Rational Numbers Challenge

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Practice problems on rationals

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sowmiya Sowmi68

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Rational Numbers Challenge


Rational Numbers ChallengeVersión en línea Practice problems on rationals por sowmiya Sowmi68 1 Represent the rational numbers 2/3, -5/4, and 1 1/2 on a single number line. a 2/3 at 0.666, -5/4 at -1.25, and 3/2 at 1.5 b 2/3 is left of -1, -5/4 is right of 1, and 3/2 is at 0 c All three lie on the positive side of zero d 2/3, -5/4, and 3/2 are equally spaced around 0 2 Find three distinct rational numbers strictly between -1/2 and 1/4. a -1/4, -1/8, 0 b -3/4, -1, 1/2 c 0, 1/4, 1/2 d -1/2, 0, 1/2 3 Simplify the expression (-1/4) + (5/12). a -1/6 b 1/6 c -1/3 d 7/12 4 A tailor has 15 3/4 metres of silk. If one kurta needs 2 1/4 metres, how many kurtas can be made? a 8 b 6 c 9 d 7 5 Find three rational numbers between 3.1415 and 3.1416. a 3.14155, 3.14156, 3.14157 b 3.1410, 3.1420, 3.1500 c 3.1411, 3.1412, 3.1413 d 3.14151, 3.14155, 3.14159 6 Can you think of any method(s) to find a rational number between any two rationals? a Take their average or use the mediant (p+r)/(q+s). b Impossible for some pairs c Only by decimal expansion d Only by converting to integers first 7 Find a rational between 7/8 and 3/4. a 11/12 b 13/16 c 7/9 d 5/6 8 Between 4 2/3 and 5, give a rational between them. a 4 1/2 b 4 2/5 c 4 5/6 d 4 3/4 9 Convert 4 2/3 and 2 5/6 to improper fractions and find a reasonable between number. a 15/3 and 16/6; between is 25/6 b 16/3 and 18/6; between is 31/6 c 13/3 and 15/6; between is 28/6 d 14/3 and 17/6; between is 29/6 10 True or False: Every rational number has a finite decimal expansion. a Only integers have finite expansions b True c False d Depends on the number Feedback 1 Each value position is relative to 0; 2/3 ≈ 0.667, -5/4 = -1.25, 3/2 = 1.5. 2 Between -1/2 and 1/4 you can choose negative and nonnegative fractions like -1/4, -1/8, and 0. 3 (-1/4)+(5/12) = (-3/12)+(5/12) = 2/12 = 1/6. 4 15 3/4 ÷ 2 1/4 = 15.75 ÷ 2.25 = 7 kurtas. 5 Any three numbers between 3.1415 and 3.1416 work; here are valid examples. 6 Common methods: average of the two rationals or the mediant between them. 7 Between 7/8 (0.875) and 3/4 (0.75) a mediant gives (7+3)/(8+4)=10/12=5/6. 8 4 2/3 = 14/3 and 5 = 15/3; 14/3 < 29/6 < 15/3, so 4 5/6 works. 9 14/3 = 4 2/3, 17/6 = 2 5/6; a between like 29/6 (4 5/6) lies between. 10 Rationals can be repeating, e.g., 1/3 = 0.333...; finite only when denominators have factors 2 and 5.

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Rational Numbers Challenge

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Rational Numbers ChallengeVersión en línea

por sowmiya Sowmi68

Represent the rational numbers 2/3, -5/4, and 1 1/2 on a single number line.

Find three distinct rational numbers strictly between -1/2 and 1/4.

Simplify the expression (-1/4) + (5/12).

A tailor has 15 3/4 metres of silk. If one kurta needs 2 1/4 metres, how many kurtas can be made?

Find three rational numbers between 3.1415 and 3.1416.

Can you think of any method(s) to find a rational number between any two rationals?

Find a rational between 7/8 and 3/4.

Between 4 2/3 and 5, give a rational between them.

Convert 4 2/3 and 2 5/6 to improper fractions and find a reasonable between number.

True or False: Every rational number has a finite decimal expansion.

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