7th Grade Math

162 Rational Numbers

SLEEP Humans sleep about _^13 of each day. If each year is equal to

365 _^14 days, determine the number of days in a year the average

human sleeps.

Words

Variable

Equation

Humans sleep about 13 of 365 1 4 days.

Let d represent the number of days a human sleeps.

d = 31 · 365 ^14

d = ^13 · 365 ^14 Write the equation.

d = _^1

3

· _1,461

4

Rename the mixed number as an improper fraction.

487

d = _^1

3

· _1,461

4

Divide 3 and 1,461 by their GCF, 3.

1

d = _^487

4

or 121 _^3

4

Multiply. Then rename as a mixed number.

The average human sleeps 121 _^3

4

days each year.

ANIMALS The house cat has an average lifespan that is _^45 of a

lion’s lifespan. If a lion’s average lifespan is 15 years, find the

average lifespan of a house cat.

Words

Variable

Equation

The lifespan of a house cat is _^45 that of the lion.

Let c represent the lifespan of a house cat.

c = 45 _ · 15

c = _ 54 · 15 Write the equation.

c = _^45 · _^151 Write the whole number 15 as an improper fraction.

3

c = _ 54 · _^15  1 Divide 5 and 15 by their GCF, 5.

1

c = _^121 or 12 Multiply, then simplify.

The average lifespan of a house cat is 12 years.

j. COOKING Lloyd wishes to make _^12 of a recipe. If the original recipe

calls for 3 _^34 cups of flour, how many cups should he use?

Meaning of Multiplication

Recall that one meaning

of 3 × 4 is three groups

with 4 in each group. In

Example 5, there are

365 4 _^1 groups with _ 31 in

each group.

Real-World Link

The average group of

lions, called a pride,

consists of about 15

lions with about _^23 of

the pride being female.

RR

T

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