Let's solve each problem step by step.
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Problem 1:
Question: There are 24 hours in a day, and scientists tell us that we should sleep for \( \frac{3}{8} \) of the day. How much time should we spend sleeping?
Solution:
1. Total hours in a day = 24.
2. Fraction of the day to be spent sleeping = \( \frac{3}{8} \).
3. Time spent sleeping = \( \frac{3}{8} \times 24 \).
\[
\frac{3}{8} \times 24 = \frac{3 \times 24}{8} = \frac{72}{8} = 9
\]
Therefore, we should spend
9 hours sleeping.
Answer: \( \boxed{9} \)
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Problem 2:
Question: The National History Museum has collected 125 dinosaurs. George has collected \( \frac{3}{5} \) of this amount. How many dinosaurs has George collected?
Solution:
1. Total number of dinosaurs collected by the museum = 125.
2. Fraction of dinosaurs collected by George = \( \frac{3}{5} \).
3. Number of dinosaurs collected by George = \( \frac{3}{5} \times 125 \).
\[
\frac{3}{5} \times 125 = \frac{3 \times 125}{5} = \frac{375}{5} = 75
\]
Therefore, George has collected
75 dinosaurs.
Answer: \( \boxed{75} \)
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Problem 3:
Question: Mr. Murrin is 160 cm tall, and his brother Tom is \( \frac{7}{8} \) as tall as him. How tall is Tom?
Solution:
1. Height of Mr. Murrin = 160 cm.
2. Fraction of Mr. Murrin's height that Tom has = \( \frac{7}{8} \).
3. Height of Tom = \( \frac{7}{8} \times 160 \).
\[
\frac{7}{8} \times 160 = \frac{7 \times 160}{8} = \frac{1120}{8} = 140
\]
Therefore, Tom is
140 cm tall.
Answer: \( \boxed{140} \)
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Problem 4:
Question: The weather forecaster says that it is \( 20^\circ \mathrm{C} \) in London but only \( \frac{7}{10} \) as hot in New York. How hot is it in New York?
Solution:
1. Temperature in London = \( 20^\circ \mathrm{C} \).
2. Fraction of the temperature in London that applies to New York = \( \frac{7}{10} \).
3. Temperature in New York = \( \frac{7}{10} \times 20 \).
\[
\frac{7}{10} \times 20 = \frac{7 \times 20}{10} = \frac{140}{10} = 14
\]
Therefore, the temperature in New York is
\( 14^\circ \mathrm{C} \).
Answer: \( \boxed{14} \)
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Problem 5:
Question: Skateboards cost £36 each in my local store. The shopkeeper says if I buy one, I can buy another for only \( \frac{7}{9} \) of the normal price. How much would a second skateboard cost?
Solution:
1. Normal price of a skateboard = £36.
2. Fraction of the normal price for the second skateboard = \( \frac{7}{9} \).
3. Price of the second skateboard = \( \frac{7}{9} \times 36 \).
\[
\frac{7}{9} \times 36 = \frac{7 \times 36}{9} = \frac{252}{9} = 28
\]
Therefore, the second skateboard costs
£28.
Answer: \( \boxed{28} \)
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Final Answers:
1. \( \boxed{9} \)
2. \( \boxed{75} \)
3. \( \boxed{140} \)
4. \( \boxed{14} \)
5. \( \boxed{28} \)
Parent Tip: Review the logic above to help your child master the concept of multiplying fractions word problems 6th grade worksheet.
