Students can practice Telangana 6th Class Maths Textbook Solutions Chapter 7 Fractions and Decimals InText Questions to get the best methods of solving problems.

## TS 6th Class Maths Solutions Chapter 7 Fractions and Decimals InText Questions

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Question 1.

How will you represent the following pictorially ?

(i) \(\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)

(ii) \(\frac{2}{8}\)

Answer:

\(\frac{2}{8}\)

(iii) \(\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)

(iv) \(\frac{5}{8}\)

Answer:

\(\frac{5}{8}\)

Question 2.

Write the fraction representing the shaded portion.

Answer:

(i) \(\frac{1}{3}\)

(ii) \(\frac{1}{4}\)

(iii) \(\frac{2}{6}\)

Do This

Question 1.

Write 5 proper fractions and draw them pictorially.

Answer:

Question 2.

Rani says that shaded portion in the given figure represents \(\frac{1}{4}\). Do you agree with her? Give reason to support your answer.

Answer:

Yes. The reason is out of fourportions only one portion is shaded.

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Question 1.

Write improper fractions represented by the following pictures.

Answer:

Answer:

Answer:

Question 2.

Represent the following fractions pictorially :

\(\frac{7}{4}, \frac{5}{3}, \frac{7}{6}\)

Answer:

Do This

Question 1.

Write the following as mixed fractions

\(\frac{7}{2}, \frac{8}{5}, \frac{9}{4}, \frac{13}{5}, \frac{17}{3}\)

Answer:

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Question 1.

Write the numerator and denominators of the following fractional numbers:

\(\frac{1}{3}, \frac{2}{5}, \frac{7}{2}, \frac{19}{3}, \frac{7}{29}, \frac{11}{13}, \frac{1}{7}, \frac{8}{3}\)

Answer:

Fraction | Numerator | Denominator |

\(\frac{1}{3}\) | 1 | 3 |

\(\frac{2}{5}\) | 2 | 5 |

\(\frac{7}{2}\) | 7 | 2 |

\(\frac{19}{2}\) | 19 | 3 |

\(\frac{7}{29}\) | 7 | 29 |

\(\frac{11}{13}\) | 11 | 13 |

\(\frac{1}{7}\) | 1 | 7 |

\(\frac{8}{3}\) | 8 | 3 |

Question 2.

Sort the following fractions into the category of proper and improper fractions. Also write improper fraction as mixed fractions:

\(\frac{1}{3}, \frac{2}{5}, \frac{7}{2}, \frac{19}{3}, \frac{7}{29}, \frac{11}{13}, \frac{1}{7}, \frac{8}{3}\)

Answer:

Improper fractions:

Proper fractions:

\(\frac{1}{3}, \frac{2}{7}, \frac{3}{5}, \frac{1}{9}\)

Do This

Question 1.

Show that following on number lines.

(i) \(\frac{7}{6}\)

Answer:

(ii) \(\frac{5}{2}\)

Answer:

(iii) \(\frac{7}{5}\)

Answer:

(iv) \(\frac{9}{6}\)

Answer:

Question 2.

Consider the following numbers. Which of these would lie on the number line

i) before 1

Answer:

Fractions before 1 are \(\frac{1}{3}, \frac{7}{9}, \frac{6}{11}\)

ii) between 1 and 2

Answer:

Fractions between 1 and 2 are \(\frac{7}{5}, \frac{9}{5}\)

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Question 1.

Write 5 fractional numbers that are in the standard form.

Answer:

Standard form of 5 fractional numbers

= \(\frac{1}{2}, \frac{2}{3}, \frac{4}{5}, \frac{5}{6}, \frac{8}{9}\)

Question 2.

Write 5 fractional numbers that are not in standard form.

Answer:

\(\frac{10}{6}, \frac{144}{100}, \frac{51}{17}, \frac{48}{16}, \frac{36}{44}\)

Question 3.

Convert the following fractions into their standard form.

i) \(\frac{7}{28}\)

ii) \(\frac{15}{90}\)

iii) \(\frac{11}{33}\)

iv) \(\frac{39}{13}\)

Answer:

Think, Discuss And Write

Question 1.

Rafi says “there can be no equivalent fractions that are also like fractions”. Do you agree with him ? Explain your answer and justify.

Answer:

Equivalent fractions = \(\frac{1}{2}, \frac{2}{4}, \frac{8}{16}, \frac{32}{64}\)

Like fraction = \(\frac{3}{2}, \frac{5}{2}, \frac{7}{2}, \frac{8}{2}, \frac{9}{2}\)

Equivalent fractions are like fractions also. So, I agree with him.

Do This

Question 1.

Identify the biggest and the smallest in these group of fractional numbers.

