Question 12 Marks
Find the fraction equivalent to $\frac{45}{60}$, having,Numerator $15$
AnswerConsider the numerator $= 15$
$\frac{45}{60}=15$
As $45\div3=15$,
we will divide both the numerator & denominator by $3.$
$\Rightarrow\frac{\frac{45}{3}}{\frac{60}{3}}=\frac{15}{20}$
View full question & answer→Question 22 Marks
Find the fraction equivalent to $\frac{45}{60}$, having,Denominator $4$
AnswerConsider the numerator $= 4$
$\frac{45}{60}=\frac{...}{4}$
As $60\div15=4$,
we will divide both the numerator & denominator by $15$
$\Rightarrow\frac{\frac{45}{15}}{\frac{60}{15}}=\frac{3}{4}$
View full question & answer→Question 32 Marks
Check whether the given fractions are equivalent:$\frac{3}{10},\frac{12}{50}$
Answer$\frac{3}{10}\times\frac{4}{4}=\frac{12}{40}$ Hence, the given fraction are not equivalent.
View full question & answer→Question 42 Marks
Solve:
$\frac{3}{22}+\frac{7}{22}$
Answer The given fractions are:
$\frac{3}{22}+\frac{7}{22}$
$=\frac{3+7}{22}$
$=\frac{10}{22}=\frac{5}{11}$
Hence the answer is $\frac{5}{11}$
View full question & answer→Question 52 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{12}{60}$
Answer$\frac{12}{60}$
$HCF$ of $12\ \&\ 60$ is $12$ Divide both the numerator & denominator by the $HCF$ of $12\ \&\ 60$
$\frac{12\div12}{60\div12}=\frac{1}{5}$
View full question & answer→Question 62 Marks
Solve: $\frac{1}{4}+\frac{0}{4}$
AnswerThe given fractions are: $\frac{1}{4}+\frac{0}{4}$ $=\frac{1+0}{4}$ $=\frac{1}{4}$ Hence the answer is $\frac{1}{4}$
View full question & answer→Question 72 Marks
Check whether the given fractions are equivalent: $\frac{7}{13},\frac{5}{11}$
Answer $\frac{7}{13}\times\frac{5}{5}=\frac{35}{65}$
$\frac{5}{11}\times\frac{7}{7}=\frac{35}{77}$
Hence, the given fraction are not equivalent.
View full question & answer→Question 82 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{15}{75}$
Answer$\frac{15}{75}$
$HCF$ of $15$ & $75$ is $15$
Divide both the numerator & denominator by the $HCF$ of $15$ & $75$
$\frac{15\div15}{75\div15}=\frac{1}{5}$
View full question & answer→Question 92 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{12}{72}$
Answer$\frac{12}{72}$
$HCF$ of $12\ \&\ 72$ is $12$ Divide both the numerator & denominator by the
$HCF$ of $12\ \&\ 72 \frac{12\div12}{72\div12}=\frac{1}{6}$
View full question & answer→Question 102 Marks
Compare the following fractions using the symbol > or <: $\frac{6}{7}$ and $\frac{6}{11}$
Answer$\frac{6}{7}>\frac{6}{11}$ because if the numerator is the same, then the fraction with smaller denominator is greater.
