Working with Fractions Class 7 Solutions Ganita Prakash Maths Chapter 8✦ Step-by-step
HBSE 7th Class Maths Solutions Chapter 8 Working with Fractions (NCERT Ganita Prakash) — every question worked out step by step. Tap Solve step by step.
Class 7 Maths Chapter 8 Working with Fractions Solutions
Key ideas used in this chapter
Multiply\(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\)
Divide÷ a fraction = × its reciprocal
Of“\(\frac{a}{b}\) of N” means \(\frac{a}{b}\times N\)
Mixed ↔ improper\(2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4}\)
8.1 Multiplication — Figure It Out (Pages 176–177)
Q1–3Word problems
(Q1) Tenzin drinks \(\frac{1}{2}\) glass daily — week & January. (Q2) Team digs 1 km canal in 8 days — 1 day & a 5-day week. (Q3) 3 families share 5 L weekly — each family in a week & in 4 weeks.
Q1 week
\(7\times\frac{1}{2}=\frac{7}{2}=3\frac{1}{2}\) glasses
Q1 January
Jan has 31 days: \(31\times\frac{1}{2}=\frac{31}{2}=15\frac{1}{2}\) glasses
Q2
1 day = \(1\div8=\frac{1}{8}\) km; week = \(5\times\frac{1}{8}=\frac{5}{8}\) km
Q3
each family = \(5\div3=\frac{5}{3}\) L; 4 weeks = \(4\times\frac{5}{3}=\frac{20}{3}=6\frac{2}{3}\) L
Q4, Q5Moon & mixed numbers
(Q4) Moon sets \(\frac{5}{6}\) h later each day; it set 10 pm Monday — how much later on Thursday? (Q5) Multiply and write as mixed: (a) \(7\times\frac{3}{5}\) (b) \(4\times\frac{1}{3}\) (c) \(\frac{9}{7}\times6\) (d) \(\frac{13}{11}\times6\).
Q4
Mon→Thu = 3 days ⇒ \(3\times\frac{5}{6}=\frac{15}{6}=2\frac{1}{2}\) hours (12:30 am)
(a),(b)
\(\frac{7\times3}{5}=\frac{21}{5}=4\frac{1}{5}\); \(\frac{4}{3}=1\frac{1}{3}\)
(c),(d)
\(\frac{9\times6}{7}=\frac{54}{7}=7\frac{5}{7}\); \(\frac{78}{11}=7\frac{1}{11}\)
Figure It Out (Pages 180–181)
Q1Unit fractions
(a) \(\frac{1}{3}\times\frac{1}{5}\) (b) \(\frac{1}{4}\times\frac{1}{3}\) (c) \(\frac{1}{5}\times\frac{1}{2}\) (d) \(\frac{1}{6}\times\frac{1}{5}\); also \(\frac{1}{12}\times\frac{1}{18}\).
Rule
multiply tops and bottoms: \(\frac{1}{a}\times\frac{1}{b}=\frac{1}{ab}\)
(a),(b)
\(\frac{1}{3\times5}=\frac{1}{15}\); \(\frac{1}{12}\)
(c),(d)
\(\frac{1}{10}\); \(\frac{1}{30}\)
last
\(\frac{1}{12}\times\frac{1}{18}=\frac{1}{216}\)
Q2Multiply fractions
(a) \(\frac{2}{3}\times\frac{4}{5}\) (b) \(\frac{1}{4}\times\frac{2}{3}\) (c) \(\frac{3}{5}\times\frac{1}{2}\) (d) \(\frac{4}{6}\times\frac{3}{5}\).
(a)
\(\frac{2\times4}{3\times5}=\frac{8}{15}\)
(b)
\(\frac{1\times2}{4\times3}=\frac{2}{12}=\frac{1}{6}\)
(c)
\(\frac{3\times1}{5\times2}=\frac{3}{10}\)
(d)
\(\frac{4\times3}{6\times5}=\frac{12}{30}=\frac{2}{5}\)
Figure It Out (Pages 183–184)
Q1Water tank
In 1 hour a tap fills \(\frac{7}{10}\) of a tank. How much in (a) \(\frac{1}{3}\) h (b) \(\frac{2}{3}\) h (c) \(\frac{3}{4}\) h (d) \(\frac{7}{10}\) h? (e) Time to fill the whole tank?
Idea
fraction filled = time × \(\frac{7}{10}\)
(a),(b)
\(\frac{1}{3}\times\frac{7}{10}=\frac{7}{30}\); \(\frac{2}{3}\times\frac{7}{10}=\frac{14}{30}=\frac{7}{15}\)
(c),(d)
\(\frac{3}{4}\times\frac{7}{10}=\frac{21}{40}\); \(\frac{7}{10}\times\frac{7}{10}=\frac{49}{100}\)
(e)
whole = 1: \(1\div\frac{7}{10}=\frac{10}{7}=1\frac{3}{7}\) hours
Q2Somu's land
Govt takes \(\frac{1}{6}\); of the rest, \(\frac{1}{2}\) to Krishna and \(\frac{1}{3}\) to Bora. Find (a) Krishna's (b) Bora's (c) Somu's share of the original land.
