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DAV Class 7 Maths – Chapter 1, Worksheet 3 Solutions

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In this post, we provide complete and step-by-step solutions for DAV Class 7 Mathematics, Chapter 1, Worksheet 3. The solutions are written in a simple and student-friendly manner to help students understand the concepts of rational numbers, standard form, equivalent rational numbers, and cross multiplication.

DAV Class 7 Maths Chapter 1 Worksheet 3 – Complete Solutions

Question 1. Write the following rational numbers in standard form.

(i) ${\displaystyle \frac{33}{77}}$

Divide the numerator and denominator by 11:

$$\frac{33}{77}=\frac{33÷11}{77÷11}=\frac{3}{7}$$

Answer: ${\displaystyle \frac{3}{7}}$

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(ii) ${\displaystyle \frac{64}{-20}}$

Divide the numerator and denominator by 4:

$$\frac{64}{-20}=\frac{64÷4}{-20÷4}$$

$$<br>$$

$$=\frac{16}{-5}$$

$$<br>$$

$$=-\frac{16}{5}$$

Answer: $-{\displaystyle \frac{16}{5}}$

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(iii) ${\displaystyle \frac{-27}{-15}}$

Divide the numerator and denominator by 3:

$$\frac{-27}{-15}=\frac{-27÷3}{-15÷3}$$$$=\frac{-9}{-5}$$$$=\frac{9}{5}$$

Answer: ${\displaystyle \frac{9}{5}}$

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(iv) ${\displaystyle \frac{-105}{98}}$

Divide the numerator and denominator by 7:

$$\frac{-105}{98}=\frac{-105÷7}{98÷7}$$$$=-\frac{15}{14}$$

Answer: $-{\displaystyle \frac{15}{14}}$

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Question 2. Find $x$ such that the rational numbers in each pair become equivalent.

(i) ${\displaystyle \frac{9}{-5}}={\displaystyle \frac{x}{10}}$

Using cross multiplication:

$$9\times 10=(-5)\times x$$$$90=-5x$$

Therefore,

$$x=\frac{90}{-5}$$$$x=-18$$

Answer: $x=-18$

Hence,

$$\frac{9}{-5}=\frac{-18}{10}$$

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(ii) ${\displaystyle \frac{8}{7}}={\displaystyle \frac{x}{-35}}$

Using cross multiplication:

$$8\times (-35)=7x$$$$-280=7x$$

Therefore,

$$x=\frac{-280}{7}$$$$x=-40$$

Answer: $x=-40$

Hence,

$$\frac{8}{7}=\frac{-40}{-35}$$

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(iii) ${\displaystyle \frac{36}{x}}=2$

Write 2 as ${\displaystyle \frac{2}{1}}$:

$$\frac{36}{x}=\frac{2}{1}$$

Using cross multiplication:

$$36\times 1=2\times x$$$$36=2x$$

Therefore,

$$x=18$$

Answer: $x=18$

Hence,

$$\frac{36}{18}=2$$

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(iv) ${\displaystyle \frac{x}{6}}={\displaystyle \frac{-13}{1}}$

Using cross multiplication:

$$x\times 1=6\times (-13)$$

Therefore,

$$x=-78$$

Answer: $x=-78$

Hence,

$$\frac{-78}{6}=\frac{-13}{1}$$

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Question 3. Check whether the following rational numbers are in standard form. If not, write them in standard form.

(i) $-{\displaystyle \frac{3}{19}}$

The HCF of 3 and 19 is 1, and the denominator is positive.

Therefore, the rational number is already in standard form.

Answer: $-{\displaystyle \frac{3}{19}}$

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(ii) ${\displaystyle \frac{4}{-7}}$

The denominator is negative. In standard form, the denominator must be positive.

Therefore,

$$\frac{4}{-7}=-\frac{4}{7}$$

Answer: $-{\displaystyle \frac{4}{7}}$

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(iii) ${\displaystyle \frac{14}{35}}$

The HCF of 14 and 35 is 7.