View full question & answer→Question 112 Marks
Arrange in descending order of the following using the symbol >: $\frac{8}{17},\frac{8}{9},\frac{8}{5},\frac{8}{13}$
AnswerWhen numerators are the same and denominators are different, then the fraction with greater denominator has a smaller value. $\frac{8}{5}>\frac{8}{9}>\frac{8}{13}>\frac{8}{17}$
View full question & answer→Question 122 Marks
Write each fraction. Arrange them in ascending and descending order using correct sign '<', '=', '>' between the fractions: 
Answer Ascending order: 
Descending order: 
View full question & answer→Question 132 Marks
Solve: $\frac{3}{15}+\frac{7}{15}$
Answer The given fractions are:
$\frac{3}{15}+\frac{7}{15}$
$=\frac{3+7}{15}$
$=\frac{10}{15}$
Hence the answer is $\frac{10}{15}$
View full question & answer→Question 142 Marks
Find answers to the following. Write and indicate how you solved them. Is $\frac{1}{15}$ equal to $\frac{4}{30}?$
AnswerNumerator of the first fraction $×$ Denominator of the second fraction $=$
Numerator of the second fraction $×$ Denominator of the first fraction
$1 \times 30 = 30$
$4 \times 15 = 60$
So, $1\times30\ne4\times15$ $\frac{1}{15}$ is equal to $\frac{4}{30}$
View full question & answer→Question 152 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{16}{100}$
Answer$\frac{16}{100}$
$HCF$ of $16\ \&\ 100$ is $4$ Divide both the numerator & denominator by the $HCF$ of $16\ \&\ 100$
$\frac{16\div4}{100\div4}=\frac{4}{25}$
View full question & answer→Question 162 Marks
Solve: $1-\frac{2}{3}+\frac{7}{3}$
AnswerThe given fractions are: $1-\frac{2}{3}+\frac{7}{3}$ $=\frac{3-2+7}{3}$ $=\frac{8}{3}$ Hence the answer is $\frac{8}{3}$
View full question & answer→Question 172 Marks
Find the fraction equivalent of $\frac{35}{42}$, having:Numerator $30$
AnswerFirstly, we will reduce $\frac{35}{42}$ into the lowest term.
Now, we will divide both the numerator & denominator by the $HCFs$ of $35$ & $42.$
$\Rightarrow\frac{35\div7}{42\div7}=\frac{5}{6}$
$\frac{5}{6}=\frac{30}{}$
Consider the numerator $= 30$
As $5 \times 6 = 30,$
we will multiply both the numerator & denominator by $6.$
$\Rightarrow\frac{5\ \times\ 6}{6\ \times\ 6}=\frac{30}{36}$
View full question & answer→Question 182 Marks
Find answers to the following. Write and indicate how you solved them.Is $\frac{5}{9}$ equal to $\frac{4}{5}?$
AnswerNumerator of the first fraction $\times $ Denominator of the second fraction $=$ Numerator of the second fraction $\times $ Denominator of the first fraction
$5 \times 5 = 25$
$4 \times 9 = 36$
So, $5\times5\ne4\times9$
$\frac{5}{9}$ is not equal to $\frac{4}{5}$
View full question & answer→Question 192 Marks
Solve: $\frac{7}{31}-\frac{4}{31}+\frac{9}{31}$
AnswerThe given fractions are: $\frac{7}{31}-\frac{4}{31}+\frac{9}{31}$ $=\frac{7-4+9}{31}$ $=\frac{12}{31}$ Hence the answer is $\frac{12}{31}$
View full question & answer→Question 202 Marks
Write the natural numbers from $102$ to $113.$ What fraction of them are prime numbers.
AnswerNatural numbers from $102$ to $113$ are $102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112$ and $113$
Prime numbers from $102$ to $113$ are $103, 107, 109$ and $113$
Out of $12$ natural numbers, $4$ are prime.
Fraction of the prime numbers $=\frac{4}{12}=\frac{1}{3}$
View full question & answer→Question 212 Marks
Find the fraction equivalent of $\frac{35}{42}$, having:Denominator $30$
AnswerFirstly, we will reduce $\frac{35}{42}$ into the lowest term.
