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Maths 2 Marks Questions

Fractions and Decimals · Uttarakhand Board (UBSE) STD 6 (Uttarakhand - English Medium). 19 questions.

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2 Marks Questions

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19 questions · timed · auto-graded

Question 12 Marks
Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?
Answer
Given, total number of fruit cake $= 1$ Ali divided one fruit cake equally among six persons. The part of cake given to one person $=\frac{1}{6}$ Hence, the required part is $\frac16$
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Question 22 Marks
Express $6\frac23$ as an improper fraction.
Answer
We know that, $6\frac23=\frac{6\times3+2}{3}$
$=\frac{20}{3}$
$\because$ Mixed fraction = Improper fraction $=\frac{\text{Whole number}\times\text{Denominator}+\text{Numerator}}{\text{Denominator}}$
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Question 32 Marks
Write $\frac56$ as a fraction with numerator $60.$
Answer
Given fraction $=\frac56$
In order to express it, as the fraction with numerator $60$, we will multiply the numerator denominator by $12,$ to make it an equivalent fraction of
$\therefore\frac56=\frac{5\times12}{6\times12}=\frac{60}{72}$
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Question 42 Marks
Round off $27.981$ to nearest tenths.
Answer
For rounding off the tenths place, we look at the hundredths place. Here, the digit at hundredths place is $8$ which is greater than $5.$ So, the digit at tenths place $9$ will be increased by $1$ and digits at the hundredths and thousandths place will be written as equal to zero. Hence, rounding off $27.981$ to nearest tenths, we get $28.$
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Question 52 Marks
Round off $75.195$ to nearest hundredths.
Answer
For rounding off to hundredths place, we look at the thousandths place. Here, the digit at thousandths place is $5$ which is equal to $5.$ So, the digit at the hundredths place $9$ will be increased by $1$ and $5$ will be written as equal to zero. Hence, rounding off $75.195$ to nearest hundredths, we get $75.200.$
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Question 62 Marks
Using the digits $2, 4, 5$ and $3$ once, write the smallest four digit decimal number.
Answer
Given digits are $2, 4, 5$ and 3. For making smallest decimal number we will arrange the given digits in ascending order after decimal point. Required decimal number $= 0.2345.$
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Question 72 Marks
What is wrong in the following additions?
Answer
On observing the sum, we find that the fractions have different denominators which could not be added directly. For adding fractions with different denominators we have to convert them into like fractions.
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Question 82 Marks
Write $\frac34$ as a fraction with denominator $44.$
Answer
Given fraction $=\frac34$ In order to express it, as a fraction with denominator $44,$ we will multiply the denominator numerator by $11,$ to make it an equivalent fraction of $\therefore\frac{5}{6}=\frac{5\times12}{6\times12}=\frac{60}{72}$
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Question 92 Marks
What should be added to $25.5$ to get $50?$
Answer
To get the required result, we have to subtract $25.5$ from $50.$
$\ \ \ \ 50.0\\ \ \underline{-25.5\ }\\ \ \underline{\ \ \ 24.5\ }$
So, $24.5$ should be added to $25.5$ to get $50.$
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Question 102 Marks
Write the fraction represented by the shaded portion of the adjoining figure:
Answer
Circle is divided into $8$ equal parts and number of shaded parts are $7.$
$\therefore$ Fraction of shaded portion to the total portion $=\frac{\text{Total number of shaded parts}}{\text{Total parts}}=\frac{7}{8}$
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Question 112 Marks
Express $\frac{11}{20}$ as a decimal.
Answer
In order to convert fraction into decimal, we first convert it into an equivalent fraction with denominator $10$ or $100$ or $1000$ and then write its numerator and mark decimal point after one place or two place or three places from right towards left, if the denominator is $10$ or $100$ or $1000$ respectively. If the numerator is short of digits, insert zeroes at the left of the numerator. $\frac{11}{20}\times\frac55=0.55$
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Question 122 Marks
Energy content of different foods are as follows:
Food
Energy Content per kg.
Wheat
$3.2$ Joules
Rice
$5.3$ Joules
Potatoes (Cooked)
$3.7$ Joules
Milk
$3.0$ Joules
Which food provides the least energy and which provides the maximum?
Express the least energy as a fraction of the maximum energy.
Answer
In the given table, we see that minimum value is $3.0J$ and maximum value is $5.3J.$
$\therefore$ Least energy by food $= 3.0J$ i.e. milk.
Food which provide the maximum energy $= 5.3J $ i.e. rice.
$\therefore$ Required fraction $=\frac{\text{Least energy}}{\text{Maximum energy}}=\frac{3.0}{5.3}=\frac{30}{53}$
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Question 132 Marks
Convert $5201$ grams into kilograms. Show the steps for the conversion.
Answer
We know that, $1\ kg = 1000g$ Now, for converting g into $\ kg,$
we have to divide the given value by $1000.$
$\therefore5201\text{g}=\frac{5201}{1000}\text{kg}=5.201\text{kg}$
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Question 142 Marks
Food remains in the stomach for a maximum of $4$ hours. For what fraction of a day does it remain there$?$
Answer
Given, maximum hours for which food remains in the stomach $= 4$
We know that, $1$ day $= 24 h.$
The fraction of a day for which food remains in the stomach $\frac{4\text{h}}{24\text{h}}=\frac16$
So, the food remains in the stomach for $\frac16$ past of the day.
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Question 152 Marks
Write $\frac{129}{8}$ as a mixed fraction.
Answer
Given, $\frac{129}{8}$ Now, $\therefore\frac{129}{8}=16\frac18$Note: In order to express an improper fraction as a mixed fraction, we first divide the numerator by denominator and obtain the quotient and remainder and then we write the mixed fraction as
$\text{Quotient}\ \frac{\text{Remainder}}{\text{Denominator}}$
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Question 162 Marks
What fraction of a straight angle is a right angle$?$
Answer
We know that, measures of right angle and straight angle are $90^\circ $ and $180^\circ .$
Now, the fraction of right angle to the straight angle $=\frac{90^\circ}{180^\circ}$
$=\frac{90\div90}{180\div90} [ \because HCF$ of $90$ and $180$ is $90]$
$=\frac12$
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Question 172 Marks
A cup is $\frac{1}{3}​$ full of milk. What part of the cup is still to be filled by milk to make it full?
Answer
Given, cup full of milk $=\frac{1}{3}$Remaining part of the cup which is not filled by milk $=1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$
Hence, part of the cup still to be filled is $=\frac{2}{3}$
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Question 182 Marks
Write the largest four digit decimal number less than $1$ using the digits $1, 5, 3$ and $8$ once.
Answer
Given digits are $1, 5, 3, 8$ and the number should be less than $1.$
So, the whole part will $0.$
Now, for making largest four digit decimal number we will arrange the given digits in descending order after decimal point. Required decimal number $= 0.8531.$
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Question 192 Marks
Round off $20.83$ to nearest tenths.
Answer
For rounding off the tenths place, we look at the hundredths place.
Here, the digit at hundredths place is $3$ which is less then $5.$
So, the digit at the tenths place $8$ will not be increased by $1$ and $3$ will be written as equal to zero.
Hence, rounding off $20.83$ to nearest tenths, we get $20.80.$
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