Remaining
\(1-\frac{1}{6}=\frac{5}{6}\)
(a)
\(\frac{1}{2}\times\frac{5}{6}=\frac{5}{12}\)
(b)
\(\frac{1}{3}\times\frac{5}{6}=\frac{5}{18}\)
(c)
\(\frac{5}{6}-\frac{5}{12}-\frac{5}{18}\); LCM 36: \(\frac{30}{36}-\frac{15}{36}-\frac{10}{36}=\frac{5}{36}\)
Q3–5Area, distance, compare
(Q3) Area of \(3\frac{3}{4}\) ft × \(9\frac{3}{5}\) ft. (Q4) 4 saplings \(\frac{3}{4}\) m apart — first to last. (Q5) Heavier: \(\frac{12}{15}\) of 500 g or \(\frac{3}{20}\) of 4 kg?
Q3
\(\frac{15}{4}\times\frac{48}{5}=\frac{720}{20}=36\) sq ft
Q4
4 saplings ⇒ 3 gaps: \(3\times\frac{3}{4}=\frac{9}{4}=2\frac{1}{4}\) m
Q5
\(\frac{12}{15}\times500=400\) g; \(\frac{3}{20}\times4000=600\) g
Answer
600 g > 400 g ⇒ \(\frac{3}{20}\) of 4 kg is heavier
8.2 Division — Figure It Out (Pages 196–198)
Q2Choose & simplify
(a) 8 m lace, \(\frac{1}{4}\) m per bag — bags? (b) \(\frac{1}{2}\) m ribbon makes 8 badges — length each? (c) \(\frac{1}{6}\) kg per loaf, 5 kg — loaves?
(a)
\(8\div\frac{1}{4}=8\times4=32\) bags (option iii)
(b)
\(\frac{1}{2}\div8=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}\) m (option iv)
(c)
\(5\div\frac{1}{6}=5\times6=30\) loaves (option iii)
Q3, Q4Flour & Patiganita
(Q3) \(\frac{1}{4}\) kg makes 12 rotis — flour for 6 rotis? (Q4) \(1\div\frac{1}{6}+1\div\frac{1}{10}+1\div\frac{1}{13}+1\div\frac{1}{9}+1\div\frac{1}{2}\).
Q3 per roti
\(\frac{1}{4}\div12=\frac{1}{4}\times\frac{1}{12}=\frac{1}{48}\) kg
Q3 for 6
\(6\times\frac{1}{48}=\frac{6}{48}=\frac{1}{8}\) kg
Q4
\(1\div\frac{1}{6}=6\), etc. ⇒ 6 + 10 + 13 + 9 + 2
Q4 answer
= 40
Q5–8Word problems
(Q5) 400-page novel, read \(\frac{1}{5}\) then \(\frac{3}{10}\) — pages left? (Q6) 16 km/L, distance on \(2\frac{3}{4}\) L? (Q7) Train \(5\frac{1}{6}\) h, plane \(\frac{1}{2}\) h — saved? (Q8) \(\frac{4}{5}\) of a cake eaten; rest split by 3 — each share?
Q5
\(\frac{1}{5}\times400=80\), \(\frac{3}{10}\times400=120\); read 200; left 400−200 = 200 pages
Q6
\(16\times2\frac{3}{4}=16\times\frac{11}{4}=44\) km
Q7
\(5\frac{1}{6}-\frac{1}{2}=\frac{31}{6}-\frac{3}{6}=\frac{28}{6}=\frac{14}{3}=4\frac{2}{3}\) hours
Q8
rest \(1-\frac{4}{5}=\frac{1}{5}\); \(\frac{1}{5}\div3=\frac{1}{15}\) each
Q9, Q12Reasoning
(Q9) Which describe \(\frac{565}{465}\times\frac{707}{676}\)? (Q12) What is \(1-\frac{1}{2}\)? Make a general statement.
Q9
each fraction > 1 (top > bottom); a number × (something > 1) grows ⇒ product > each & > 1 ⇒ (a), (c), (e)
Q12
\(1-\frac{1}{2}=\frac{1}{2}\); in general \(\frac{1}{n}-\frac{1}{n+1}=\frac{1}{n(n+1)}\)
Q10Shaded square (figure)
The big square is split into 4 quarters; in the bottom-right quarter a region is shaded. What fraction of the whole is shaded?
Step 1
the bottom-right quarter = \(\frac{1}{4}\) of the whole
Step 2
that quarter is cut into 8 equal triangles; 3 are shaded ⇒ \(\frac{3}{8}\) of the quarter
Answer
\(\frac{3}{8}\times\frac{1}{4}=\frac{3}{32}\) of the whole square
Q11Ant colony (figure)
Ants split into two equal halves at each junction (red dot), then reach the mango tree or the sugarcane field. What fraction reaches each source?
Step 1
at each junction the group halves, so a path crossing k junctions carries \(\frac{1}{2^k}\) of the ants.
Step 2
add the fractions of all branches ending at the mango tree, and of all ending at the sugarcane field.
Check
the two totals add up to 1 (the whole colony); the mango tree, with more incoming roads, gets the larger share.