Now, we will divide both the numerator & denominator by the $HCFs$ of $35$ & $42.$
$\Rightarrow\frac{35\div7}{42\div7}=\frac{5}{6}$
$\frac{5}{6}=\frac{}{30}$
Consider the denominator $= 30$
As $6 \times 5 = 30,$
we will multiply both the numerator & denominator by $5.$
$\Rightarrow\frac{5\ \times\ 5}{6\ \times\ 5}=\frac{25}{30}$
View full question & answer→Question 222 Marks
Write the fractions and check whether they are equivalent or not:
Answer
Fraction $=\frac{1}{2}$
Fraction $=\frac{2}{4}=\frac{1}{2}$
Fraction $=\frac{3}{6}=\frac{1}{2}$
Fraction $=\frac{4}{8}=\frac{1}{2}$
Yes, they are equivalent. View full question & answer→Question 232 Marks
Check whether the given fractions are equivalent:$\frac{4}{11},\frac{32}{88}$
Answer$\frac{4}{11}\times\frac{8}{8}=\frac{32}{88}$ Hence, the given fraction are equivalent.
View full question & answer→Question 242 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{2}{12}$
Answer$\frac{2}{12}$
$HCF$ of $2$ & $12$ is $2$ Divide both the numerator & denominator by the $HCF$ of $2$ & $12$
$\frac{2\div2}{12\div2}=\frac{1}{6}$
View full question & answer→Question 252 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{10}{60}$
Answer$\frac{10}{60}$
$HCF $ of $10\ \&\ 60$ is $10$ Divide both the numerator & denominator by the $HCF$ of $10\ \&\ 60$
$\frac{10\div10}{60\div10}=\frac{1}{6}$
View full question & answer→Question 262 Marks
Compare the following fractions using the symbol > or <: $\frac{3}{7}$ and $\frac{5}{7}$
Answer$\frac{3}{7}<\frac{5}{7}$
because $3 < 5$ and the denominator is the same.
View full question & answer→Question 272 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form:
$\frac{16}{96}$
Answer$\frac{16}{96}$
$HCF$ of $16$ & $96$ is $16$
Divide both the numerator & denominator by the $HCF$ of $16$ & $96$
$\frac{16\div16}{96\div16}=\frac{1}{6}$
View full question & answer→Question 282 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{3}{18}$
Answer$\frac{3}{18} HCF$ of $3\ \&\ 18$ is $3$ Divide both the numerator & denominator by the $HCF$ of $3\ \&\ 18 \frac{3\div3}{18\div3}=\frac{1}{6}$
View full question & answer→Question 292 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form:
$\frac{8}{50}$
Answer$\frac{8}{50}$
$HCF$ of $8\ \&\ 50$ is $2$
Divide both the numerator & denominator by the $HCF$ of $8\ \&\ 50$
$\frac{8\div2}{50\div2}=\frac{4}{25}$
View full question & answer→Question 302 Marks
Find answers to the following. Write and indicate how you solved them. Is $\frac{9}{16}$ equal to $\frac{5}{9}?$
AnswerNumerator of the first fraction $\times $ Denominator of the second fraction $=$
Numerator of the second fraction $\times $ Denominator of the first fraction
$9 \times 9 = 81$
$5 \times 16 = 80$
So, $9\times9\ne5\times16$
$\frac{9}{16}$ is not equal to $\frac{5}{9}$
View full question & answer→Question 312 Marks
Find the fraction equivalent of $\frac{35}{42}$, having:Numerator $15$
AnswerFirstly, we will reduce $\frac{35}{42}$ into the lowest term.
Now, we will divide both the numerator & denominator by the $HCFs$ of $35\ \&\ 42.$
$\Rightarrow\frac{35\div7}{42\div7}=\frac{5}{6}$
$\frac{5}{6}=\frac{15}{}$
Consider the numerator $= 15$
As $5 \times 3 = 15,$
we will multiply both the numerator & denominator by $3.$
$\Rightarrow\frac{5\ \times\ 3}{6\ \times\ 3}=\frac{15}{18}$
View full question & answer→Question 322 Marks
Compare the following fractions using the symbol > or <: $\frac{8}{3}$ and $\frac{8}{13}$
Answer$\frac{8}{3}<\frac{8}{13}$, because if the numerator is the same, then the fraction with smaller denominator is greater.
View full question & answer→Question 332 Marks
Mukesh has a box of $24$ pencils. He gives half of them of Sunita. How many does sunita get? How many does Mukesh still have?