Therefore,

$$\frac{14}{35}=\frac{14÷7}{35÷7}$$$$=\frac{2}{5}$$

Answer: ${\displaystyle \frac{2}{5}}$

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(iv) ${\displaystyle \frac{8}{-72}}$

First, make the denominator positive:

$$\frac{8}{-72}=-\frac{8}{72}$$

The HCF of 8 and 72 is 8.

Therefore,

$$-\frac{8}{72}=-\frac{8÷8}{72÷8}$$$$=-\frac{1}{9}$$

Answer: $-{\displaystyle \frac{1}{9}}$

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Question 4. Fill in the blanks.

(i) ${\displaystyle \frac{2}{7}}={\displaystyle \frac{8}{x}}={\displaystyle \frac{y}{-63}}$

First,

$$\frac{2}{7}=\frac{8}{x}$$

Using cross multiplication:

$$2x=7\times 8$$$$2x=56$$

Therefore,

$$x=28$$

Now,

$$\frac{2}{7}=\frac{y}{-63}$$

Using cross multiplication:

$$7y=2\times (-63)$$$$7y=-126$$

Therefore,

$$y=-18$$

Answer: $x=28,y=-18$

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(ii) ${\displaystyle \frac{9}{36}}={\displaystyle \frac{-49}{x}}={\displaystyle \frac{-84}{y}}$

First,

$$\frac{9}{36}=\frac{-49}{x}$$

Using cross multiplication:

$$9x=36\times (-49)$$

Since $36÷9=4$,

$$x=4\times (-49)$$$$x=-196$$

Now,

$$\frac{9}{36}=\frac{-84}{y}$$

Using cross multiplication:

$$9y=36\times (-84)$$

Therefore,

$$y=4\times (-84)$$$$y=-336$$

Answer: $x=-196,y=-336$

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(iii) ${\displaystyle \frac{105}{x}}={\displaystyle \frac{y}{-99}}={\displaystyle \frac{-5}{-11}}$

First simplify:

$$\frac{-5}{-11}=\frac{5}{11}$$

Therefore,

$$\frac{105}{x}=\frac{5}{11}$$

Using cross multiplication:

$$105\times 11=5x$$$$1155=5x$$

Therefore,

$$x=231$$

Now,

$$\frac{y}{-99}=\frac{5}{11}$$

Using cross multiplication:

$$11y=5\times (-99)$$$$11y=-495$$

Therefore,

$$y=-45$$

Answer: $x=231,y=-45$

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Quick Revision – Rational Numbers

Standard Form of a Rational Number

A rational number is said to be in standard form when:

1. The numerator and denominator have no common factor other than 1.

2. The denominator is positive.

Important Rule

If the denominator is negative, shift the negative sign to the numerator:

$$\frac{a}{-b}=-\frac{a}{b}$$

Cross Multiplication Rule

If

$$\frac{a}{b}=\frac{c}{d}$$

then,

$$a\times d=b\times c$$

This rule is very useful for finding missing values in equivalent rational numbers.

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Final Answers at a Glance

Question	Answer
1(i)	${\displaystyle \frac{3}{7}}$
1(ii)	$-{\displaystyle \frac{16}{5}}$
1(iii)	${\displaystyle \frac{9}{5}}$
1(iv)	$-{\displaystyle \frac{15}{14}}$
2(i)	$x=-18$
2(ii)	$x=-40$
2(iii)	$x=18$
2(iv)	$x=-78$
3(i)	$-{\displaystyle \frac{3}{19}}$
3(ii)	$-{\displaystyle \frac{4}{7}}$
3(iii)	${\displaystyle \frac{2}{5}}$
3(iv)	$-{\displaystyle \frac{1}{9}}$
4(i)	$x=28,y=-18$
4(ii)	$x=-196,y=-336$
4(iii)	$x=231,y=-45$

Conclusion

These solutions cover DAV Class 7 Maths Chapter 1, Worksheet 3 with clear working steps. Students can use this worksheet to revise standard form of rational numbers, equivalent rational numbers, HCF, and cross multiplication.

For more DAV school solutions, Maths worksheets, notes, and study materials, keep learning with YASRAJ Studies. 📖✏️