(i) \(\frac{1}{7}, \frac{3}{7}, \frac{2}{7}, \frac{5}{7}\)

Answer:

Biggest fraction = \(\frac{5}{7}\)

Smallest fraction = \(\frac{1}{7}\)

(ii) \(\frac{1}{9}, \frac{13}{9}, \frac{11}{9}, \frac{5}{9}\)

Answer:

Biggest fraction = \(\frac{13}{9}\)

Smallest fraction = \(\frac{1}{9}\)

(iii) \(\frac{1}{3}, \frac{5}{3}, \frac{17}{3}, \frac{9}{3}\)

Answer:

Biggest fraction = \(\frac{17}{3}\)

Smallest fraction = \(\frac{1}{3}\)

Question 2.

Which of these is the smaller fraction ?

(i) \(\frac{2}{5}, \frac{3}{7}\)

Answer:

(ii) \(\frac{7}{8}, \frac{5}{4}\)

Answer:

(iii) \(\frac{3}{11}, \frac{1}{2}\)

Answer:

(iv) \(\frac{5}{6}, \frac{2}{3}\)

Answer:

Question 3.

Write the following fractional number in ascending order.

(i) \(\frac{1}{7}, \frac{13}{7}, \frac{11}{7}, \frac{5}{7}, \frac{15}{7}\)

Answer:

Ascending order:

\(\frac{1}{7}<\frac{5}{7}<\frac{11}{7}<\frac{13}{7}<\frac{15}{7}\)

(ii) \(\frac{2}{3}, \frac{5}{6}, \frac{3}{9}, \frac{24}{18}\)

Answer:

(iii) \(\frac{2}{3}, \frac{1}{2}, \frac{5}{6}, \frac{7}{12}\)

Answer:

(iv) \(\frac{1}{5}, \frac{1}{2}, \frac{1}{8}, \frac{1}{3}, \frac{1}{12}\)

Answer:

Do this

Question 1.

Write the following in descending order.

i) \(\frac{1}{9}, \frac{13}{9}, \frac{11}{9}, \frac{15}{9}, \frac{3}{9}\)

Answer:

ii) \(\frac{1}{6}, \frac{2}{3}, \frac{3}{9}, \frac{5}{6}\)

Answer:

iii) \(\frac{1}{5}, \frac{9}{5}, \frac{3}{5}, \frac{6}{5}\)

Answer:

Descending Order = \(\frac{9}{5}>\frac{6}{5}>\frac{3}{5}>\frac{1}{5}\)

iv) \(\frac{1}{4}, \frac{1}{2}, \frac{1}{8}, \frac{3}{4}\)

Answer:

Descending Order = \(\frac{3}{4}>\frac{1}{2}>\frac{1}{4}>\frac{1}{8}\)

Question 8.

Simplify:

(i) \(\frac{1}{18}+\frac{1}{18}\)

Answer:

\(\frac{1}{18}+\frac{1}{18}=\frac{1+1}{18}=\frac{2}{18}=\frac{1}{9}\)

(ii) \(\frac{8}{15}+\frac{3}{15}\)

Answer:

\(\frac{8}{15}+\frac{3}{15}=\frac{8+3}{15}=\frac{11}{15}\)

(iii) \(\frac{7}{7}-\frac{5}{7}\)

Answer:

\(\frac{7}{7}-\frac{5}{7}=\frac{7-5}{7}=\frac{2}{7}\)

(iv) \(\frac{1}{22}+\frac{21}{22}\)

Answer:

\(\frac{1}{22}+\frac{21}{22}=\frac{1+21}{22}=\frac{22}{22}\) = 1

(v) \(\frac{12}{15}-\frac{7}{15}\)

Answer:

\(\frac{12}{15}-\frac{7}{15}=\frac{12-7}{15}=\frac{5}{15}=\frac{1}{3}\)

(vi) \(\frac{5}{8}+\frac{3}{8}\)

Answer:

\(\frac{5}{8}+\frac{3}{8}=\frac{5+3}{8}=\frac{8}{8}\) = 1

(vii) 1 – \(\frac{2}{3}\left(1=\frac{3}{3}\right)\)

Answer:

1 – \(\frac{5}{8}+\frac{3}{8}=\frac{5+3}{8}=\frac{8}{8}\) [∵ 1 = \(\frac{3}{3}\)]

(viii) \(\frac{1}{4}+\frac{0}{4}\)

Answer:

\(\frac{1}{4}+\frac{0}{4}=\frac{1+0}{4}=\frac{1}{4}\)

(ix) 3 – \(\frac{12}{5}\)

Answer:

3 – \(\frac{12}{5}=\frac{3 \times 5}{1 \times 5}-\frac{12}{5}=\frac{15}{5}-\frac{12}{5}=\frac{15-12}{5}=\frac{3}{5}\)

Question 9.