AnswerGiven, Mukesh has $24$ pencils. Sunita gets half of mukesh’s pencils. Sunita gets $242$ pencils, that is, $12$ pencils. Number of pencils mukesh still has $= 24 - 12 = 12$
View full question & answer→Question 342 Marks
Check whether the given fractions are equivalent:$\frac{5}{9},\frac{30}{54}$
Answer$\frac{5}{9}\times\frac{6}{6}=\frac{30}{54}$ Hence, the given fraction are equivalent.
View full question & answer→Question 352 Marks
Check whether the given fractions are equivalent:$\frac{9}{27},\frac{25}{75}$
Answer$\frac{9}{27}=\frac{\frac{9}{9}}{\frac{27}{9}}=\frac{1}{3}$ $\frac{25}{75}=\frac{\frac{25}{25}}{\frac{75}{25}}=\frac{1}{3}$ Hence, the given fraction are equivalent.
View full question & answer→Question 362 Marks
Find the equivalent fraction of $\frac{3}{5}$, having:Denominator $30$
AnswerConsider the denominator $= 30$
$\frac{3}{5}=\frac{....}{30}$ As $5 \times 6 = 30,$
we will multiply both the numerator & denominator by $6,$
we have $\Rightarrow\frac{3}{5}\times\frac{6}{6}=\frac{18}{30}$
View full question & answer→Question 372 Marks
Find answers to the following. Write and indicate how you solved them. Is $\frac{4}{5}$ equal to $\frac{16}{20}?$
AnswerNumerator of the first fraction $\times $ Denominator of the second fraction $=$ Numerator of the second fraction $\times $ Denominator of the first fraction
$4 \times 20 = 80 $
$16 \times 5 = 80$
So, $4\times20=16\times5$ $\frac{4}{5}$ is equal to $\frac{16}{20}$
View full question & answer→Question 382 Marks
Find the equivalent fraction of $\frac{3}{5}$, having:Numerator $21$
AnswerConsider the numerator $= 30$
$\frac{3}{5}=21$
As $5 \times 7 = 21,$
we will multiply both the numerator & denominator by $7,$
we have $\Rightarrow\frac{3}{5}\times\frac{7}{7}=\frac{21}{35}$
View full question & answer→Question 392 Marks
Compare the following fractions using the symbol > or <: $\frac{1}{5}$ and $\frac{4}{15}$
Answer$\frac{1}{5}=\frac{1}{5}\times\frac{3}{3}=\frac{3}{15}$ therefore, $\frac{3}{15}<\frac{4}{15}$(Because $3 < 4$ and the denominator is the same)
View full question & answer→Question 402 Marks
Find the fraction equivalent to $\frac{45}{60}$, having,Denominator $240$
AnswerConsider the denominator $= 240$
$\frac{45}{60}=\frac{.....}{240}$ As $60 \times 4 = 240,$ we will multiply both the numerator & denominator by $4.$
$\Rightarrow\frac{45\ \times\ 4}{60\ \times\ 4}=\frac{180}{240}$
View full question & answer→Question 412 Marks
Find the equivalent fraction of $\frac{3}{5}$, having:Numerator $9$
Answer$\frac{3}{5}=9$ Consider the numerators $= 9$ As $3 \times 3 = 9,$
we will multiply both the numerator & denominator by $3$
$\Rightarrow\frac{3}{5}\times\frac{3}{3}=\frac{9}{15}$
View full question & answer→Question 422 Marks
The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing to its simplest form: $\frac{3}{15}$
Answer$\frac{3}{15} HCF$ of $3\ \&\ 15$ is $3$
Divide both the numerator & denominator by the $HCF$ of $3\ \&\ 15$
$\frac{3\div3}{15\div3}=\frac{1}{5}$
View full question & answer→Question 432 Marks
Arrange the following fractions in the ascending order: $\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$
Answer$\frac{9}{14}>\frac{13}{28}>\frac{11}{35}>\frac{2}{7}$
View full question & answer→Question 442 Marks
Arrange the following fractions in the ascending order: $\frac{2}{5},\frac{3}{4},\frac{1}{2},\frac{3}{5}$
Answer$LCM$ of $2, 4$ and $5$ is $20$
$\frac{2}{5}=\frac{2}{5}\times\frac{4}{4}=\frac{8}{20}$
$\frac{3}{4}=\frac{3}{4}\times\frac{5}{5}=\frac{15}{20}$
$\frac{1}{2}=\frac{1}{2}\times\frac{10}{10}=\frac{10}{20}$
$\frac{3}{5}=\frac{3}{5}\times\frac{4}{4}=\frac{12}{20}$
When denominators are the same and numerators are different,
then the fraction with greater numerator has a larger value.
