Math Problem Statement

Divya has 100 rupees. She spent 3/5 of it. How much did she spend? A storybook has 40 pages. Ruby read 3/4 of it. How many pages did she read? Jatin walks 3 1/2 km in a day. How many kilometers does he walk in a week? A packet had 1 1/2 kg of washing powder. Half of the washing powder was used. How much washing powder was left?

Solution

Here are the questions extracted from the image along with their solutions:


1. Divya has 100 rupees. She spent 35\frac{3}{5} of it. How much did she spend?

To calculate the amount spent: Amount spent=35×100=60rupees.\text{Amount spent} = \frac{3}{5} \times 100 = 60 \, \text{rupees}.

Answer: Divya spent 60 rupees.


2. A storybook has 40 pages. Ruby read 34\frac{3}{4} of it. How many pages did she read?

To calculate the pages Ruby read: Pages read=34×40=30pages.\text{Pages read} = \frac{3}{4} \times 40 = 30 \, \text{pages}.

Answer: Ruby read 30 pages.


3. Jatin walks 3123 \frac{1}{2} km in a day. How many kilometers does he walk in a week?

First, convert the mixed fraction 3123 \frac{1}{2} to an improper fraction: 312=72.3 \frac{1}{2} = \frac{7}{2}.

Distance walked in a week: Weekly distance=72×7=492=24.5km.\text{Weekly distance} = \frac{7}{2} \times 7 = \frac{49}{2} = 24.5 \, \text{km}.

Answer: Jatin walks 24.5 km in a week.


4. A packet had 1121 \frac{1}{2} kg of washing powder. Half of the washing powder was used. How much washing powder was left?

First, convert the mixed fraction 1121 \frac{1}{2} to an improper fraction: 112=32.1 \frac{1}{2} = \frac{3}{2}.

Amount of washing powder used: Used powder=12×32=34kg.\text{Used powder} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \, \text{kg}.

Amount left: Remaining powder=3234=6434=34kg.\text{Remaining powder} = \frac{3}{2} - \frac{3}{4} = \frac{6}{4} - \frac{3}{4} = \frac{3}{4} \, \text{kg}.

Answer: 34\frac{3}{4} kg of washing powder was left.


Let me know if you'd like detailed steps for any of these! Below are some related questions to expand your understanding:

  1. If Divya spent 25\frac{2}{5} instead of 35\frac{3}{5}, how much would she have left?
  2. If Ruby read 23\frac{2}{3} of a 90-page storybook, how many pages would she have read?
  3. If Jatin increased his daily walk by 1121 \frac{1}{2} km, how many kilometers would he walk in a week?
  4. If only 13\frac{1}{3} of the washing powder was used, how much would remain?
  5. Can you calculate Ruby's reading pace if she reads 5 pages in 10 minutes?

Tip: When solving problems with fractions, always simplify the final result for clarity.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Basic Arithmetic Operations
Proportion

Formulas

Fraction multiplication: (a/b) * n
Mixed number conversion: a b/c = (a * c + b) / c
Subtraction of fractions: a/b - c/d = (ad - bc) / bd

Theorems

Fundamental properties of fractions
Distributive property

Suitable Grade Level

Grade 5-6