Fill in the missing fractions.

i) \(\frac{7}{10}\) – ___ = \(\frac{3}{10}\)

Answer:

ii) __ – \(\frac{3}{21}=\frac{5}{21}\)

Answer:

iii) ___ – \(\frac{3}{3}=\frac{3}{6}\)

Answer:

iv) ___ – \(\frac{5}{27}=\frac{12}{27}\)

Answer:

Question 10.

Narendra painted \(\frac{2}{3}\) area of the wall in his room. His brother Ritesh helped and painted \(\frac{1}{3}\) area of the wall. How much did they paint together ?

Answer:

Area of the wall painted by Narendra = \(\frac{2}{3}\)

Area of the wall painted by Ritesh = \(\frac{1}{3}\)

Area of the wall painted by both

Narendra and Ritesh = \(\frac{2}{3}+\frac{1}{3}\)

= \(\frac{2+1}{3}=\frac{3}{3}\) = 1

Narendra and his brother Ritesh painted the complete wall.

Question 11.

Neha was given \(\frac{5}{7}\) of a basket of bananas. What fraction of bananas was left in the basket?

Answer:

The part of a basket of bananas given to Neha = \(\frac{5}{7}\)

The part of bananas left in the basket

= 1 – \(\frac{5}{7}=\frac{1 \times 7}{1 \times 7}-\frac{5}{7}=\frac{7}{7}-\frac{5}{7}=\frac{7-5}{7}=\frac{2}{7}\)

Question 12.

A piece of rod \(\frac{7}{8}\) metre long is broken into two pieces. One piece was \(\frac{1}{4}\) metre long. How long is the other piece?

Answer:

Length of a piece of rod = \(\frac{7}{8}\) metre

Length of one broken piece of rod = \(\frac{1}{4}\) metre.

Length of the other piece = \(\frac{7}{8}-\frac{1}{4}\)

= \(\frac{7}{8}-\frac{1 \times 2}{4 \times 2}=\frac{7}{8}-\frac{2}{8}=\frac{7-2}{8}=\frac{5}{8}\)m

∴ \(\frac{5}{8}\)m long is the other piece.

Question 13.

Renu takes 2\(\frac{1}{5}\) minutes to walk 5 around the school ground. Snigdha takes \(\frac{7}{4}\) minutes to do the same. Who takes less time and by what fraction?

Answer:

Time taken by Renu to walk around the school ground = 2\(\frac{1}{5}\) minutes

= \(\frac{11}{5}\) minutes

Time taken by Snigdha to walk around the school ground = \(\frac{7}{4}\) minutes

To find the person who takes less time to do the same, we write the fractions \(\frac{11}{5}\) and \(\frac{7}{4}\) having the same denominators.

\(\frac{11}{5} \times \frac{4}{4}=\frac{44}{20} ; \frac{7}{4} \times \frac{5}{5}=\frac{35}{20}\)

We know that \(\frac{35}{20}<\frac{44}{20}\)

Therefore, Snigdha takes \(\frac{9}{20}\) minutes less time to walk around the school ground.

(∵ \(\frac{44}{20}-\frac{35}{20}=\frac{44-35}{20}=\frac{9}{20}\))

Try These

Question 1.

(i) Write fractions for the following decimal and also find how many tenth parts are there in each :

0.4, 0.2, 0.8, 1.6, 5.4, 555.3, 0.9

Answer:

0.4 = \(\frac{4}{10}\)

0.2 = \(\frac{2}{10}\)

0.8 = \(\frac{8}{10}\)

4 tenth parts 2 tenth parts 8 tenth parts

1.6 = 1\(\frac{6}{10}\) = 1 + \(\frac{6}{10}\) 6 tenth parts

5.4 = 5\(\frac{4}{10}\) = 5 + \(\frac{4}{10}\) 4 tenth parts

555.3 = 553 + \(\frac{3}{10}\) = 3 tenth parts

0.9 = \(\frac{9}{10}\) = 9 tenth parts

(ii) Complete the following table.

Answer:

Tens (10) | Ones (1) | One-tenth (1/10) | Decimal number |

3 | 5 | 7 | 35.7 |

6 | 9 | 4 | 69.4 |

7 | 6 | 3 | 76.3 |

(iii) Complete the following table.

Answer:

(iv) Measure the length of these line segments and fill it in the table given below.

Answer:

Do This

Question 1.

Fill in the blanks.

(i) 325 paise = _________ rupees _________ paise = ₹ _________

(ii) 570 paise = _________ rupees _________ paise = ₹ _________

(iii) 2050 paise = _________ rupees _________ paise = ₹ _________

Answer:

(i) 325 paise = 3 rupees 25 paise = ₹ 3.25

(ii) 570 paise = 5 rupees 70 paise = ₹ 5.70

(iii) 2050 paise = 20 rupees 50 paise = ₹ 20.50

Do This

Question 1.

Find: i) 0.39 + 0.26

ii) 0.8 + 0.07

iii) 1.45 + 1.90

iv) 3.44 + 1.58

Answer: