 0.43
= 0.30315
Question 21.
84% of 1.906
Answer:
0.30315
Explanation:
84% of 1.906
= \(\frac{84}{100}\) of 1.906
= 1.906 x 0.84
= 1.60104
Question 22.
75% of .7575
Answer:
0.568125
Explanation:
75% of .7575
= \(\frac{75}{100}\) of 0.7575
= 0.7575 x 0.75
= 0.568125
Question 23.
Jessie deposited $824.25 of his babysitting money into . an account that pays 4.5% interest. How much will he have in his account at the end of one year?
Answer:
$861.35
Explanation:
Jessie deposited $824.25 of his babysitting money into an account that pays 4.5% interest.
SI = PRT/100
SI = 824.25 x 4.5 x 1 = 37.09125
Total amount in his account at the end of one year,
Amount = Principle + interest
Amount = 824.25 + 37.09125
Amount = $861.35
Question 24.
What is the annual rate of interest on a loan of $1,500 if you have paid a total of $120 in interest after two years?
Answer:
4%
Explanation:
The annual rate of interest on a loan of $1,500.
If paid a total of $120 in interest after two years,
SI = PRT/100
120 = 1500.00 x R x 2
R = 120 / 1500 x 2
R = 0.04
R= 4%
Question 25.
Chris bought a jacket that was marked $50 before tax. He paid $53.50 after tax. What percent tax did he pay? ______________
If the jacket was on sale and was originally marked $75, by what percent did the price decrease? ______________
Answer:
7%, 33%
Explanation:
A jacket that was marked $50 before tax.
He paid $53.50 after tax,
53.5 – 50 = 3
3.5/50 = 0.07 = 7%
The jacket was on sale and was originally marked $75,
by what percent did the price decrease.
50/75 x100 = 66.66
100 – 66.66 = 33.33
33% or 33.33%
Provide the ordered pairs for the points plotted on the graph.
Question 26.
A ______________
Answer:
A(1,3)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, A(1,3).
Question 27.
B _______________
Answer:
B(4, 4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, B(4, 4).
Question 28.
C _______________
Answer:
C(-5, 2)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, C(-5, 2)
Question 29.
D _______________
Answer:
B(4, -4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, B(4, -4).
Question 30.
E _______________
Answer:
E(-4, -2)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, E(-4, -2).
Question 31.
F _______________
Answer:
F(7, 6)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, F(7, 6).
Question 32.
G _______________
Answer:
G(-2, 5)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, G(-2, 5).
Question 33.
H _______________
Answer:
H(-6, -6)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, H(-6, -6).
Question 34.
I _______________
Answer:
H(-3, 8)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, H(-3, 8).
Question 35.
J _______________
Answer:
J(3,- 8)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, J(3,- 8).
Plot the following points on the grid provided:
Question 36.
A (1, 4)
Answer:
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, A(1, 4) is marked as above in the x, y plain.
Question 37.
B (4, 1)
Answer:
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, b(4, 1) is marked as above in the x, y plain.
Question 38.
C (3, 9)
Answer:
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, C(3, 9) is marked as above in the x, y plain.
Question 39.
D (-9, -3)
Answer:
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, D(-9, -3) is marked as above in the x, y plain.
Question 40.
E (-4, 4)
Answer:
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, E(-4, 4) is marked as above in the x, y plain.
Question 41.
F (-1, -4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, A(-1, -4) is marked as above in the x, y plain.
Question 42.
A train has 7 cars and can carry 224 people. If the train adds 2 extra cars, how many people can it carry? What is the unit rate per car?
Answer:
32 unit rate per car
64 people can carry
Explanation:
A train has 7 cars and can carry 224 people
one car carry = 224/7 = 32
each car carry 32 people
If the train adds 2 extra cars
7 + 2 = 9 cars
9 cars x 32 = 288
288 – 224 = 64 people.
Question 43.
How fast is Car A going?
Answer:
Speed = 1 mile per minute
Explanation:
Speed = Distance / Time
Speed = 5 / 5
Speed = 1 mile per minute
Question 44.
How fast is Car B going?
Answer:
Speed = 3 miles per minute
Explanation:
Speed = Distance / Time
Speed = 9 / 3
Speed = 3 miles per minute
Question 45.
How far will Car A have gone after 5 minutes?
Answer:
5 miles
Explanation:
Speed = 1 mile per minute
Time = 5 minutes.
Distance = speed x time
Distance = 1 x 5 miles