$\frac{8}{20}<\frac{10}{20}<\frac{12}{20}<\frac{15}{20}$
Or, $\frac{2}{5}<\frac{1}{2}<\frac{3}{5}<\frac{3}{4}$
View full question & answer→Question 452 Marks
Solve: $\frac{5}{12}+\frac{1}{12}$
AnswerThe given fractions are:$\frac{5}{12}+\frac{1}{12}$
$=\frac{1+2}{5}$
$=\frac{3}{5}$
Hence the answer is $\frac{3}{5}$
View full question & answer→Question 462 Marks
Solve: $\frac{0}{15}+\frac{2}{15}+\frac{1}{15}$
AnswerThe given fractions are: $\frac{0}{15}+\frac{2}{15}+\frac{1}{15}$ $=\frac{0+2+1}{15}$ $=\frac{3}{15}=\frac{1}{5}$ Hence the answer is $\frac{1}{5}$
View full question & answer→Question 472 Marks
Compare the following fractions using the symbol > or <: $\frac{4}{9}$ and $\frac{15}{8}$
Answer$\frac{4}{9}=\frac{4}{9}\times\frac{8}{8}=\frac{32}{72}$
$\frac{15}{8}=\frac{15}{8}\times\frac{9}{9}=\frac{135}{72}$
$\frac{32}{72}<\frac{135}{72}$, because $135 > 32$ and the denominator is the same.
Therefore, $\frac{4}{9}<\frac{15}{8}$
View full question & answer→Question 482 Marks
Arrange the following fractions in the ascending order: $\frac{5}{9},\frac{3}{12},\frac{1}{3},\frac{4}{15}$
Answer$LCM$ of $9, 12, 3$ and $15$ is $180$
$\frac{5}{9}=\frac{5}{9}\times\frac{20}{20}=\frac{100}{180}$
$\frac{3}{12}=\frac{3}{12}\times\frac{15}{5}=\frac{45}{180}$
$\frac{1}{3}=\frac{1}{3}\times\frac{60}{60}=\frac{60}{180}$
$\frac{4}{15}=\frac{4}{15}\times\frac{12}{12}=\frac{48}{180}$
When denominators are the same and numerators are different,
then the fraction with greater numerator has a larger value.
$\frac{5}{9}>\frac{1}{3}>\frac{4}{15}>\frac{3}{12}$
View full question & answer→Question 492 Marks
Write the natural numbers form $2$ to $12$. What fraction of them are prime numbers$?$
AnswerNatural numbers from $2$ to $12$ are $2, 3, 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11$ and $12$
Prime numbers from $2$ to $12 $ are $2, 3 , 5 , 7$ and $11$ Out of $11$ numbers, $5$ are prime.
Fraction of the prime numbers $= 511$
View full question & answer→Question 502 Marks
Solve:
$3\frac{2}{7}+\frac{1}{7}-2\frac{3}{7}$
AnswerThe given fractions are:
$3\frac{2}{7}+\frac{1}{7}-2\frac{3}{7}=\frac{23}{7}+\frac{1}{7}-\frac{17}{7}$
$=\frac{23+1-17}{7}$
$=\frac{7}{7}=1$
Hence the answer is $1$
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