The mixed number
can be written as 2.125.
ANSWER: 2.125
1-1 Rational Numbers
Write the fraction or mixed number as a
decimal.
3. 1. SOLUTION: means 33 ÷ 40.
SOLUTION: Divide 33 by 40.
means 2 ÷ 5.
Divide 2 by 5.
The fraction
can be written as 0.4.
The fraction
ANSWER: 0.4
can be written as 0.825.
ANSWER: 0.825
2. 4. SOLUTION: SOLUTION: can be written as
.
means 4 ÷ 33.
Divide 17 by 8.
Divide 4 by 33.
The mixed number
Since the remainders follow a repetitive pattern, the
can be written as 2.125.
fraction
ANSWER: 2.125
can be written as .
ANSWER: 3. SOLUTION: means 33 ÷ 40.
Divide 33 by 40.
5. SOLUTION: means –6 ÷ 11.
Divide 6 by 11 and add a negative sign.
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fraction
can be written as .
ANSWER: ANSWER: 1-1 Rational Numbers
7. Identify Repeated Reasoning The table shows
statistics about the students at Carter Junior High.
5. SOLUTION: means –6 ÷ 11.
Divide 6 by 11 and add a negative sign.
Since the remainders follow a repetitive pattern, the
fraction
can be written as .
ANSWER: a. Express the fraction of students with no siblings as
a decimal.
b. Find the decimal equivalent for the fraction of
students with three siblings.
c. Write the fraction of students with one sibling as a
decimal. Round to the nearest thousandth.
d. Write the fraction of students with two siblings as
a decimal. Round to the nearest thousandth.
SOLUTION: a. The fraction of students with no siblings is
6. .
means 1 ÷ 15. Divide 1 by 15.
SOLUTION: can be written as
.
Divide 323 by 45 and add a negative sign.
The decimal of students with no siblings is
.
b. The fraction of students with three siblings is
.
means 1 ÷ 6. Divide 1 by 6.
Since the remainder repeats, the mixed number
can be written as .
ANSWER: The decimal of students with three siblings is
.
7. Identify Repeated Reasoning The table shows
statistics about the students at Carter Junior High.
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c. The fraction of students with one sibling is . To
find the decimal of students with one sibling divide
the numerator, 1, by the denominator, 3.
1
0.33333…
3 Look at the digit to the right of the thousandths place.
Since 3 ≤ 5, round down.
The decimal of students with one sibling is 0.333.Page 2
d. The fraction of students with two siblings is
.
c. The fraction of students with one sibling is . To
find the decimal of students with one sibling divide
the numerator, 1, by the denominator, 3.
1-1 Rational Numbers
1
0.33333…
3 Look at the digit to the right of the thousandths place.
Since 3 ≤ 5, round down.
The decimal of students with one sibling is 0.333.
ANSWER: 9. –7.32
SOLUTION: To write –7.32 as a fraction, identify the integer, –7,
and what position the 0.32 part of the decimal is in.
The 2 in 0.32 is in the hundredths position, so write
d. The fraction of students with two siblings is
.
To find the decimal of students with two siblings
divide the numerator, 5, by the denominator, 12. Use
a calculator.
the fraction 32 hundredths or
5
12
0.41666…
Look at the digit to the right of the thousandths place.
Since 6 ≥ 5, round up.
The decimal of students with two siblings is 0.417.
integer, –7, in front:
. Then put the
. This fraction is not in
simplest form, so it needs to be reduced.
ANSWER: a.
b.
c. 0.333
d. 0.417
ANSWER: Write the decimal as a fraction or mixed
number in simplest form.
8. –0.4
10. SOLUTION: To write
as a fraction, determine what part of the number repeats. Since the line is only above the
2,
= 0.222…. We need to find the fraction for
0.222….
Assign a variable to the value
. Let N = 0.222….
Then perform operations on N to determine its
fractional value. Because one digit repeats, multiply
each side by 10. Multiplying by 10 moves the decimal
point one place to the right. Then subtract N =
0.222… to eliminate the repeating part. Simplify and
divide each side by 9.
N = 0.222…
10(N) = 10(0.222…)
10N = 2.22…
– N = 0.222…
9N = 2
SOLUTION: To write –0.4 as a fraction, identify what position the
decimal is in. The 4 is in the tenths place, so write the
fraction four tenths or
. Then put the negative
sign in front. This fraction is not in simplest form, so
it needs to be reduced.
