4-1 Estimate Products of Fractions
Estimate the product. Use a bar diagram if needed.
1. SOLUTION: Use compatible numbers to find a multiple of 4 close to 21.
You can also use a bar diagram. 20 is compatible to 21. Divide a bar diagram into 4 equal sections to represent
fourths. Label the entire diagram 20. Determine what number goes in each section of the bar diagram. is about 5.
So,
2. of 22 SOLUTION: Use compatible numbers to find a multiple of 7 close to 22.
If
of 21 is 3, then of 21 is 5 × 3, or 15.
You can also use a bar diagram. 22 is close to 21. Divide a bar diagram into seven sections to represent sevenths
and label the diagram 21. Shade 5 sections to represent five sevenths. Determine what number goes in each section
of the bar diagram. So,
of 22 is about 15.
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4-1 Estimate
Products of Fractions
So, of 22 is about 15.
3. SOLUTION: 1×0=0
So,
is about 0.
4. SOLUTION: 4 × 3 = 12
So,
is about 12.
5. Cyrus is inviting 11 friends over for pizza. He would like to have enough pizza so each friend can have
of a pizza. About how many pizzas should he order?
SOLUTION: Use compatible numbers to find a multiple of 4 close to 11.
So, Cyrus should order 3 pizzas.
6. Hakeem’s front porch measures
feet by 4 feet. Estimate the area of his front porch.
SOLUTION: 10 × 4 = 40
So, the area of Hakeem’s front porch is about 40 square feet.
7. Use Math Tools Refer to the graphic novel frame for Exercises a–b.
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10 × 4 = 40
4-1 Estimate
Products of Fractions
So, the area of Hakeem’s front porch is about 40 square feet.
7. Use Math Tools Refer to the graphic novel frame for Exercises a–b.
a. If each bag holds
pounds, estimate how many pounds of birdseed Elisa, Luis, and Dwayne purchased.
b. Suppose each bag costs $14.99. Estimate the total cost of 5 bags.
SOLUTION: a. Round
pounds to 4 pounds. They bought 5 bags: 4 × 5 = 20. So, the kids purchased about 20 pounds of
birdseed.
b. Round $14.99 to $15. 15 × 5 = 75. So, the total cost of 5 bags of birdseed was about $75.
Estimate the area of the rectangle. 8. SOLUTION: eSolutions Manual - Powered by Cognero
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a. Round
pounds to 4 pounds. They bought 5 bags: 4 × 5 = 20. So, the kids purchased about 20 pounds of
birdseed. Products of Fractions
4-1 Estimate
b. Round $14.99 to $15. 15 × 5 = 75. So, the total cost of 5 bags of birdseed was about $75.
Estimate the area of the rectangle. 8. SOLUTION: 8 × 6 = 48
So, the area of the rectangle is about 48 square feet.
9. SOLUTION: 10 × 3 = 30
So, the area of the rectangle is about 30 square inches.
10. Seattle, Washington, received rain on
of the days in a recent month. If this pattern continues, about
how many days would it not rain in 90 days?
SOLUTION: If it rains on
If
of the days, then it does not rain on of 100 is 10, then of the days. You know that of 100 is 10.
of 100 is 3 × 10, or 30.
So, in 90 days, it would not rain on about 30 of those days.
11. Justify Conclusions By what fraction would you multiply
so that the product is about 5? Explain your reasoning.
SOLUTION: Since we need a product that is about, use estimation. Round
to 9 to make the multiplication easier. Think what fraction you would multiply by 9 to get a product of 5.
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If
of 100 is 10, then of 100 is 3 × 10, or 30.
4-1 Estimate Products of Fractions
So, in 90 days, it would not rain on about 30 of those days.
11. Justify Conclusions By what fraction would you multiply
so that the product is about 5? Explain your reasoning.
SOLUTION: Since we need a product that is about, use estimation. Round
to 9 to make the multiplication easier. Think what fraction you would multiply by 9 to get a product of 5.
12. Persevere with Problems Determine which point on the number line could be the graph of the product of the
numbers graphed at C and D. Explain your reasoning.
SOLUTION: Point C is located at
same as
and Point D is located at
. Point N is the closest point to
. The product of
and is .
is about the
. So, the graph of the product of points C and D could be
Point N.
13. Reason Inductively Is the best estimate for the area of the square 2 square yards or 6 square yards? Explain
your reasoning. SOLUTION: 3×2=6
So, the area of the rectangle is about 6 square yards. eSolutions Manual - Powered by Cognero
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