Question

Represent the rational number 1/5, 6/5, -9/7 on number line

Answer 1

☆ Question ☆

Represent the rational number 1/5, 6/5, -9/7 on number line.

☆ To find ☆

Represent the rational numbers on number line.

☆ Rule ☆

• First we have to draw the number lines for each rational number.

• We have to take point 0 and set off equal distance on both sides of 0.

• Then, trace out the whole integers on both sides of 0. The negative integers will lie on the left side of 0 and the positive integers will lie on the right side of 0.

• Then divide the distance between two integers into equal number of parts (as required) to get the rational numbers.

☆ Solution ☆

• For 1/5,

Since 1/5 is a positive integer, it will lie on the right side. We have to divide the segment between 0 and 1 into 5 parts and get the first point as 1/5. Refer to the first number line in the attachment.

• For 6/5,

6/5 = 1 ¹/₅

Since 6/5 is a positive integer, it will lie on the right side. We have to divide the segment between 1 and 2 into 5 parts and get the first point as 6/5. Refer to the second number line in the attachment.

• For -9/7,

-9/7 = -1 ²/₇

Since -9/7 is a negative integer, it will lie on the left side. We have to divide the segment between -1 and -2 into 7 parts and get the second point as -9/7. Refer to the third number line in the attachment.

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☆ Knowledge Corner ☆

✪ More about Rational Numbers ✪

Rational numbers →

• The numbers in the form p/q, where p and q are integers and q ≠ 0, are called rational numbers.
• Rational numbers can be both positive and negative.
• 0 is a rational number as it can be written as 0/1, 0/2, 0/4 etc.
• Every fraction is a rational number but every rational number is not be a fraction.

Positive rational numbers →

A rational number is said to be positive if it's numerator and denominator are either both positive or both negative.

Negative rational numbers →

A rational number is said to be negative if its numerator and denominator are of opposite signs.

Points to know →

• Every positive rational number is greater than 0.
• Every negative rational number is less than 0.

Two properties of rational numbers →

If a/b is a rational number and m is a non-zero integer then,

☞ a/b = (a×m)/(b×m)

If a/b is a rational number and m is a common divisor of a and b then,

☞ a/b = (a÷m)/(b÷m)

Standard form of a rational number →

A rational number a/b is said to be in standard form if a and b are integers having no common divisor other than 1 and b is positive.  

    

๑ Hope this helps you. ๑