ANSWER: 9. –7.32
N =
SOLUTION: To write –7.32 as a fraction, identify the integer, –7,
and what position the 0.32 part of the decimal is in.
The 2 in 0.32 is in the hundredths position, so write
the fraction 32 hundredths or
integer, –7, in front:
The decimal
can be written as .
ANSWER: . Then put the
. This fraction is not in
Copy and Solve Write the decimal as a fraction
or mixed number in simplest form. Show your
work on a separate piece of paper.
simplest form, so it needs to be reduced.
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ANSWER: SOLUTION: To write
Page 3
as a fraction, determine what part of
ANSWER: ANSWER: 1-1 Rational Numbers
Copy and Solve Write the decimal as a fraction
or mixed number in simplest form. Show your
work on a separate piece of paper.
11. SOLUTION: To write
as a fraction, determine what part of
the number repeats. Since the line is above the 45,
= –0.454545…. The negative sign will be
retained in the fraction, so we need to find the
fraction for 0.454545….
Assign a variable to the value
. Let N =
0.454545…. Then perform operations on N to
determine its fractional value. Because two digits
repeat, multiply each side by 100. Multiplying by 100
moves the decimal point two places to the right. Then
subtract N = 0.454545… to eliminate the repeating
part. Simplify and divide each side by 99. Then put
the negative sign in front.
N = 0.454545…
100(N) = 100(0.454545…)
100N = 45.4545…
– N = 0.454545…
99N = 45
N =
12. SOLUTION: To write
as a fraction, determine what part of the number repeats. Since the line is only above the
7,
= 2.777…. 2 is a whole number and will be
retained in the mixed number, so we need to find the
fraction for 0.777….
Assign a variable to the value
. Let N = 0.777….
Then perform operations on N to determine its
fractional value. Because one digit repeats, multiply
each side by 10. Multiplying by 10 moves the decimal
point one place to the right. Then subtract N =
0.777… to eliminate the repeating part. Simplify and
divide each side by 9. Then add the whole number, 2.
N = 0.777…
10(N) = 10(0.777…)
10N = 7.77…
– N = 0.777…
9N = 7
N =
The decimal
can be written as .
ANSWER: This fraction is not in simplest form, so it needs to be
reduced.
13. 5.55
The decimal
can be written as .
ANSWER: SOLUTION: To write 5.55 as a fraction, identify the whole
number, 5, and what position the 0.55 part of the
decimal is in. The second 5 in 0.55 is in the
hundredths position, so write the fraction 55
hundredths or
12. front:
SOLUTION: To write
as a fraction, determine what part of the number repeats. Since the line is only above the
7,
= 2.777…. 2 is a whole number and will be
retained in the mixed number, so we need to find the
fraction for 0.777….
Assign a variable to the value
. Let N = 0.777….
Then perform operations on N to determine its
fractional value. Because one digit repeats, multiply
each side by 10. Multiplying by 10 moves the decimal
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one place
to the
right. Then subtract N =
0.777… to eliminate the repeating part. Simplify and
divide each side by 9. Then add the whole number, 2.
. Then put the whole number, 5, in
. This fraction is not in simplest form, so
it needs to be reduced.
ANSWER: Be Precise Write the length of the insect as a
fraction or mixed number and as a decimal.
14. Page 4
ANSWER: ANSWER: in.; 0.875 in.
1-1 Rational Numbers
Be Precise Write the length of the insect as a
15. fraction or mixed number and as a decimal.
14. SOLUTION: The ruler section is divided into sixteenths of an inch.
The ant is 14 sixteenths long. So, the length of the ant
is
inch. This fraction is not in simplest form, so it SOLUTION: The ruler section is divided into sixteenths of an inch.
The grasshopper is 1 and one sixteenth inch long. So,
the grasshopper is
can be written as inches long.
. Divide 17 by 16.
needs to be reduced.
The ant is
inch long.
means 7 ÷ 8. Divide 7 by 8.
The mixed number
can be written as 1.0625. The grasshopper is 1.0625 inches long.
ANSWER: in.; 1.0625 in.
The fraction
can be written as 0.875. The ant is 0.875 inch long.
ANSWER: in.; 0.875 in.
15. SOLUTION: The ruler section is divided into sixteenths of an inch.
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grasshopper
is 1byand
one sixteenth inch long. So,
the grasshopper is
inches long.
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